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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

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$$ \displaylines{---} $$
$$ \displaylines{ \mathbf{\color{Green}{H_{0}:\;All\;samples\;has\;been\;drawn\;from\;the\;same\;population\;}} \\ \\ \mathbf{\color{Green}{H_{a}:\;H_{0}\;is\;false}} \\ \\ \mathbf{\color{Green}{The\;submitted\;data\;is\;below}} } $$
$$ Treatment\;1 $$
$$ Treatment\;2 $$
$$ Treatment\;3 $$
$$ 1 $$
$$ 1 $$
$$ 3 $$
$$ 2 $$
$$ 3 $$
$$ 6 $$
$$ 3 $$
$$ 4 $$
$$ 7 $$
$$ 4 $$
$$ 4 $$
$$ 1 $$
$$ 5 $$
$$ 3 $$
$$ 2 $$
$$ - $$
$$ 7 $$
$$ - $$
$$ - $$
$$ 4 $$
$$ - $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Now\;we\;have\;to\;create\;rank\;of\;each\;value}} \\ \\ \mathbf{\color{Green}{If\;2\;or\;more\;values\;are\;equal.\;Take\;average\;and\;give\;equal\;rank}} \\ \\ } $$
$$ Values $$
$$ Treatment $$
$$ rank $$
$$ 1 $$
$$ Treatment\;1 $$
$$ 2.0 $$
$$ 2 $$
$$ Treatment\;1 $$
$$ 4.5 $$
$$ 3 $$
$$ Treatment\;1 $$
$$ 7.5 $$
$$ 4 $$
$$ Treatment\;1 $$
$$ 11.5 $$
$$ 5 $$
$$ Treatment\;1 $$
$$ 14.0 $$
$$ 1 $$
$$ Treatment\;2 $$
$$ 2.0 $$
$$ 3 $$
$$ Treatment\;2 $$
$$ 7.5 $$
$$ 4 $$
$$ Treatment\;2 $$
$$ 11.5 $$
$$ 4 $$
$$ Treatment\;2 $$
$$ 11.5 $$
$$ 3 $$
$$ Treatment\;2 $$
$$ 7.5 $$
$$ 7 $$
$$ Treatment\;2 $$
$$ 16.5 $$
$$ 4 $$
$$ Treatment\;2 $$
$$ 11.5 $$
$$ 3 $$
$$ Treatment\;3 $$
$$ 7.5 $$
$$ 6 $$
$$ Treatment\;3 $$
$$ 15.0 $$
$$ 7 $$
$$ Treatment\;3 $$
$$ 16.5 $$
$$ 1 $$
$$ Treatment\;3 $$
$$ 2.0 $$
$$ 2 $$
$$ Treatment\;3 $$
$$ 4.5 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Now\;replace\;original\;value\;with\;rank}} \\ \\ } $$
$$ $$
$$ Treatment\;1 $$
$$ Treatment\;2 $$
$$ Treatment\;3 $$
$$ $$
$$ 2.0 $$
$$ 2.0 $$
$$ 7.5 $$
$$ $$
$$ 4.5 $$
$$ 7.5 $$
$$ 15.0 $$
$$ $$
$$ 7.5 $$
$$ 11.5 $$
$$ 16.5 $$
$$ $$
$$ 11.5 $$
$$ 11.5 $$
$$ 2.0 $$
$$ $$
$$ 14.0 $$
$$ 7.5 $$
$$ 4.5 $$
$$ $$
$$ - $$
$$ 16.5 $$
$$ - $$
$$ $$
$$ - $$
$$ 11.5 $$
$$ - $$
$$ T_{i} $$
$$ 39.5 $$
$$ 68.0 $$
$$ 45.5 $$
$$ n_{i}\; $$
$$ 5 $$
$$ 7 $$
$$ 5 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Where,\;T_{i}\;is\;sum\;of\;all\;ranks\;in\;a\;treatment}} \\ \\ \mathbf{\color{Green}{n_{i}\;is\;total\;number\;of\;values\;in\;a\;treatment}} \\ \\ \mathbf{\color{Green}{First\;we\;have\;to\;find\;}} \sum_{i=1}^{n}\frac{T_{i}^{2}}{n_{i}} \\ \\ \Rightarrow \frac{39.5^{2}}{5}+\frac{68.0^{2}}{7}+\frac{45.5^{2}}{5} \\ \\ \Rightarrow 312.05+660.571429+414.05 \\ \\ \Rightarrow 1386.671429 \\ \\ \mathbf{\color{Green}{N\;=\;Total\;number\;of\;values}} \\ \\ \Rightarrow N= 5+7+5 \\ \\ \Rightarrow 17 \\ \\ \mathbf{\color{Green}{Now,\;we\;have\;to\;find\;H\;=\;}} \frac{12}{N(N+1)} *(\sum_{i=1}^{n}\frac{T_{i}^{2}}{n_{i}}) -3(N+1) \\ \\ \Rightarrow \frac{12}{17(17+1)} *(1386.671429) -3*(17+1) \\ \\ \Rightarrow 54.379272-54.000000 \\ \\ \Rightarrow \mathbf{\color{Red}{0.379272}} \\ \\ df=k-1 \\ \\ \Rightarrow 3-1 \\ \\ \Rightarrow 2 \\ \\ p\;value\;for\;\chi^{2}\;=\;0.379272\;and\;df\;=\;2\;is\; p= 0.82726 \\ \\ p-value\;is\;more\;than\;\alpha \\ \\ So\;There\;is\;not\;enough\;evidence\;to\;reject\;H_{0}\; } $$