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Levene's Test Calculator


Levene's test is a type of test used to check the homogeneity of variance. There are many types of tests for homogeneity of variance. Levene's test is the most popular test for homogeneity of variance. A very detailed step-by-step solution is provided in this calculator.

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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$$ \displaylines{---} $$
$$ \displaylines{ \mathbf{\color{Green}{H_{0}:\;Population\;variance\;of\;each\;treatment\;are\;equal}} \\ \\ \mathbf{\color{Green}{H_{a}:\;H_{0}\;is\;false}} \\ \\ \mathbf{\color{Green}{The\;submitted\;data\;is\;below}} } $$
$$ $$
$$ Treatment\;1 $$
$$ Treatment\;2 $$
$$ Treatment\;3 $$
$$ $$
$$ 1 $$
$$ 1 $$
$$ 3 $$
$$ $$
$$ 2 $$
$$ 3 $$
$$ 6 $$
$$ $$
$$ 3 $$
$$ 4 $$
$$ 7 $$
$$ $$
$$ 4 $$
$$ 4 $$
$$ 1 $$
$$ $$
$$ 5 $$
$$ 3 $$
$$ 2 $$
$$ $$
$$ - $$
$$ 7 $$
$$ - $$
$$ $$
$$ - $$
$$ 4 $$
$$ - $$
$$ T_{i} $$
$$ 15 $$
$$ 26 $$
$$ 19 $$
$$ n_{i} $$
$$ 5 $$
$$ 7 $$
$$ 5 $$
$$ \frac{T_{i}}{n_{i}}= \bar{Y_{i}} $$
$$ 3.0 $$
$$ 3.714286 $$
$$ 3.8 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Where\;T_{i},\;n_{i},\;}} \mathbf{\color{Green}{\bar{Y_{i}}\;are\;total\;sum,\;size,\;mean\;of\;i^{th}\;treatment\;.}} \\ \\ \mathbf{\color{Green}{Now\;do\;this\;for\;every\;value\;}} \mathbf{\color{Red}{X_{i,j}=\mid Y_{i,j} - \bar{Y_{i}}\mid}} \\ \\ \;\mathbf{\color{Green}{Where\;Y_{i,j}\;is\;j^{th}\;case\;from\;i^{th}\;treatment}} \\ \\ \mathbf{\color{Green}{Using\;X_{i,j}\;make\;below\;table,All\;further\;calculations\;are\;based\;on\;below\;table}} } $$
$$ $$
$$ Treatment\;1 $$
$$ Treatment\;2 $$
$$ Treatment\;3 $$
$$ $$
$$ 2.0 $$
$$ 2.714286 $$
$$ 0.8 $$
$$ $$
$$ 1.0 $$
$$ 0.714286 $$
$$ 2.2 $$
$$ $$
$$ 0.0 $$
$$ 0.285714 $$
$$ 3.2 $$
$$ $$
$$ 1.0 $$
$$ 0.285714 $$
$$ 2.8 $$
$$ $$
$$ 2.0 $$
$$ 0.714286 $$
$$ 1.8 $$
$$ $$
$$ - $$
$$ 3.285714 $$
$$ - $$
$$ $$
$$ - $$
$$ 0.285714 $$
$$ - $$
$$ \sum_{}^{}X_{i} $$
$$ 6.0 $$
$$ 8.285714 $$
$$ 10.8 $$
$$ n_{i} $$
$$ 5 $$
$$ 7 $$
$$ 5 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Now\;we\;have\;to\;find\;Sum\;of\;Squares\;between\;treatments}} \\ \\ \mathbf{\color{Green}{Overall\;average\;=\;\bar{x}\;=}} \frac{Total\;sum\;of\;each\;group}{Total\;size\;of\;each\;group} \\ \\ \Rightarrow \frac{6.0+8.285714+10.8}{5+7+5} = \frac{25.085714}{17.0} \\ \\ \Rightarrow \bar{x} = 1.47563 \\ \\ } $$
$$ No $$
$$ \sum_{}^{}X_{i} $$
$$ n_{i} $$
$$ \frac{\sum_{}^{}X_{i}}{n_{i}}= \bar{x_{i}} $$
$$ \bar{x} $$
$$ \bar{x_{i}} - \bar{x} $$
$$ (\bar{x_{i}} - \bar{x})^2 $$
$$ n_{i}*((\bar{x_{i}} - \bar{x})^2) $$
$$ 1 $$
$$ 6.0 $$
$$ 5 $$
$$ 1.2 $$
$$ 1.47563 $$
$$ -0.27563 $$
$$ 0.075972 $$
$$ 0.37986 $$
$$ 2 $$
$$ 8.285714 $$
$$ 7 $$
$$ 1.183673 $$
$$ 1.47563 $$
$$ -0.291957 $$
$$ 0.085239 $$
$$ 0.596673 $$
$$ 3 $$
$$ 10.8 $$
$$ 5 $$
$$ 2.16 $$
$$ 1.47563 $$
$$ 0.68437 $$
$$ 0.468362 $$
$$ 2.34181 $$
$$ $$
$$ $$
$$ $$
$$ $$
$$ $$
$$ $$
$$ Total $$
$$ 3.318343 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{SSG}} = \mathbf{\color{Green}{\sum_{i=1}^{k}n_{i}*((\bar{x_{i}} - \bar{x})^2)}} = \mathbf{\color{Red}{3.318343}} \\ \\ \mathbf{\color{Green}{Now\;we\;have\;to\;find\;Sum\;of\;Squares\;of\;Error}} \\ \\ \mathbf{\color{Green}{\bar{x_{i}}\;is\;mean\;of\;i^{th}\;treatment}} } $$
$$ Treatment\;no $$
$$ x $$
$$ \bar{x_{i}} $$
$$ x- \bar{x_{i}} $$
$$ (x- \bar{x_{i}})^{2} $$
$$ 1 $$
$$ 2.0 $$
$$ 1.2 $$
$$ 0.8 $$
$$ 0.64 $$
$$ 1 $$
$$ 1.0 $$
$$ 1.2 $$
$$ -0.2 $$
$$ 0.04 $$
$$ 1 $$
$$ 0.0 $$
$$ 1.2 $$
$$ -1.2 $$
$$ 1.44 $$
$$ 1 $$
$$ 1.0 $$
$$ 1.2 $$
$$ -0.2 $$
$$ 0.04 $$
$$ 1 $$
$$ 2.0 $$
$$ 1.2 $$
$$ 0.8 $$
$$ 0.64 $$
$$ 2 $$
$$ 2.714286 $$
$$ 1.183673 $$
$$ 1.530613 $$
$$ 2.342776 $$
$$ 2 $$
$$ 0.714286 $$
$$ 1.183673 $$
$$ -0.469387 $$
$$ 0.220324 $$
$$ 2 $$
$$ 0.285714 $$
$$ 1.183673 $$
$$ -0.897959 $$
$$ 0.80633 $$
$$ 2 $$
$$ 0.285714 $$
$$ 1.183673 $$
$$ -0.897959 $$
$$ 0.80633 $$
$$ 2 $$
$$ 0.714286 $$
$$ 1.183673 $$
$$ -0.469387 $$
$$ 0.220324 $$
$$ 2 $$
$$ 3.285714 $$
$$ 1.183673 $$
$$ 2.102041 $$
$$ 4.418576 $$
$$ 2 $$
$$ 0.285714 $$
$$ 1.183673 $$
$$ -0.897959 $$
$$ 0.80633 $$
$$ 3 $$
$$ 0.8 $$
$$ 2.16 $$
$$ -1.36 $$
$$ 1.8496 $$
$$ 3 $$
$$ 2.2 $$
$$ 2.16 $$
$$ 0.04 $$
$$ 0.0016 $$
$$ 3 $$
$$ 3.2 $$
$$ 2.16 $$
$$ 1.04 $$
$$ 1.0816 $$
$$ 3 $$
$$ 2.8 $$
$$ 2.16 $$
$$ 0.64 $$
$$ 0.4096 $$
$$ 3 $$
$$ 1.8 $$
$$ 2.16 $$
$$ -0.36 $$
$$ 0.1296 $$
$$ Total $$
$$ $$
$$ $$
$$ $$
$$ 15.89299 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{from\;above\;table\;we\;get\;SSE\;=\;Total\;=\;}} \mathbf{\color{Red}{15.89299}} \\ \\ SS(total) = SSG+SSE \\ \\ \Rightarrow 3.318343\;+\;15.892990\;=\; 19.211333 \\ \\ \;\mathbf{\color{Red}{Test\;table}} } $$
$$ Source $$
$$ Degrees\;of\;Freedom $$
$$ Sum\;of\;Squares $$
$$ Mean\;Square $$
$$ F $$
$$ p $$
$$ Groups $$
$$ k-1 $$
$$ SSG $$
$$ MSG=\frac{SSG}{k-1} $$
$$ F $$
$$ p $$
$$ Error $$
$$ n-k $$
$$ SSE $$
$$ MSE=\frac{SSE}{n-k} $$
$$ $$
$$ $$
$$ Total $$
$$ n-1 $$
$$ SS(total) $$
$$ Sample Variance=\frac{SS(total)}{n-1} $$
$$ $$
$$ $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Where\;k,n\;are\;number\;of\;groups\;and\;overall\;sample\;size}} \\ \\ \mathbf{\color{Green}{k\;=\;3}} \\ \\ \mathbf{\color{Green}{n\;=\;17}} } $$
$$ Source $$
$$ Degrees\;of\;Freedom $$
$$ Sum\;of\;Squares $$
$$ Mean\;Square $$
$$ F $$
$$ p $$
$$ Groups $$
$$ 2 $$
$$ 3.318343 $$
$$ 1.659172 $$
$$ 1.46155 $$
$$ 0.265178 $$
$$ Error $$
$$ 14 $$
$$ 15.89299 $$
$$ 1.135214 $$
$$ $$
$$ $$
$$ Total $$
$$ 16 $$
$$ 19.211333 $$
$$ 1.200708 $$
$$ $$
$$ $$
$$ \displaylines{} $$
$$ \displaylines{} $$