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Factor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in four observed variables mainly reflect the variations in two unobserved variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors, plus "error" terms. The information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Computationally this technique is equivalent to low rank approximation of the matrix of observed variables. Factor analysis originated in psychometrics, and is used in behavioral sciences, social sciences, marketing, product management, operations research, and other applied sciences that deal with large quantities of data.
Factor analysis is related to principal component analysis (PCA), but the two are not identical. Latent variable models, including factor analysis, use regression modelling techniques to test hypotheses producing error terms, while PCA is a descriptive statistical technique.[1] There has been significant controversy in the field over the equivalence or otherwise of the two techniques (see exploratory factor analysis versus principal components analysis).[citation needed]
- 1 Statistical model
- 2 Practical implementation
- 3 Factor analysis in psychometrics
- 4 Exploratory factor analysis versus principal components analysis
- 5 Factor analysis in marketing
- 6 Factor analysis in physical sciences
- 7 Factor analysis in microarray analysis
- 8 Implementation
- 9 See also
- 10 References
- 11 Further reading
- 12 External links
Statistical model[edit]
Suppose we have a set of observable random variables, with means .
Suppose for some unknown constants and unobserved random variables , where and , where , we have
Here, the are independently distributed error terms with zero mean and finite variance, which may not be the same for all . Let , so that we have
In matrix terms, we have
If we have observations, then we will have the dimensions , , and . Each column of and denote values for one particular observation, and matrix does not vary across observations.
Also we will impose the following assumptions on .
- and are independent.
- (to make sure that the factors are uncorrelated)
Any solution of the above set of equations following the constraints for is defined as the factors, and as the loading matrix.
Suppose . Then note that from the conditions just imposed on , we have
Note that for any orthogonal matrix if we set and , the criteria for being factors and factor loadings still hold. Hence a set of factors and factor loadings is identical only up to orthogonal transformation.
The following example is for expository purposes, and should not be taken as being realistic. Suppose a psychologist proposes a theory that there are two kinds of intelligence, "verbal intelligence" and "mathematical intelligence", neither of which is directly observed. Evidence for the theory is sought in the examination scores from each of 10 different academic fields of 1000 students. If each student is chosen randomly from a large population, then each student's 10 scores are random variables. The psychologist's theory may say that for each of the 10 academic fields, the score averaged over the group of all students who share some common pair of values for verbal and mathematical "intelligences" is some constant times their level of verbal intelligence plus another constant times their level of mathematical intelligence, i.e., it is a combination of those two "factors". The numbers for a particular subject, by which the two kinds of intelligence are multiplied to obtain the expected score, are posited by the theory to be the same for all intelligence level pairs, and are called "factor loadings" for this subject. For example, the theory may hold that the average student's aptitude in the field of taxonomy is
- {10 × the student's verbal intelligence} + {6 × the student's mathematical intelligence}.
The numbers 10 and 6 are the factor loadings associated with taxonomy. Other academic subjects may have different factor loadings.
Two students having identical degrees of verbal intelligence and identical degrees of mathematical intelligence may have different aptitudes in taxonomy because individual aptitudes differ from average aptitudes. That difference is called the "error" — a statistical term that means the amount by which an individual differs from what is average for his or her levels of intelligence (see errors and residuals in statistics).
The observable data that go into factor analysis would be 10 scores of each of the 1000 students, a total of 10,000 numbers. The factor loadings and levels of the two kinds of intelligence of each student must be inferred from the data.
Mathematical model of the same example[edit]
In the example above, for i = 1, ..., 1,000 the ith student's scores are given by . The purpose of factor analysis is to characterize the correlations between the variables of which is a particular instance, or observation. In order that the variables be on equal footing, they are standardized:
where the sample mean is:
and the sample variance is given by:
The instantiated model is then:
or, more succintly:
- is the ith student's standardized score for the kth subject
- is the mean of the students' scores for the kth subject (assumed to be zero, for simplicity, in the example as described above, which would amount to a simple shift of the scale used): where i=1...1000 and k=1...10.
- is the ith student's "verbal intelligence",
- is the ith student's "mathematical intelligence",
- are the factor loadings for the kth student, for j = 1, 2.
- is the difference between the ith student's standardized score in the kth subject and the average score in the kth subject of all students whose levels of verbal and mathematical intelligence are the same as those of the ith student,
In matrix notation, we have
- N is 1000 students
- z is a 10 × 1,000 matrix of observable standardized random variables,
- L is a 10 × 2 matrix of factor loadings (unobservable constants, ten academic topics, each with two intelligence parameters that determine success in that topic),
- F is a 2 × 1,000 matrix of unobservable random variables (two intelligence parameters for each of 1000 students),
- ε is a 10 × 1,000 matrix of unobservable random variables.
Observe that by doubling the scale on which "verbal intelligence"—the first component in each column of F—is measured, and simultaneously halving the factor loadings for verbal intelligence makes no difference to the model. Thus, no generality is lost by assuming that the standard deviation of verbal intelligence is 1. Likewise for mathematical intelligence. Moreover, for similar reasons, no generality is lost by assuming the two factors are uncorrelated with each other. In other words:
where is the Kronecker delta (0 when and 1 when ).The errors are independent of the factors:
The "errors" ε are taken to be independent of each other. The variances of the "errors" associated with the 10 different subjects are not assumed to be equal. In other words:
Note that, since any rotation of a solution is also a solution, this makes interpreting the factors difficult. See disadvantages below. In this particular example, if we do not know beforehand that the two types of intelligence are uncorrelated, then we cannot interpret the two factors as the two different types of intelligence. Even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence without an outside argument.
The values of the loadings L, the averages μ, and the variances of the "errors" ε must be estimated given the observed data X and F (the assumption about the levels of the factors is fixed for a given F). The "fundamental theorem" may be derived from the above conditions:
The term on the left is just the correlation matrix of the observed data, and its diagonal elements will be 1's. The last term on the right will be a diagonal matrix with terms less than unity. The first term on the right is the "reduced correlation matrix" and will be equal to the correlation matrix except for its diagonal values which will be less than unity. These diagonal elements of the reduced correlation matrix are called "communalities":
Practical implementation[edit]
This section needs additional citations for verification. (April 2012) |
Type of factor analysis[edit]
Exploratory factor analysis (EFA) is used to identify complex interrelationships among items and group items that are part of unified concepts.[2] The researcher makes no "a priori" assumptions about relationships among factors.[2]
Confirmatory factor analysis (CFA) is a more complex approach that tests the hypothesis that the items are associated with specific factors.[2] CFA uses structural equation modeling to test a measurement model whereby loading on the factors allows for evaluation of relationships between observed variables and unobserved variables.[2] Structural equation modeling approaches can accommodate measurement error, and are less restrictive than least-squares estimation.[2] Hypothesized models are tested against actual data, and the analysis would demonstrate loadings of observed variables on the latent variables (factors), as well as the correlation between the latent variables.[2]
Types of factoring[edit]
Principal component analysis (PCA): PCA is a widely used method for factor extraction, which is the first phase of EFA.[2] Factor weights are computed in order to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left.[2] The factor model must then be rotated for analysis.[2]
Canonical factor analysis, also called Rao's canonical factoring, is a different method of computing the same model as PCA, which uses the principal axis method. Canonical factor analysis seeks factors which have the highest canonical correlation with the observed variables. Canonical factor analysis is unaffected by arbitrary rescaling of the data.
Common factor analysis, also called principal factor analysis (PFA) or principal axis factoring (PAF), seeks the least number of factors which can account for the common variance (correlation) of a set of variables.
Image factoring: based on the correlation matrix of predicted variables rather than actual variables, where each variable is predicted from the others using multiple regression.
Alpha factoring: based on maximizing the reliability of factors, assuming variables are randomly sampled from a universe of variables. All other methods assume cases to be sampled and variables fixed.
Factor regression model: a combinatorial model of factor model and regression model; or alternatively, it can be viewed as the hybrid factor model,[3] whose factors are partially known.
Factor loadings: The factor loadings, also called component loadings in PCA, are the correlation coefficients between the variables (rows) and factors (columns). Analogous to Pearson's r, the squared factor loading is the percent of variance in that indicator variable explained by the factor. To get the percent of variance in all the variables accounted for by each factor, add the sum of the squared factor loadings for that factor (column) and divide by the number of variables. (Note the number of variables equals the sum of their variances as the variance of a standardized variable is 1.) This is the same as dividing the factor's eigenvalue by the number of variables.
Interpreting factor loadings: By one rule of thumb in confirmatory factor analysis, loadings should be .7 or higher to confirm that independent variables identified a priori are represented by a particular factor, on the rationale that the .7 level corresponds to about half of the variance in the indicator being explained by the factor. However, the .7 standard is a high one and real-life data may well not meet this criterion, which is why some researchers, particularly for exploratory purposes, will use a lower level such as .4 for the central factor and .25 for other factors. In any event, factor loadings must be interpreted in the light of theory, not by arbitrary cutoff levels.
In oblique rotation, one gets both a pattern matrix and a structure matrix. The structure matrix is simply the factor loading matrix as in orthogonal rotation, representing the variance in a measured variable explained by a factor on both a unique and common contributions basis. The pattern matrix, in contrast, contains coefficients which just represent unique contributions. The more factors, the lower the pattern coefficients as a rule since there will be more common contributions to variance explained. For oblique rotation, the researcher looks at both the structure and pattern coefficients when attributing a label to a factor. Principles of oblique rotation can be derived from both cross entropy and its dual entropy.[4]
Communality: The sum of the squared factor loadings for all factors for a given variable (row) is the variance in that variable accounted for by all the factors, and this is called the communality. The communality measures the percent of variance in a given variable explained by all the factors jointly and may be interpreted as the reliability of the indicator.
Spurious solutions: If the communality exceeds 1.0, there is a spurious solution, which may reflect too small a sample or the researcher has too many or too few factors.
Uniqueness of a variable: That is, uniqueness is the variability of a variable minus its communality.
Eigenvalues:/Characteristic roots: The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. The ratio of eigenvalues is the ratio of explanatory importance of the factors with respect to the variables. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant with more important factors. Eigenvalues measure the amount of variation in the total sample accounted for by each factor.
Extraction sums of squared loadings: Initial eigenvalues and eigenvalues after extraction (listed by SPSS as "Extraction Sums of Squared Loadings") are the same for PCA extraction, but for other extraction methods, eigenvalues after extraction will be lower than their initial counterparts. SPSS also prints "Rotation Sums of Squared Loadings" and even for PCA, these eigenvalues will differ from initial and extraction eigenvalues, though their total will be the same.
Factor scores (also called component scores in PCA): are the scores of each case (row) on each factor (column). To compute the factor score for a given case for a given factor, one takes the case's standardized score on each variable, multiplies by the corresponding loadings of the variable for the given factor, and sums these products. Computing factor scores allows one to look for factor outliers. Also, factor scores may be used as variables in subsequent modeling.
Criteria for determining the number of factors[edit]
Using one or more of the methods below, the researcher determines an appropriate range of solutions to investigate. Methods may not agree. For instance, the Kaiser criterion may suggest five factors and the scree test may suggest two, so the researcher may request 3-, 4-, and 5-factor solutions discuss each in terms of their relation to external data and theory.
Comprehensibility: A purely subjective criterion would be to retain those factors whose meaning is comprehensible to the researcher. This is not recommended[citation needed].
Kaiser criterion: The Kaiser rule is to drop all components with eigenvalues under 1.0 – this being the eigenvalue equal to the information accounted for by an average single item. The Kaiser criterion is the default in SPSS and most statistical software but is not recommended when used as the sole cut-off criterion for estimating the number of factors as it tends to overextract factors.[5]
Variance explained criteria: Some researchers simply use the rule of keeping enough factors to account for 90% (sometimes 80%) of the variation. Where the researcher's goal emphasizes parsimony (explaining variance with as few factors as possible), the criterion could be as low as 50%
Scree plot: The Cattell scree test plots the components as the X axis and the corresponding eigenvalues as the Y-axis. As one moves to the right, toward later components, the eigenvalues drop. When the drop ceases and the curve makes an elbow toward less steep decline, Cattell's scree test says to drop all further components after the one starting the elbow. This rule is sometimes criticised for being amenable to researcher-controlled "fudging". That is, as picking the "elbow" can be subjective because the curve has multiple elbows or is a smooth curve, the researcher may be tempted to set the cut-off at the number of factors desired by his or her research agenda.
Horn's Parallel Analysis (PA): A Monte-Carlo based simulation method that compares the observed eigenvalues with those obtained from uncorrelated normal variables. A factor or component is retained if the associated eigenvalue is bigger than the 95th of the distribution of eigenvalues derived from the random data. PA is one of the most recommendable rules for determining the number of components to retain,[citation needed] but only few programs include this option.[6]
However, before dropping a factor below one's cutoff, the analyst(s) should create scores for a data set based on the factor loadings and check the scores' correlation with any given dependent variable(s) of interest. Scores based on a factor with a very small eigenvalue can correlate strongly with dependent variables, in which case dropping such a factor from a theoretical model may reduce its predictive validity.
Rotation methods[edit]
The unrotated output maximises variance accounted for by the first and subsequent factors, and forcing the factors to be orthogonal. This data-compression comes at the cost of having most items load on the early factors, and usually, of having many items load substantially on more than one factor. Rotation serves to make the output more understandable, by seeking so-called "Simple Structure": A pattern of loadings where items load most strongly on one factor, and much more weakly on the other factors. Rotations can be orthogonal or oblique (allowing the factors to correlate).
Varimax rotation is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor (column) on all the variables (rows) in a factor matrix, which has the effect of differentiating the original variables by extracted factor. Each factor will tend to have either large or small loadings of any particular variable. A varimax solution yields results which make it as easy as possible to identify each variable with a single factor. This is the most common rotation option. However, the orthogonality (i.e., independence) of factors is often an unrealistic assumption. Oblique rotations are inclusive of orthogonal rotation, and for that reason, oblique rotations are a preferred method.[7]
Quartimax rotation is an orthogonal alternative which minimizes the number of factors needed to explain each variable. This type of rotation often generates a general factor on which most variables are loaded to a high or medium degree. Such a factor structure is usually not helpful to the research purpose.
Equimax rotation is a compromise between Varimax and Quartimax criteria.
Direct oblimin rotation is the standard method when one wishes a non-orthogonal (oblique) solution – that is, one in which the factors are allowed to be correlated. This will result in higher eigenvalues but diminished interpretability of the factors. See below.[clarification needed]
Promax rotation is an alternative non-orthogonal (oblique) rotation method which is computationally faster than the direct oblimin method and therefore is sometimes used for very large datasets.
Factor analysis in psychometrics[edit]
Charles Spearman pioneered the use of factor analysis in the field of psychology and is sometimes credited with the invention of factor analysis. He discovered that school children's scores on a wide variety of seemingly unrelated subjects were positively correlated, which led him to postulate that a general mental ability, or g, underlies and shapes human cognitive performance. His postulate now enjoys broad support in the field of intelligence research, where it is known as the g theory.
Raymond Cattell expanded on Spearman's idea of a two-factor theory of intelligence after performing his own tests and factor analysis. He used a multi-factor theory to explain intelligence. Cattell's theory addressed alternate factors in intellectual development, including motivation and psychology. Cattell also developed several mathematical methods for adjusting psychometric graphs, such as his "scree" test and similarity coefficients. His research led to the development of his theory of fluid and crystallized intelligence, as well as his 16 Personality Factors theory of personality. Cattell was a strong advocate of factor analysis and psychometrics. He believed that all theory should be derived from research, which supports the continued use of empirical observation and objective testing to study human intelligence.
Applications in psychology[edit]
Factor analysis is used to identify "factors" that explain a variety of results on different tests. For example, intelligence research found that people who get a high score on a test of verbal ability are also good on other tests that require verbal abilities. Researchers explained this by using factor analysis to isolate one factor, often called crystallized intelligence or verbal intelligence, which represents the degree to which someone is able to solve problems involving verbal skills.
Factor analysis in psychology is most often associated with intelligence research. However, it also has been used to find factors in a broad range of domains such as personality, attitudes, beliefs, etc. It is linked to psychometrics, as it can assess the validity of an instrument by finding if the instrument indeed measures the postulated factors.
- Reduction of number of variables, by combining two or more variables into a single factor. For example, performance at running, ball throwing, batting, jumping and weight lifting could be combined into a single factor such as general athletic ability. Usually, in an item by people matrix, factors are selected by grouping related items. In the Q factor analysis technique, the matrix is transposed and factors are created by grouping related people: For example, liberals, libertarians, conservatives and socialists, could form separate groups.
- Identification of groups of inter-related variables, to see how they are related to each other. For example, Carroll used factor analysis to build his Three Stratum Theory. He found that a factor called "broad visual perception" relates to how good an individual is at visual tasks. He also found a "broad auditory perception" factor, relating to auditory task capability. Furthermore, he found a global factor, called "g" or general intelligence, that relates to both "broad visual perception" and "broad auditory perception". This means someone with a high "g" is likely to have both a high "visual perception" capability and a high "auditory perception" capability, and that "g" therefore explains a good part of why someone is good or bad in both of those domains.
- "...each orientation is equally acceptable mathematically. But different factorial theories proved to differ as much in terms of the orientations of factorial axes for a given solution as in terms of anything else, so that model fitting did not prove to be useful in distinguishing among theories." (Sternberg, 1977[8]). This means all rotations represent different underlying processes, but all rotations are equally valid outcomes of standard factor analysis optimization. Therefore, it is impossible to pick the proper rotation using factor analysis alone.
- Factor analysis can be only as good as the data allows. In psychology, where researchers often have to rely on less valid and reliable measures such as self-reports, this can be problematic.
- Interpreting factor analysis is based on using a "heuristic", which is a solution that is "convenient even if not absolutely true".[9] More than one interpretation can be made of the same data factored the same way, and factor analysis cannot identify causality.
Exploratory factor analysis versus principal components analysis[edit]
While exploratory factor analysis and principal component analysis are treated as synonymous techniques in some fields of statistics, this has been criticised (e.g. Fabrigar et al., 1999;[10] Suhr, 2009[11]). In factor analysis, the researcher makes the assumption that an underlying causal model exists, whereas PCA is simply a variable reduction technique.[12] Researchers have argued that the distinctions between the two techniques may mean that there are objective benefits for preferring one over the other based on the analytic goal.
Arguments contrasting PCA and EFA[edit]
Fabrigar et al. (1999)[10] address a number of reasons used to suggest that principal components analysis is equivalent to factor analysis:
- It is sometimes suggested that principal components analysis is computationally quicker and requires fewer resources than factor analysis. Fabrigar et al. suggest that the ready availability of computer resources have rendered this practical concern irrelevant.
- PCA and factor analysis can produce similar results. This point is also addressed by Fabrigar et al.; in certain cases, whereby the communalities are low (e.g., .40), the two techniques produce divergent results. In fact, Fabrigar et al. argue that in cases where the data correspond to assumptions of the common factor model, the results of PCA are inaccurate results.
- There are certain cases where factor analysis leads to 'Heywood cases'. These encompass situations whereby 100% or more of the variance in a measured variable is estimated to be accounted for by the model. Fabrigar et al. suggest that these cases are actually informative to the researcher, indicating a misspecified model or a violation of the common factor model. The lack of Heywood cases in the PCA approach may mean that such issues pass unnoticed.
- Researchers gain extra information from a PCA approach, such as an individual's score on a certain component – such information is not yielded from factor analysis. However, as Fabrigar et al. contend, the typical aim of factor analysis – i.e. to determine the factors accounting for the structure of the correlations between measured variables – does not require knowledge of factor scores and thus this advantage is negated. It is also possible to compute factor scores from a factor analysis.
Variance versus covariance[edit]
Factor analysis takes into account the random error that is inherent in measurement, whereas PCA fails to do so. This point is exemplified by Brown (2009),[13] who indicated that, in respect to the correlation matrices involved in the calculations:
"In PCA, 1.00s are put in the diagonal meaning that all of the variance in the matrix is to be accounted for (including variance unique to each variable, variance common among variables, and error variance). That would, therefore, by definition, include all of the variance in the variables. In contrast, in EFA, the communalities are put in the diagonal meaning that only the variance shared with other variables is to be accounted for (excluding variance unique to each variable and error variance). That would, therefore, by definition, include only variance that is common among the variables."
— Brown (2009), Principal components analysis and exploratory factor analysis – Definitions, differences and choices
For this reason, Brown (2009) recommends using factor analysis when theoretical ideas about relationships between variables exist, whereas PCA should be used if the goal of the researcher is to explore patterns in their data.
Differences in procedure and results[edit]
The differences between principal components analysis and factor analysis are further illustrated by Suhr (2009):
- PCA results in principal components that account for a maximal amount of variance for observed variables; FA account for common variance in the data.[11]
- PCA inserts ones on the diagonals of the correlation matrix; FA adjusts the diagonals of the correlation matrix with the unique factors.[11]
- PCA minimizes the sum of squared perpendicular distance to the component axis; FA estimates factors which influence responses on observed variables.[11]
- The component scores in PCA represent a linear combination of the observed variables weighted by eigenvectors; the observed variables in FA are linear combinations of the underlying and unique factors.[11]
- In PCA, the components yielded are uninterpretable, i.e. they do not represent underlying 'constructs'; in FA, the underlying constructs can be labeled and readily interpreted, given an accurate model specification.[11]
Factor analysis in marketing[edit]
The basic steps are:
- Identify the salient attributes consumers use to evaluate products in this category.
- Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes.
- Input the data into a statistical program and run the factor analysis procedure. The computer will yield a set of underlying attributes (or factors).
- Use these factors to construct perceptual maps and other product positioning devices.
Information collection[edit]
The data collection stage is usually done by marketing research professionals. Survey questions ask the respondent to rate a product sample or descriptions of product concepts on a range of attributes. Anywhere from five to twenty attributes are chosen. They could include things like: ease of use, weight, accuracy, durability, colourfulness, price, or size. The attributes chosen will vary depending on the product being studied. The same question is asked about all the products in the study. The data for multiple products is coded and input into a statistical program such as R, SPSS, SAS, Stata, STATISTICA, JMP, and SYSTAT.
The analysis will isolate the underlying factors that explain the data using a matrix of associations.[14] Factor analysis is an interdependence technique. The complete set of interdependent relationships is examined. There is no specification of dependent variables, independent variables, or causality. Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions. This reduction is possible because some attributes may be related to each other. The rating given to any one attribute is partially the result of the influence of other attributes. The statistical algorithm deconstructs the rating (called a raw score) into its various components, and reconstructs the partial scores into underlying factor scores. The degree of correlation between the initial raw score and the final factor score is called a factor loading.
- Both objective and subjective attributes can be used provided the subjective attributes can be converted into scores.
- Factor analysis can identify latent dimensions or constructs that direct analysis may not.
- It is easy and inexpensive.
- Usefulness depends on the researchers' ability to collect a sufficient set of product attributes. If important attributes are excluded or neglected, the value of the procedure is reduced.
- If sets of observed variables are highly similar to each other and distinct from other items, factor analysis will assign a single factor to them. This may obscure factors that represent more interesting relationships.[clarification needed]
- Naming factors may require knowledge of theory because seemingly dissimilar attributes can correlate strongly for unknown reasons.
Factor analysis in physical sciences[edit]
Factor analysis has also been widely used in physical sciences such as geochemistry, ecology, and hydrochemistry.[15]
In groundwater quality management, it is important to relate the spatial distribution of different chemical parameters to different possible sources, which have different chemical signatures. For example, a sulfide mine is likely to be associated with high levels of acidity, dissolved sulfates and transition metals. These signatures can be identified as factors through R-mode factor analysis, and the location of possible sources can be suggested by contouring the factor scores.[16]
In geochemistry, different factors can correspond to different mineral associations, and thus to mineralisation.[17]
Factor analysis in microarray analysis[edit]
Factor analysis can be used for summarizing high-density oligonucleotide DNA microarrays data at probe level for Affymetrix GeneChips. In this case, the latent variable corresponds to the RNA concentration in a sample.[18]
Factor analysis has been implemented in several statistical analysis programs since the 1980s: SAS, BMDP and SPSS.[19] It is also implemented in the R programming language (with the factanal function), OpenOpt, and the statistical software package Stata. Rotations are implemented in the GPArotation R package.
See also[edit]
Wikimedia Commons has media related to Factor analysis. |
- Design of experiments
- Formal concept analysis
- Higher-order factor analysis
- Independent component analysis
- Multilinear PCA
- Multilinear subspace learning
- Non-negative matrix factorization
- Perceptual mapping
- Product management
- Q methodology
- Recommendation system
- Varimax rotation
- Generalized Structured Component Analysis
- ^ Bartholomew, D.J.; Steele, F.; Galbraith, J.; Moustaki, I. (2008). Analysis of Multivariate Social Science Data. Statistics in the Social and Behavioral Sciences Series (2nd ed.). Taylor & Francis. ISBN 1584889608.
- ^ a b c d e f g h i Polit DF Beck CT (2012). Nursing Research: Generating and Assessing Evidence for Nursing Practice, 9th ed. Philadelphia, USA: Wolters Klower Health, Lippincott Williams & Wilkins.
- ^ Meng, J. (2011). "Uncover cooperative gene regulations by microRNAs and transcription factors in glioblastoma using a nonnegative hybrid factor model". International Conference on Acoustics, Speech and Signal Processing.
- ^ Liou, C.-Y.; Musicus, B.R. (2008). "Cross Entropy Approximation of Structured Gaussian Covariance Matrices". IEEE Transactions on Signal Processing 56 (7): 3362–3367. doi:10.1109/TSP.2008.917878.
- ^ Bandalos, D.L.; Boehm-Kaufman, M.R. (2008). "Four common misconceptions in exploratory factor analysis". In Lance, Charles E.; Vandenberg, Robert J. Statistical and Methodological Myths and Urban Legends: Doctrine, Verity and Fable in the Organizational and Social Sciences. Taylor & Francis. pp. 61–87. ISBN 978-0-8058-6237-9.
- ^ * Ledesma, R.D.; Valero-Mora, P. (2007). "Determining the Number of Factors to Retain in EFA: An easy-to-use computer program for carrying out Parallel Analysis". Practical Assessment Research & Evaluation 12 (2): 1–11.
- ^ Russell, D.W. (December 2002). "In search of underlying dimensions: The use (and abuse) of factor analysis in Personality and Social Psychology Bulletin". Personality and Social Psychology Bulletin 28 (12): 1629–46. doi:10.1177/014616702237645.
- ^ Sternberg, R. J. (1977). Metaphors of Mind: Conceptions of the Nature of Intelligence. New York: Cambridge University Press. pp. 85–111.[verification needed]
- ^ Richard B. Darlington (2004) "Factor Analysis". Retrieved July 22, 2004.
- ^ a b Fabrigar et al. (1999). "Evaluating the use of exploratory factor analysis in psychological research.". Psychological Methods.
- ^ a b c d e f Suhr, Diane (2009). "Principal component analysis vs. exploratory factor analysis". SUGI 30 Proceedings. Retrieved 5 April 2012.
- ^ SAS Statistics. "Principal Components Analysis". SAS Support Textbook.
- ^ Brown, J. D. (January 2009). "Principal components analysis and exploratory factor analysis – Definitions, differences and choices.". Shiken: JALT Testing & Evaluation SIG Newsletter. Retrieved 16 April 2012.
- ^ Ritter, N. (2012). A comparison of distribution-free and non-distribution free methods in factor analysis. Paper presented at Southwestern Educational Research Association (SERA) Conference 2012, New Orleans, LA (ED529153).
- ^ Subbarao, C.; Subbarao, N.V.; Chandu, S.N. (December 1996). "Characterisation of groundwater contamination using factor analysis". Environmental Geology 28 (4): 175–180. doi:10.1007/s002540050091.
- ^ Love, D.; Hallbauer, D.K.; Amos, A.; Hranova, R.K. (2004). "Factor analysis as a tool in groundwater quality management: two southern African case studies". Physics and Chemistry of the Earth 29: 1135–43. doi:10.1016/j.pce.2004.09.027.
- ^ Barton, E.S.; Hallbauer, D.K. (1996). "Trace-element and U—Pb isotope compositions of pyrite types in the Proterozoic Black Reef, Transvaal Sequence, South Africa: Implications on genesis and age". Chemical Geology 133: 173–199. doi:10.1016/S0009-2541(96)00075-7.
- ^ Hochreiter, Sepp; Clevert, Djork-Arné; Obermayer, Klaus (2006). "A new summarization method for affymetrix probe level data". Bioinformatics 22 (8): 943–9. doi:10.1093/bioinformatics/btl033. PMID 16473874.
- ^ MacCallum, Robert (June 1983). "A comparison of factor analysis programs in SPSS, BMDP, and SAS". Psychometrika 48 (48). doi:10.1007/BF02294017.
Further reading[edit]
- Child, Dennis (2006). The Essentials of Factor Analysis (3rd ed.). Continuum International. ISBN 978-0-8264-8000-2.
- Fabrigar, L.R.; Wegener, D.T.; MacCallum, R.C.; Strahan, E.J. (September 1999). "Evaluating the use of exploratory factor analysis in psychological research". Psychological Methods 4 (3): 272–299. doi:10.1037/1082-989X.4.3.272.
- Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington DC: American Psychological Association. ISBN 1591470935.
External links[edit]
- Factor Analysis. Retrieved July 23, 2004, from http://www2.chass.ncsu.edu/garson/pa765/factor.htm
- Raymond Cattell. Retrieved July 22, 2004, from http://www.indiana.edu/~intell/rcattell.shtml
- Exploratory Factor Analysis - A Book Manuscript by Tucker, L. & MacCallum R. (1993). Retrieved June 8, 2006, from: http://www.unc.edu/~rcm/book/factornew.htm
- Garson, G. David, "Factor Analysis," from Statnotes: Topics in Multivariate Analysis. Retrieved on April 13, 2009 from http://www2.chass.ncsu.edu/garson/pa765/statnote.htm
- Factor Analysis at 100 —conference material
- FARMS - Factor Analysis for Robust Microarray Summarization, an R package —software


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GW exceeds the legal limit with this roundup of the 50 fastest masters of the fretboard.
It's the place where true, universal emotion comes from
It's been stuck in my head for minutes and seconds and hours...
Fender has announced the release of the Tim Armstrong Deluxe guitar, a six-string acoustic model designed in conjunction with Rancid founder Tim Armstrong.
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American Defense AD-VPG 5-Lug Rail for AD-170 Riser Aluminum Matte
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Tech Forecast Post-it Notes Teams Up With Evernote To Bridge Analog And Digital The companies are offering co-branded note-taking products for a digital age. Read More » By Alice Truong
Co.Exist Meet The 14-Year-Old Girl Who Developed A Low-Cost Water Purification System Deepika Kurup just won $25,000 for a device that uses the power of the sun to kill bacteria in water. Read More » By Ariel Schwartz
Fast Company Five Fundamentals of Fanatical Leadership If you've ever worked for a boss that was openly enthusiastic about what they did, then you know how infectious that becomes for the entire company. These individuals can set the course for helping the organization separate itself from the pack by passionately ignoring the status quo and the naysayers who protect it. While not crazy, leaders like these are most certainly fanatical about changing an industry and perhaps even a culture mindset. Read More » By Reid Carr
Masters of Design 2011 The Nine Passions Of 3M's Mauro Porcini Meet the audace global design guru who has infused his elegante sensibility into a once-blando $27 billion American conglomerate. Read More » By Chuck Salter
Fast Company An Alternative To Plastic, Grown From Mushrooms Evocative is taking on non-biodegradable and toxic polystyrene by mixing agricultural products with a fungus. It is already working with Dell and Steelcase on packaging materials, and with Ford on bumpers and side doors. But can it compete when it has to grow a product instead of churning it out from a factory? Read More » By Ben Schiller ADVERTISEMENT
Fast Company 3M's Visual Impact Scanner Knows What Your Eyes Want After decades' worth of vision research, Minnesota-based conglomerate 3M has tuned up its Visual Attention Service, an algorithm that can scan all types of content to determine exactly where the average human eye is most likely to be drawn. Read More » By Austin Carr
Co.Design Materials Giant 3M Aims To Elevate Its Brand, By Pushing Sexy Concepts [Slideshow] When you think of the name 3M, you usually think of Post-it notes and packing tape, but recently at the Milan Furniture Fair, the company made their first foray into the world of high-end design. The exhibition, Infinite Innovation, is meant to show 3M's foundational innovations, that stand behind everything from interaction design to architectural interiors. "Of course, it's safer for us in the long run to control the whole product. But we're already innovating, people just don't know it's us," said John Olfelt, a 3M architect and project manager. Read More » By Shoham Arad
Co.Design How 3M Gave Everyone Days Off and Created an Innovation Dynamo In 1974, 3M scientist Art Fry came up with a clever invention. He thought if he could apply an adhesive (dreamed up by colleague Spencer Silver several years earlier) to the back of a piece of paper, he could create the perfect bookmark, one that kept place in his church hymnal. He called it the Post-It Note. Read More » By Kaomi Goetz
Fast Company Today's Most Innovative Companies by Popular Demand Harris Interactive polled close to 30,000 folks to find out what companies have the best reputations in corporate America. A yet-to-be-released part of that study tested the public on which companies had the most innovative products and services. Harris provided Fast Company with the list. Here are three of the top five, stacked against our own list of innovators. Read More » By Austin Carr
Fast Company Out of the Box Solutions for Sustainable Shipping Even in the Great Recession, businesses in every industry are pushing forward with sustainability because boosting profitability and going green go hand in hand. Still, it can be surprising how much of their eco-benefit often comes from beyond their walls through factors like shipping and packaging. Partners like Hisco that deliver greener shipping solutions from Read More » By Glenn Croston


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My Friend Dahmer
Item Details
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a graphic novel
pt. 1. The strange boy
pt. 2. A secret life
pt. 3. The Dahmer fan club
pt. 4. Becoming the monster
pt. 5. Fade to black
Community Activity
Add a CommentThere's always that guy or girl in your class. This is of story of that guy actually becoming a serial killer. There's enough out there about infamous serial killer Jeffrey Dahmer but this is the story, as much as can be said, of his youth. Of how isolated he was in school and just how his spiral began. I think what I like best about this is how honest it is. Backderf doesn't claim to be closer to him than he was, he supplements with other sources as needed (there are comprehensive notes in the back), and explains why certain people are omitted. It's a disturbing but also tragic book. The tragedy, as the author states, stops after Dahmer kills his first victim but you just wonder if there was some way he could have been saved. That somebody could have noticed or done something even though there was probably nothing to be done
An intimate look at Jeffrey Dahmer told through the eyes of a former friend before Dahmer was an infamous serial killer. I was nervous to read this because of the subject matter, but I'm glad I read it. The story is Backderf's story and it is well researched and not told lightly.
oftentimes hard to take but still compelling. not for the faint of heart though. many of the graphic details are in the appendix. still interesting as it gives a rare story of someone who knew a murderer "way back when"
A deeply unsettling but fascinating must-read. Bear in mind that it doesn't go into the details of the crimes for which Dahmer is best known, so you may want to do a little research before or after you read this.
A scrupulously told story that asks all the right questions and wisely refuses to provide answers. In 1991 Derf unexpectedly found himself at the fringes of infamy, and after decades of effort, in this book he wrings the experience of all it's worth. Autobio comics and reportage combine in this compelling work.
A very interesting read. It's a very well described account of Dahmer's life that actually backed up by facts (they are even listed in the back of the book in great detail). I really enjoyed reading this book and didn't put it down until finshed it.
a fascinating and insightful look at Dahmer's life during high school. sad and disturbing, but also rings true (the depiction of 70s high school life)
A disturbing remembrance, especially with the illustrations where everyone looks oddly outsized, bulbous, and overraged for high school. But he nails the '70s vibe in his drawings.


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Oil of Oregano Blend, 1 fl oz (30 ml), From Now Foods
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BlackBerry 10.1 OS update for Z10 phone posted in error
BlackBerry Z10 owners on AT&T still can't get the latest update to the BlackBerry operating system.
Earlier on Friday, the BlackBerry OS 10.1 update for the BlackBerry Z10 smartphone was rolled out via AT&T. But that update was actually posted in error, a BlackBerry spokesperson told CNET.
BlackBerry now advises Z10 users who receive a software update notification to disregard it. The company said it's working closely with AT&T to deploy the official update soon.
This means that AT&T and BlackBerry are still behind in launching BB OS 10.… Read more


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Alison Moore is senior vice president, Digital Platforms, for Home Box Office, responsible for overseeing the strategy, development and operation of HBO's multiplatform digital products: HBO/MAX GO, HBO.com, Cinemax.com, HBO Social Media platforms, as well as HBO/MAX On Demand and Affiliate Product initiatives. Moore was named to this position in July 2010.
Moore first joined HBO as a marketing manager in 1995, responsible for developing promotional marketing programs with affiliate partners. She left the company in 1999, returning to HBO in 2003 as director, Brand Development. She was promoted to vice president, Brand Strategy and Digital Platforms in May 2006, overseeing HBO's consumer websites, online video, social and promotional platforms, as well as HBO's brand advertising and promotional strategy.
During her hiatus from HBO, Moore was instrumental in helping launch two internet start-ups: in 1999, as director, B2B Marketing, for Flooz.com, she created and launched Flooz B2B marketing and promotional strategies; and in 2000 she co- founded DatSat, where as vice president, Market Development, she was responsible for overseeing business development and marketing strategies. In 2001, she briefly consulted at JP Morgan Chase in the Small Business Financial Services division, creating business development plans for one of the division's start-up investments. From 2001 to 2003, she was director, Product Strategy, at Cablevision, where she was responsible for product strategy, marketing and branding of Optimum Online, Cablevision's award-winning consumer broadband service.
She began her career at Turner Broadcasting, Inc. in Atlanta, GA, where she served as manager, Affiliate Relations and Marketing from 1992 to 1995.
Moore holds a BA in Political Science from the University of Georgia.
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Randy Kennedy reported from this year's Venice Biennale.
Go to BlogYour search for New School in Venice Biennale returned 1 articles
At least eight countries will be first-timers at the Venice Biennale in 2013; a Franz Kline painting will be auctioned at Christie's; and Glenn Ligon designs a neon work for the New School.
October 26, 2012, FridaySEARCH 1 ARTICLES ABOUT THE VENICE BIENNALE:
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The Pew Charitable Trusts is driven by the power of knowledge to solve today's most challenging problems. Pew applies a rigorous, analytical approach to improve public policy, inform the public and stimulate civic life.
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Publication: NPR's All Things Considered
05/23/2008 - Jay Nelson of the Pew Environment Group appeared on NPR's "All Things Considered" to speak on the news that the Bush administration is considering launching one of the biggest conservation programs in U.S. history.If implemented, President George W. Bush could, with the stroke of a pen, protect vast stretches of U.S. territorial waters from fishing, oil exploration and other forms of commercial development. The initiative could also create some of the largest marine reserves in the world — far larger than national parks like Yellowstone or the Grand Canyon.A spokesman for the White House Council on Environmental Quality confirmed that the administration is considering the initiative but declined to discuss details, saying they are still under review.The idea is drawing strong support from conservationists who typically have been harshly critical of the Bush administration's overall environmental record. But some of the possible reserves are already attracting opposition from local leaders and industry groups and from some members of Congress.* * *The groups — along with government agencies and other interested parties – ultimately developed a "wish list" that included about 30 potential marine monuments. They ranged from small reserves in U.S. coastal waters to vast swaths around U.S. territories in the distant Central Pacific. The candidates stretched "from Bar Harbor, Maine, to Dutch Harbor, Alaska" and beyond, says Jay Nelson of the Washington-based Pew Environment Group.Listen to the program on "All Things Considered" and read the related story Bush Eyes Unprecedented Conservation Program on NPR's Web site.


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Definition of denumerable in English:
Line breaks: de|numer|ablePronunciation: /dɪˈnjuːm(ə)rəb(ə)l
Mathematics- Able to be counted by a one-to-one correspondence with the infinite set of integers.More example sentences
- The non-denumerable infinity of real numbers (and thus of points in space and of events in time) is much larger than the merely denumerable infinity of integers.
- The paper discusses denumerable sets, i.e. those which are in 1-1 correspondence with the natural numbers.
- More example sentences
- At least five mathematicians tried to prove denumerability of the value set, to which the names of two of them are attached.
- I don't know how to approach it… but know that it is based on the concept of denumerability of real numbers.
- Combining with his proof of the denumerability of rational numbers, it proves the existence of irrational numbers without actually constructing any irrational number.
- More example sentences
- The most famous was his diagonal argument which seems to show that there must be orders of infinity, and specifically that the non-denumerably infinite is distinct from the denumerably infinite.
- This amounts to saying the transfinite whole is not equal to the sum of its denumerably infinite parts.
- This way of reasoning is also present in finite and denumerably infinite collections.
Pronunciation: /-ˈbɪlɪti/
early 20th century: from late Latin denumerare 'count out' + -able.


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Tahoe Reno Industrial Center (TRIC) is a massive 107,000 acre park that encompasses a developable 30,000 acre industrial complex with pre-approved industrial and manufacturing uses.
Located nine (9) miles east of Reno on I-80, in a pro-growth Nevada county, the four 5,000 acre phases now available for development include:
- Rail serviced sites
- Municipal water and sewer utility companies
- High pressure gas to all sites
- Five (5) generating power plants on site with more than 900 megawatts of electrical power available to all park users
Are you looking to expand or consolidate your operations in a business-friendly county? Do you need to establish a new west coast warehouse and distribution center? Do you have a manufacturing process that requires special allowances or permits? We are ready to guide your discovery and serve your every need. We can help you navigate our state and local government process, provide in-depth statistical profiles and help you identify top service provides in our region. It is a key part of the TRIC promise of partnership and performance.
Visionary development. Unrivaled transportation advantages. Opportunity as far as the eye can see. If you're ready to expand your company's horizons and stake your claim on the all-important western frontier, there's only one place to do it. Tahoe Reno Industrial Center.


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A 100-kilowatt wind turbine was recently installed at the Toledo Electrical Joint Apprenticeship Training Committee (JATC) in Rossford, Ohio. READ MORE
May 2011: Safety
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The entire performance of a fiber optic (or copper) network depends on the performance of the patchcords used for interconnects and for connecting communications equipment, bu READ MORE
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The U.S. Environmental Protection Agency (EPA) announced updated standards for lighting fixtures to qualify for the Energy Star label, an efficiency program. Effective Oct. READ MORE
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The University of North Texas (UNT) has received a $2 million grant from the State Energy Conservation Office to install three wind turbines that will feed the electrical gri READ MORE
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Computer Resources
Computers are available for word processing, to access reference databases on CD-ROM or online, and for Internet access. Pages can be printed from all computers.
Word Processing and World Wide Web
Thirty computers are available for word processing and Internet access at the main library. There are also study rooms with Internet access for laptop computers. Childrens Internet computers for patrons in the sixth grade and under are filtered. Each branch has four computers for Internet and Word processing as well as a filtered children's Internet and a children's word processor without Internet access. There are also programs for spreadsheets and databases. Please present your library card to the librarian to sign up for 60 minutes of Internet access. Patrons using the Internet must abide by the library's Internet Access Policy.
Online Reference Databases
All three library locations have computers with reference database access. These databases include magazine articles, newspapers, business information, and various research topics. Many of these resources can also be searched from home.
Home | Library Catalog | About the Library | Library Resources Building Project | Kids | Teens | Internet Resources


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Welcome to the RapDogs.com.
If you're new to the site, then introduce yourself with a quick post in here. Members are welcome to respond to posts to increase post count, once per thread.
In this forum talk about anything from 808 kicks to favorite night spots. If it doesn't fit on one of our other forums it goes here. No newbie links - read our rules before you post. NO commercial posts.
Post links to websites that you think would be of interest to our members. No bulk advertising please. If you are a newbie, do not post links in our other forums or they may be edited or blocked permanently. No Commercial Posts, links to sites that sell product or links to similiar topic forums.
Let us know what you'd like to see to make this board a better place for members. Also let us know about ideas for new forum subjects.
Starting battle forum for members with under 100 posts.
For members with 100+ posts and one previous win.
Over 300 posts and three wins from lower battle forums.
Jump in a tournament and give it a shot. Art is just opinion so don't get your panties in a wad if you don't win. Art is serious but we demand you have fun. Only mod can start threads, but anyone can jump in.
Audio battles only - post links to audio files. If you just want feedback on audio, then peep our seperate audio forum.
Jump in with whatever you got.
Subjects are started, jump in and continue the story line.
State your beef here and then take it to the Main Battle Arena.
Post links to your audio recordings to get honest feedback from our members. No commercial posts. Do not post links to audio files until you have 100 posts and are giving feedback on other audio posts.
Here's for poetry and writings that don't fit under the rap categories. Yes, we realize that rap is poetry too...
There are currently 106 users online. 0 members and 106 guests
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Welcome to our newest member, SheerieF4


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iPhone 5 officially launched at Apple press event, 16:9 4-inch screen and more
Apple has unveiled its new iPhone, the iPhone 5, at a press event in San Francisco. It's the thinnest and lightest iPhone yet, weighing just 112g and measuring just 7.6mm in depth. It does, as expected, come with a 16:9 4-inch 326ppi Retina display, with... read the full article.


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Rossiskaya Gazeta and Vozrozheniye
December 13, 1995, in near Grozny, Russia
Kagirov, a reporter for the Moscow daily newspaper Rossiyskaya Gazeta and the local paper Vozrozheniye, was shot and killed in an ambush in Chechnya. Kagirov and three local police officers were traveling in a car near Grozny when they were attacked. The three officers were also killed.Medium: Print
Job: Print Reporter
Beats Covered: War
Gender: Male
Local or Foreign: Local
Freelance: No
Type of Death: Crossfire/Combat-Related
Suspected Source of Fire: Military Officials


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Whether real or as a print, snakeskin is having a resort moment for clothes and accessories.
Sign in using your Facebook or Twitter account, or simply type your comment below as a guest by entering your email and name. Your email address will not be shared. Please note that WWD reserves the right to remove profane, distasteful or otherwise inappropriate language.Ads by Google


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Herb Butter Spread
From EatingWell.com
Try this herb butter spread with olive oil to top corn on the cob, fresh bread, or baked potatoes. Make a few batches at a time and store in the refrigerator for an easy way to jazz up side dishes. Use it cold or let it come to room temperature before serving.
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Nutritional Information
(per serving)
Calories | 57 |
Total Fat | 6g |
Saturated Fat | 2g |
Cholesterol | 8mg |
Sodium | 146mg |
Total Carbohydrate | -- |
Dietary Fiber | -- |
Sugars | -- |
Protein | -- |
Calcium | -- |
Carin Krasner
U.S. | Metric | Conversion chart |
- 1 tablespoon(s) butter, at room temperature
- 1 tablespoon(s) extra-virgin olive oil
- 1 tablespoon(s) finely chopped fresh herbs, such as basil, parsley, or chives
- 1/4 teaspoon(s) salt
- 1/4 teaspoon(s) pepper
- Mash butter in a small bowl with the back of a spoon until soft and creamy. Stir in oil until combined. Mix in herbs, salt, and pepper.
Exchanges: 1 fat
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A Weekend Market in Paris, A Panorama
Ever go to a market expecting one thing, only to find something refreshingly different? That's how it was with our visit to the Saturday morning market near Pont de l'Alma in Paris' 16th arrondissement. It's only a stone's throw away from the Eiffel Tower, Champs Elysee and a handful of Paris top ten sights. Given all this, we figured the market fancy, polished, and full of tour groups.
It wasn't. Continue Reading »


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With a likely win on Sunday that would mean they have swept us two seasons in a row. We can't even do that to the Browns.
With a likely win on Sunday that would mean they have swept us two seasons in a row. We can't even do that to the Browns.
Playing Fantasy Football does not qualify you to be the in the front office or on the coaching staff of the Pittsburgh Steelers. They are professionals and you are not!
2014 Draft
1. Eric Ebron, TE
2. Calvin Pryor, S
3 (Comp). Jaylen Watkins, CB
4. Justin Ellis, DT/NT
5a. Brandon Coleman, WR
5b. Brent Urban, DE
6. Prince Shembo, OLB
7a. Aaron Colvin, CB
7b. Storm Johnson, RB
If they can beat us by 2 touchdowns 4 times in a row with our starters healthy then I would say they own us. With the exception of the first game of the year last year it has been a field goal that won it. That is not owning anyone.
If they win on Sunday, they will have beaten a team with Byron Leftwich at QB in the first game and Charlie Batch at QB in the second game. Would that count as "owning" us? Imagine if we played them with Ben Roethlisberger vs. Tyrod Taylor? If you look at the first game this season where they "owned" us, an injury-riddled Byron Leftwich actually had 35 more passing yards than Flacco, and our defense held Ray Rice to 40 yards on 20 carries. We handed them 10 points on a silver platter via a punt return for a TD and a Wallace fumble deep in our end (already in FG range). Other than those two gifts, our defense held the mighty Ravens to a single FG. Does that count as "owning" us? I concede nothing to the purple mob.
My post-combine mock draft:
1. NT Louis Nix, Notre Dame
2. TE Austin Seferian-Jenkins, Washington
3c. S Deone Bucannon, Washington State
4. OT James Hurst, North Carolina
5. WR Jeff Janis, Saginaw Valley State
5c. CB Walt Aikens, Liberty
6. DE Deandre Coleman, California
7. ILB Max Bullough, Michigan State
The Ravens could beat us 100-0 twice for 10 seasons and they'd still suck.
I would say their players don't seem as frail as ours.
If the Ravens win on Sunday, Mike Tomlin will have a 6-6 record vs the Ravens, not counting the playoff win that sent us to XLIII...
That isn't ownership...that's just a good rivalry...
Since the Browns returns to the league in 1999, the Steelers are 22-5 vs the Browns, not including the 2002 playoff win...that is ownership...
No, it just means they've won the last 4 games provided they win this weekend).
1.15) Ra'Shede Hageman - DE
2.47) Jason Verrett - CB
3.comp) Brandon Coleman - WR
4.114) Terence Brooks - FS
"Before you can win a game, you have to not lose it." -- Chuck Noll
Ask a Raven fan if they would take the 3 (or 4, if they win this week) game win streak they currently enjoy... or the one-season, three game sweep (including the AFCC game) that we enjoyed over them a couple years back.


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Kennesaw Apartments for Rent
Search Apartments in Kennesaw
"Last year, I would have walked on burning coals for a site with a map mash-up. Now when we move your site will be my first stop for information.." - Kennesaw,GA
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Kennesaw Apartment Rental Market
Household Income
Household Income City State City Compared to State Less than $10,000 3.5% 10.1% -6.6% $10,000 to $14,999 1.9% 5.9% -4.0% $15,000 to $19,999 2.1% 5.9% -3.8% $20,000 to $24,999 3.2% 6.4% -3.2% $25,000 to $29,999 4.4% 6.4% -2.0% $30,000 to $34,999 5.2% 6.2% -1.0% $35,000 to $39,999 5.2% 5.9% -0.7% $40,000 to $44,999 5.8% 5.8% +0.0% $45,000 to $49,999 6.3% 5.1% +1.2% $50,000 to $59,999 11.9% 9.2% +2.7% $60,000 to $74,999 17.8% 10.5% +7.3% $75,000 to $99,999 17.3% 10.4% +6.9% $100,000 to $124,999 7.7% 5.2% +2.5% $125,000 to $149,999 3.7% 2.5% +1.2% $150,000 to $199,999 3.3% 2.2% +1.1% $200,000 or more 0.7% 2.4% -1.7% -
Cost of Living
Share of Household Income Spent on Rent City State City Compared to State Less than 10.0% 3.4% 6.5% -3.1% 10.0% to 14.9% 15.6% 11.8% +3.8% 15.0% to 19.9% 13.3% 14.6% -1.3% 20.0% to 24.9% 20.3% 12.8% +7.5% 25.0% to 29.9% 11.4% 10.2% +1.2% 30.0% to 34.9% 6.0% 7.3% -1.3% 35.0% to 39.9% 7.6% 5.1% +2.5% 40.0% to 49.9% 10.5% 6.5% +4.0% 50.0% or more 9.2% 16.5% -7.3% Not computed 2.8% 8.6% -5.8% -
Age Demographic of Renters
Age Demographic of Renters City State City Compared to State 15 to 24 years 12.9% 14.3% -1.4% 25 to 34 years 36.2% 31.6% +4.6% 35 to 44 years 26.3% 23.0% +3.3% 45 to 54 years 15.2% 14.1% +1.1% 55 to 64 years 5.6% 7.2% -1.6% 65 to 74 years 1.7% 4.7% -3.0% 75 to 84 years 1.7% 3.6% -1.9% 85 years and over 0.4% 1.4% -1.0% -
Travel Time to Work
Travel Time to Work City State City Compared to State Less than 30 minutes 15.6% 30.7% -15.1% 30 to 44 minutes 21.6% 24.4% -2.8% 45 to 59 minutes 19.5% 15.6% +3.9% 60 or more minutes 43.3% 29.2% +14.1%
Source: 2000 Census
Kennesaw, Georgia
Kennesaw is a suburb of Atlanta, Georgia with a current population of just under 33,000 people. Named for the mountain it sits on, it is also the highest peak in the area with an altitude of 1808 feet. It was the site of major Civil War battles, railroad town and, today, a listee for being on of the best towns for families.
When searching for your Kennesaw apartment, know that the town is somewhat walkable and you will want to own a car to get around. The town excels at being resident friendly with high interaction between town government and residents.It's proud of its history and its future.
Battle of LIttle Kennesaw
Civil War sites are some of the most popular attractions for both families and historians. Little Kennesaw Mountain was a pivotal point in the war and Moon's Station contains a great deal of history. Swift-Cantrell Park is a 42 acre area offering many recreational facilities and free wi-fi too. The Smith-Gilbert Gardens are not only a plant lover's paradise but offers a wonderful place just to stroll and lounge around. The downtown historical district provides not only insight into Kennesaw's past but offers great shopping and restaurants.
Fried Pickles and Other Delicacies
Barbeque is the first delicacy you should try in Kennesaw, and Big Shanty is the place to do it. Great portions and fantastic meats slow smoked. At the Trackside Grill, you should try their fried pickles. One of those things that sounds awful but is really good.Sweet Tomatoes is a salad bar but what a salad bar, and just the thing when you want to eat healthy. Italian places like Carrabba's and Provino's offer up huge portions of your favorite pastas and pizzas. Your Kennesaw apartment is going to be close to many good places but start with these.
Line Dancing
Bailey's and Sidelines are both excellent bars to hang out in and make new friends.Both are casual, have the coldest beer and best bar food. Los Cabos makes a mean margarita and has karaoke some nights too. Line dance at Cowboy's, go Irish at Johnnie McCracken's, or have tapas with drinks at The Cave. With the great nightclubs of Atlanta just down the road, Kennesaw is convenient and the best of small town living.
Average Apartment Rent in Kennesaw, Georgia
# Bedrooms | Feb | Jan | Dec | 3 Month % change |
Studio | N/A | N/A | N/A | 0% |
1 Bed | $882 | N/A | $862 | 2.3% |
2 Bed | $1,127 | $1,091 | $1,024 | 10.1% |
3 Bed | $1,222 | $1,272 | $1,107 | 10.4% |
See how Home Rentals compare in Kennesaw
Kennesaw Apartment Rental Trends
Apartments in Kennesaw have competitive rents so be sure to use our apartment finder to get the best deal. In December the average rent for a 1 Bedroom Kennesaw apartment cost $862. If you need a roommate, try finding a 2 bedroom apartment rental. An average 2 bedroom Kennesaw apartment was $1,024 in December. The average apartment rent for a 3 bedroom apartment in December was $1,107. Start your apartment search by checking out some of the Kennesaw rentals listed below.Rent Apartments Near Kennesaw, Georgia
Check out these great communities and cities near Kennesaw for apartments for rent:
- Alpharetta Apartments
- Atlanta Apartments
- Decatur Apartments
- Duluth Apartments
- Lawrenceville Apartments
- Lithonia Apartments
- Marietta Apartments
- Norcross Apartments
- Roswell Apartments
- Stone Mountain Apartments
Map & Local Information
Local Talk
Get answers about Kennesaw from local experts or tell us what you love about it.
Is Kennesaw a good place for families?
With big city opportunities and a suburban charm, it's no wonder Kennesaw was named on Family Circle's 2007 list of the 10 Best Towns for Families. Kennesaw boasts an affordable cost of living, ample employment opportunities, top rated schools, a quality health care system, a comfortable climate, and an abundance of green space. Life in Kennesaw is as stress-free as it gets, with outstanding air quality, plentiful parks and recreational programs, and 130 acres of parklands. The city also hosts its very own special events throughout the year including outdoor movies, summer concerts, and the annual favorite Pigs and Peaches BBQ Festival.
Is Kennesaw famous for any kind of restaurant or food in particular? What's the local favorite?
"Slices larger than your head!" boasts Kennesaw's favorite pizza joint Big Pie in the Sky. Located on Baker Road, this restaurant serves up huge and delicious slices of thin-crust pizza with specials such as the West Coast Pesto, topped with chicken, pesto, and cream cheese, and the Big Kahuna with bacon, ham, pineapple, and feta cheese. This local establishment was featured on the Travel Channel's Man vs. Food for their infamous Carnivore Challenge (You'll have to see this firsthand to truly appreciate it!). With massive 30" pizzas, a cozy atmosphere, a convenient location with plenty of parking, and always great service, it's no wonder Big Pie has become a Kennesaw favorite.
Is Kennesaw a town where I'll need a car to get around?
Yes. Like most cities in Southern Florida, Kennesaw has some public transportation, but not much. Kennesaw is served by Cobb County Transit. Bus routes 40, 45, and 100 make stops in Kennesaw. Most residents of Kennesaw find it necessary to use a car to get around.
Is Kennesaw a good place for younger people?
With a population of close to 30,000, Kennesaw is not the best place for young people. Not unless they are young people with families. Kennesaw's combination of good schools, low crime, and a high rate of home ownership make it ideal for families with children. As such, Kennesaw lacks a viable nightlife, but it could be a good place for younger people seeking some peace and quiet.
Will I need a car in Kennesaw?
Having a car is imperative in Kennesaw. Less than 1 percent uses public transportation to get around on a daily basis, while just about 85 percent drives a car as their primary mode of transportation. Since Kennesaw doesn't have a true public transit system to speak of, most of that less than 1 percent is using taxis. The landscape is very car-oriented, and pedestrians and cyclists are discouraged by the fact that sidewalks and bike lanes are not always present.


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Most people OK buying goods via mobile devices
A significant number of people are comfortable shopping and paying for items through their mobile devices, according to a new report from mobile media firm JiWire.
JiWire's latest Mobile Audience Insights Report (PDF) found that 79 percent of 5,000 people surveyed are OK paying online via their cell phones or tablets.
Though most of those polled are still making relatively small purchases (less than $100), 50 percent said they're comfortable spending more than $100 using a cell phone, while almost 20 percent said they're OK buying things worth more than $500.
Beyond paying for items, more consumers are also researching products via their mobile devices. JiWire found that 71 percent of those polled had researched future purchases on their phone or tablet before buying the item. Among those, 31 percent later bought the item in a store, 40 percent bought it online through a PC, and 20 percent bought it directly from their mobile device.… Read more


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Home & Garden
Natalia Wall Mount Jewelry Mirror
Sophisticated yet simple, this silver jewelry mirror provides an assortment of storage options and is the perfect solution to keep you organized. The clean, modern design brings both form and function into your home. The unit offers 14 hanging hooks, 16 earring notches, four cushioned ring holders, and a shelf for assorted pieces. This elegant wall mount jewelry mirror will be a beautiful addition to any bedroom, walk-in closet, bathroom or entryway.
The handcrafted touch of artisan skill creates variations in color, size and design. If buying two of the same item, slight differences should be expected. Note: color discrepancies may occur between this product and your computer screen.- 17" W x 4.75" D x 32.25" H
- 2 rows for hanging items, 7 hooks each
- 2 rows or earring storage, 8 notches each
- 4 rows of ring storage
- 1 shelf for assorted pieces
- 3mm mirror
- Silver finish
- Constructed of hardwoods, MDF, and black felt lining
- No assembly required; ready to hang
$199.99 -
Home & Garden
Get ready for the holidays with holiday decor, or create an outdoor oasis with garden and patio furniture and fashions that are fun and functional.
Mirage Mirrored Cabinet
Perfect for any room, this glamorous mirrored cabinet is a perfect compliment for your home. With its mirrored finish, it adapts to any surroundings without overpowering yet, catches your eye with its unique presence. The practical size and function works as well in the living room as it does bedside. Finishing the piece off is a combination of two drawers and one large double door storage cabinet with faux crystal knobs.- 28" W x 13" D x 28" H
- Two drawers: 10.5" W x 10.25" D x 5" H
- Double door cabinet: 27" W x 11" D x 14.5" H
- Area under table: 23.5" W x 8.25" D x 3.75" H
- Mirrored finish with faux crystal knobs
- Painted silver wood trim
- Assembly required
$279.99 -
Home & Garden
Get ready for the holidays with holiday decor, or create an outdoor oasis with garden and patio furniture and fashions that are fun and functional.
Vogue Chrome Wall Mirror
The contemporary elegance of this wall mirror will bring a pleasantly distinct style to your home. The metal frame is finished in brilliant chrome that will add a "wow" factor to your home. This elegant mirror can be used to achieve a formal atmosphere or a casual contemporary home setting.- 22" W x 1.25" D x 36" H
- Chrome frame
- 5mm Glass Mirror
- Durable metal frame
- Ready to hang
- No assembly required
$99.99 -
Decorative Wall Mirror
Adorn your walls with this brilliant decorative wall mirror, perfect for hanging on an empty wall or above a console table. Geometric shapes surround the large mirror creating a dramatic abstract effect. Try hanging this mirror in your living room or home office for a brand new look that you are sure to love.- 32.25" W x 4.5" D x 32" H
- Mirror measures 18.25" W x 18.25" L
- Textured espresso finished metal
- Constructed of metal and mirror
- Easy as hanging a picture
$199.99 -
Narita Espresso Swivel Top Media Stand
Perfect for any room in the house, this contemporary media stand has a swiveling top. With the ability to easily re-position your TV, any seat can be the best seat in the house. One medium shelf below the TV fits your media player and provides a hole through the back for easy cord management. Below the shelf are two doors that open to reveal an adjustable shelf perfect for storing all of your favorite media. The espresso finish completes the unit with an elegant contemporary styling.- Overall unit: 28" W x 15.75" D x 31" H
- Each door measures 13" W x 1" D x 17.75" H
- Rich Espresso Finish
- Holds up to a 30" flat panel TV
- Spacious opening for media equipment
- Openings in back for easy cord management
- Rubberwood, veneer and MDF
- Assembly required
$279.99 -
Fairmont Espresso Media Tower
This espresso media tower brings an elegant solution to the common problem of storing TV receivers, videos, game consoles and accessories. The character of the Ash wood grain is brought to life with a bold stain and complemented with oil rubbed metal hardware. The cabinet is divided in half by the center shelf with1 adjustable shelf above and below. 4 cord management openings provide an added convenience for organization. The bottom drawer is perfect for game controllers, magazines or an extra blanket. Add two units to your media room for a symmetrical balance on either side of your entertainment center.- 23.75" W x 15" D x 52.25" H
- Fixed Shelves: 19" W x 13" D x 18" W
- One adjustable shelve between each fixed shelf
- Drawer: 17" W x 11" D x 5.5" H
- Rich Espresso Finish
- Tempered Glass Door
- Constructed with Chinese Oak Hardwood and Ash Veneer
- Assembly Required
$299.99 -
Decorative Bakers Rack with Wine Storage
An excellent addition to any kitchen, this coffee brown baker's rack not only puts things in a good location, but it also provides storage for those hard to place items. The rectangular metal frame provides a rigid construction while incorporating lovely decorative scrolls on either side. There is a bottom shelf that sits just 6" off the floor measuring 15" deep, 34" wide, and 16" tall as well as a tabletop working surface that is 15" tall, 15.5" deep and 34" wide. Both of which are finished with a rich mahogany stain. A wonderful 6 bottle wine rack directly beneath it also enhances the main working surface. The upper two 8" deep shelves have inlaid clear glass to provide a beautiful display area. The top shelf also hosts a rack for wine glasses on the bottom side.
Features:- 34.25" W x 17" D x 67.75" Tall
- Coffee brown finish
- 6 bottle wine rack
- Mahogany veneer counter
- Metal and tempered glass construction
- Assembly required
$249.99 -
Adriano Wall-Mount Wine Storage
Ideal for your kitchen, dining or even living room; this artistic wine rack is both beautiful and functional. Complementary earth tones will perfectly accent your home while six of your favorite wines are displayed in a beautiful manner. Whether you are a frequent entertainer or just a wine enthusiast, this wonderful piece is sure to be a welcome addition to your home.- 8.75" W x 7" D x 33.25" H
- Wall mounted wine rack
- Multi-colored in earth tones
- Holds up to six of your favorite wines
- Constructed of metal
- The handcrafted touch of artisan skill creates variations in color and design.
- Color discrepancies may occur between this product and your computer screen
- Easy as hanging a picture
$69.99 -
Crafted for the modern home, this beautiful espresso desk provides convenient workspace for your laptop and bills. The rich espresso finish gives a modern update to a traditional design creating a versatile piece of furniture. The top hutch provides adequate storage and boasts two moderate sized drawers. The front of the desk has three drawers that span the full width of the unit.
- Overall unit - 36" W x 19" D x 38.25" tall
- Five spacious drawers
- Desktop cord management
- Contemporary espresso finish
- Matching solid wood hardware.
- MDF; Solid wood; Veneer; assembly required
$279.99 -
Espresso 2-Drawer Writing Desk
Designed with transitional appeal, this writing desk is sure to create a wonderful accent among your decor. Two deep drawers are accessible from the front of the desk with dual color matched knobs. The elegant espresso finish creates a blend of styles that makes this piece blend with traditional or contemporary decor. Add this beautiful writing desk to your home for convenience and class.- 42.5" W x 23" D x 30" H
- Two drawers measuring 15" W x 15" D x 2" H
- Transitional Styling
- Espresso Finish
- Assembly Required
$199.99 -
Photo Display Wall-Mount Jewelry Armoire
Organize all of your jewelry into this classically designed wall-mount armoire. Inside the rectangular case are hooks, racks and more to make all your baubles easy to manage and arrange. Each unit comes with three different size picture mats to display pictures of you and your loved ones in the front of the case. Perfect for the closet, bedroom, or bathroom to add jewelry storage with ease.- 12" W x 3.5" D x 22" H
- Can hold up to 14 pairs of earrings on 2 earring racks
- 6 hooks inside to store necklaces and bracelets
- 6 cubby holes for ring and earring storage
- Interior dimensions: 10.5" W x 2.5" D x 17.75" H
- Black velvet lines interior of case
- One mat with five 4.5"W x 2.5"H openings to hold horizontal 5"W x 3"H photos
- One mat with four 5.5"W x 3.5"H openings to hold horizontal 6"W x 4"H photos
- One mat with three 6.5"W x 4.5"H openings to hold horizontal 7"W x 5"H photos
- Hardwood, wood veneer, and MDF
- Easy as hanging a picture
Select a color from the drop-down box.$99.99 -
This media center utilizes one large open shelf in the middle above one large drawer to fit electronics and media equipment. There are window paned cabinet doors on either side housing one adjustable shelf each. The top of this piece measures 52" wide by 16" deep making it capable of holding a wide range of TV's and equipment. So much space brings form and function into your home. The doors of the cabinets have glass windows and magnetic latches.
- 52" W x 16" D x 24" Tall
- Center storage is 19" wide
- Side cabinets are 13.5" wide
- Adjustable shelf in each cabinet
- Tempered glass doors
- 1 drawer for hidden storage 18" W x 14" D x 5.5" Tall
- Assembly required
$349.99 -
Faux Leather Storage Bench - Espresso/Black
Ideal for the bedroom, dining room, kitchen, or entry, this stylish storage bench is a classic masterpiece. With an open back, the espresso-stained frame creates an eloquent presence with its solid wood construction, straight lines, and tall arm rests. Measuring 18" high, the seat is enclosed on each side with the sleigh style arms with decorative "X" braces. Lift the seat up to reveal two convenient storage bins for quilts, umbrellas, or crafts that measure 16" long, 18" wide, and 4" deep each. Sure to increase elegance, this bench seat is a must have for any home.
Features:- 42" W x 18" D x 26" Tall
- Rich Espresso Finish
- Black Faux Leather Seat
- Seat lifts for added storage
- Assembly Required
$219.99 -
3-Drawer Black Country Bench
Keep it simple and clutter free with this adorable country bench. This painted black bench provides not only a place to sit and relax, but also three convenient drawers that measure 10.5" long, 7.5" wide, and 3.5" deep allowing you to stash away anything from hats and gloves, to your dog's leash and toys. The simplistic design of this bench is achieved from the traditional vertical slat back and sides. This three-drawer bench adds storage and creates the perfect entryway accent with its style and functionality.
Features:- 40" x 19.5" x 36" Tall
- Black Finish
- Three drawers for storage
- Hardwood, MDF & Veneer Construction
- Assembly Required
$199.99 -
Tristan Hall Tree Entry Bench
Solve your entry way clutter problems with this Celtic hall tree bench. This bench creates a unique look in your home with its gorgeous elongated design. Paired with substantial functionality, this piece allows you to hang coats, store your dog's leash and even have a seat when you come home from a busy day at work. Add function and style to your beloved home with this quaint entry bench.- 24.5" W x 18.25" D x 72" H
- Rattan Basket: 20" W x 17" D x 6" H
- Seat Height: 19" H
- Dark Brown Textured Finish
- Beige Microfiber Tufted Cushion
- 4 Double hooks
- Metal Construction
- Constructed of metal, CA foam, rattan, MDF
- Assembly required
$179.99 -
Wall Mount Craft Storage Rack with Baskets - Black
This wall mount craft storage rack with baskets is the best way to get your workspace clean and your crafting supplies organized. With three espresso rattan woven baskets to put your tools out of sight and a spacious shelf to organize all your boxes and bows, you'll never have a messy workspace again. This unit is the perfect solution for any home.- 35.5" W x 8.5" D x 27.5" H
- Top shelf measures 34.5" W x 7.5" D x 2.25" H
- Comes with 3 rattan baskets
- Each basket measures 10 x 7 x 3.75"H
- Fitted with 5 hooks and 2 racks
- Black and espresso finish
- Metal tubing, and rattan basket construction
- Assembly required
$119.99 -
Modesto Cocktail Table
Rich and curvaceous, this espresso cocktail table is a wonderful accent to any transitional styling. The black metal frame has legs that arch inward to create a distinct look that adds a sense of flow to your room. Gracing the top of the frame is a beautifully stained espresso top that gushes with style. Add this cocktail table to your home today for an instant upgrade.
Features:- 42" W x 24" D x 18" Tall
- Rich Espresso Finish
- Elaborate arched legs
- Durable metal frame
- Assembly required
$179.99 -
Mirage Mirrored Cocktail
Perfect for any room, this glamorous mirrored console table will perfectly complement your home. With its mirrored finish, it adapts to any surroundings without overpowering yet catches your eye with its unique presence. This elegant table can be used to achieve a formal atmosphere or a casual contemporary home setting.- 42" W x 23.75" D x 20.25" H
- Max weight capacity 100 lbs
- Constructed of mirror and MDF
- Assembly required
$249.99 -
Vogue Cocktail Table
The contemporary elegance of this cocktail table will bring a pleasantly distinct style to your home. The metal frame is finished in black with the edges rubbed away to show the copper finish below. The base of this sturdy table consists of a curved "X" which supports the solid top frame with inlaid glass. This elegant table can be used to achieve a formal atmosphere or a casual contemporary home setting.
Features:- 42" W x 24" D x 20" Tall
- Painted black finish w/ copper distressing
- Durable metal frame construction
- Tempered glass top
- Assembly required
$199.99 -
Panorama Cocktail Table
Complete your living room with this stunning cocktail table. With solid wood and glass construction, this contemporary walnut finished table would look lovely next to any sofa or chair. The table displays a modern glass see through top to display your shell or picture collections within for all to see, and features an extra storage shelf beneath the table top. This piece is sure to be a welcome addition to any home.
Features:- 42" W x 22" D x 20" H
- 2 drawers measuring 17.25" x 16.25" D x 2.25" H
- Each drawer has 4 equal removable compartments
- Bottom shelf measures 41.75" W x 16.5" D x 9.5" H
- Hardwood, wood veneer, MDF, and tempered glass construction
- Assembly required
$249.99 - $279.99


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We found
2 lodge parks
within 20 miles Wadebridge
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