figure - descriptive statistics for wine attributes separated by wine quality the summary table depicted in figure - shows us descriptive statistics for various wine attributes subset by wine quality ratings interestinglymean alcohol levels seem to increase based on the rating of the wine quality we also see that ph levels are almost consistent across the wine samples of varying quality is there any way to statistically prove thiswe will see that in the following section inferential statistics the general notion of inferential statistics is to draw inferences and propositions of population using data sample the idea is to use statistical methods and models to draw statistical inferences from given hypotheses each hypothesis consists of null hypothesis and an alternative hypothesis based on statistical test resultsif the result is statistically significant based on pre-set significance levels ( if obtained -value is less than significance level)we reject the null hypothesis in favor of the alternative hypothesis otherwiseif the results is not statistically significantwe conclude that our null hypothesis was correct coming back to our problem from the previous sectiongiven multiple data groups or subsets of wine samples based on wine quality ratingis there any way to prove that mean alcohol levels or ph levels vary significantly among the data groupsa great statistical model to prove or disprove the difference in mean among subsets of data is to use the one-way anova test anova stands for "analysis of variance,which is nifty statistical model and can be used to analyze statistically significant differences among means or averages of various groups this is basically achieved using statistical test that helps us determine whether or not the means of several groups are equal usually the null hypothesis is represented as mn where is the number of data groups or subsets and it indicates that the group means for the various groups are not very different from each other based on statistical significance levels the alternative hypotheseshatells us that there exists at least two group means that are statistically significantly different from each other usually the -statistic and the associated -value from it is used to determine the statistical significance typically -value less than is taken to be statistically significant result where we reject the null hypothesis in favor of the original we recommend reading up standard book on inferential statistics to gain more in-depth knowledge regarding these concepts