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# Kruskal-Wallis Test Calculator

Kruskal wallis test is a non parametric test. Every step is provided as if it is solved by hand. You can learn how to calculate a Kruskal-Wallis Test by submitting any sample values. H statistic and the p-value is calculated and shown below

INSTRUCTION: Use ',' or new line to separate between values

## You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{H_{0}:\;All\;samples\;has\;been\;drawn\;from\;the\;same\;population\;}} \\ \\ \mathbf{\color{Green}{H_{a}:\;H_{0}\;is\;false}} \\ \\ \mathbf{\color{Green}{The\;submitted\;data\;is\;below}} }$$
$$Treatment\;1$$
$$Treatment\;2$$
$$Treatment\;3$$
$$1$$
$$1$$
$$3$$
$$2$$
$$3$$
$$6$$
$$3$$
$$4$$
$$7$$
$$4$$
$$4$$
$$1$$
$$5$$
$$3$$
$$2$$
$$-$$
$$7$$
$$-$$
$$-$$
$$4$$
$$-$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Now\;we\;have\;to\;create\;rank\;of\;each\;value}} \\ \\ \mathbf{\color{Green}{If\;2\;or\;more\;values\;are\;equal.\;Take\;average\;and\;give\;equal\;rank}} \\ \\ }$$
$$Values$$
$$Treatment$$
$$rank$$
$$1$$
$$Treatment\;1$$
$$2.0$$
$$2$$
$$Treatment\;1$$
$$4.5$$
$$3$$
$$Treatment\;1$$
$$7.5$$
$$4$$
$$Treatment\;1$$
$$11.5$$
$$5$$
$$Treatment\;1$$
$$14.0$$
$$1$$
$$Treatment\;2$$
$$2.0$$
$$3$$
$$Treatment\;2$$
$$7.5$$
$$4$$
$$Treatment\;2$$
$$11.5$$
$$4$$
$$Treatment\;2$$
$$11.5$$
$$3$$
$$Treatment\;2$$
$$7.5$$
$$7$$
$$Treatment\;2$$
$$16.5$$
$$4$$
$$Treatment\;2$$
$$11.5$$
$$3$$
$$Treatment\;3$$
$$7.5$$
$$6$$
$$Treatment\;3$$
$$15.0$$
$$7$$
$$Treatment\;3$$
$$16.5$$
$$1$$
$$Treatment\;3$$
$$2.0$$
$$2$$
$$Treatment\;3$$
$$4.5$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Now\;replace\;original\;value\;with\;rank}} \\ \\ }$$

$$Treatment\;1$$
$$Treatment\;2$$
$$Treatment\;3$$

$$2.0$$
$$2.0$$
$$7.5$$

$$4.5$$
$$7.5$$
$$15.0$$

$$7.5$$
$$11.5$$
$$16.5$$

$$11.5$$
$$11.5$$
$$2.0$$

$$14.0$$
$$7.5$$
$$4.5$$

$$-$$
$$16.5$$
$$-$$

$$-$$
$$11.5$$
$$-$$
$$T_{i}$$
$$39.5$$
$$68.0$$
$$45.5$$
$$n_{i}\;$$
$$5$$
$$7$$
$$5$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Where,\;T_{i}\;is\;sum\;of\;all\;ranks\;in\;a\;treatment}} \\ \\ \mathbf{\color{Green}{n_{i}\;is\;total\;number\;of\;values\;in\;a\;treatment}} \\ \\ \mathbf{\color{Green}{First\;we\;have\;to\;find\;}} \sum_{i=1}^{n}\frac{T_{i}^{2}}{n_{i}} \\ \\ \Rightarrow \frac{39.5^{2}}{5}+\frac{68.0^{2}}{7}+\frac{45.5^{2}}{5} \\ \\ \Rightarrow 312.05+660.571429+414.05 \\ \\ \Rightarrow 1386.671429 \\ \\ \mathbf{\color{Green}{N\;=\;Total\;number\;of\;values}} \\ \\ \Rightarrow N= 5+7+5 \\ \\ \Rightarrow 17 \\ \\ \mathbf{\color{Green}{Now,\;we\;have\;to\;find\;H\;=\;}} \frac{12}{N(N+1)} *(\sum_{i=1}^{n}\frac{T_{i}^{2}}{n_{i}}) -3(N+1) \\ \\ \Rightarrow \frac{12}{17(17+1)} *(1386.671429) -3*(17+1) \\ \\ \Rightarrow 54.379272-54.000000 \\ \\ \Rightarrow \mathbf{\color{Red}{0.379272}} \\ \\ df=k-1 \\ \\ \Rightarrow 3-1 \\ \\ \Rightarrow 2 \\ \\ p\;value\;for\;\chi^{2}\;=\;0.379272\;and\;df\;=\;2\;is\; p= 0.82726 \\ \\ p-value\;is\;more\;than\;\alpha \\ \\ So\;There\;is\;not\;enough\;evidence\;to\;reject\;H_{0}\; }$$
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