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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

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{H_{0}:\;Population\;variance\;of\;each\;treatment\;are\;equal}} \\ \\ \mathbf{\color{Green}{H_{a}:\;H_{0}\;is\;false}} \\ \\ \mathbf{\color{Green}{The\;submitted\;data\;is\;below}} }$$

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

$$1$$
$$1$$
$$3$$

$$2$$
$$3$$
$$6$$

$$3$$
$$4$$
$$7$$

$$4$$
$$4$$
$$1$$

$$5$$
$$3$$
$$2$$

$$-$$
$$7$$
$$-$$

$$-$$
$$4$$
$$-$$
$$T_{i}$$
$$15$$
$$26$$
$$19$$
$$n_{i}$$
$$5$$
$$7$$
$$5$$
$$\frac{T_{i}}{n_{i}}= \bar{Y_{i}}$$
$$3.0$$
$$3.714286$$
$$3.8$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Where\;T_{i},\;n_{i},\;}} \mathbf{\color{Green}{\bar{Y_{i}}\;are\;total\;sum,\;size,\;mean\;of\;i^{th}\;treatment\;.}} \\ \\ \mathbf{\color{Green}{Now\;do\;this\;for\;every\;value\;}} \mathbf{\color{Red}{X_{i,j}=\mid Y_{i,j} - \bar{Y_{i}}\mid}} \\ \\ \;\mathbf{\color{Green}{Where\;Y_{i,j}\;is\;j^{th}\;case\;from\;i^{th}\;treatment}} \\ \\ \mathbf{\color{Green}{Using\;X_{i,j}\;make\;below\;table,All\;further\;calculations\;are\;based\;on\;below\;table}} }$$

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

$$2.0$$
$$2.714286$$
$$0.8$$

$$1.0$$
$$0.714286$$
$$2.2$$

$$0.0$$
$$0.285714$$
$$3.2$$

$$1.0$$
$$0.285714$$
$$2.8$$

$$2.0$$
$$0.714286$$
$$1.8$$

$$-$$
$$3.285714$$
$$-$$

$$-$$
$$0.285714$$
$$-$$
$$\sum_{}^{}X_{i}$$
$$6.0$$
$$8.285714$$
$$10.8$$
$$n_{i}$$
$$5$$
$$7$$
$$5$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Now\;we\;have\;to\;find\;Sum\;of\;Squares\;between\;treatments}} \\ \\ \mathbf{\color{Green}{Overall\;average\;=\;\bar{x}\;=}} \frac{Total\;sum\;of\;each\;group}{Total\;size\;of\;each\;group} \\ \\ \Rightarrow \frac{6.0+8.285714+10.8}{5+7+5} = \frac{25.085714}{17.0} \\ \\ \Rightarrow \bar{x} = 1.47563 \\ \\ }$$
$$No$$
$$\sum_{}^{}X_{i}$$
$$n_{i}$$
$$\frac{\sum_{}^{}X_{i}}{n_{i}}= \bar{x_{i}}$$
$$\bar{x}$$
$$\bar{x_{i}} - \bar{x}$$
$$(\bar{x_{i}} - \bar{x})^2$$
$$n_{i}*((\bar{x_{i}} - \bar{x})^2)$$
$$1$$
$$6.0$$
$$5$$
$$1.2$$
$$1.47563$$
$$-0.27563$$
$$0.075972$$
$$0.37986$$
$$2$$
$$8.285714$$
$$7$$
$$1.183673$$
$$1.47563$$
$$-0.291957$$
$$0.085239$$
$$0.596673$$
$$3$$
$$10.8$$
$$5$$
$$2.16$$
$$1.47563$$
$$0.68437$$
$$0.468362$$
$$2.34181$$






$$Total$$
$$3.318343$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{SSG}} = \mathbf{\color{Green}{\sum_{i=1}^{k}n_{i}*((\bar{x_{i}} - \bar{x})^2)}} = \mathbf{\color{Red}{3.318343}} \\ \\ \mathbf{\color{Green}{Now\;we\;have\;to\;find\;Sum\;of\;Squares\;of\;Error}} \\ \\ \mathbf{\color{Green}{\bar{x_{i}}\;is\;mean\;of\;i^{th}\;treatment}} }$$
$$Treatment\;no$$
$$x$$
$$\bar{x_{i}}$$
$$x- \bar{x_{i}}$$
$$(x- \bar{x_{i}})^{2}$$
$$1$$
$$2.0$$
$$1.2$$
$$0.8$$
$$0.64$$
$$1$$
$$1.0$$
$$1.2$$
$$-0.2$$
$$0.04$$
$$1$$
$$0.0$$
$$1.2$$
$$-1.2$$
$$1.44$$
$$1$$
$$1.0$$
$$1.2$$
$$-0.2$$
$$0.04$$
$$1$$
$$2.0$$
$$1.2$$
$$0.8$$
$$0.64$$
$$2$$
$$2.714286$$
$$1.183673$$
$$1.530613$$
$$2.342776$$
$$2$$
$$0.714286$$
$$1.183673$$
$$-0.469387$$
$$0.220324$$
$$2$$
$$0.285714$$
$$1.183673$$
$$-0.897959$$
$$0.80633$$
$$2$$
$$0.285714$$
$$1.183673$$
$$-0.897959$$
$$0.80633$$
$$2$$
$$0.714286$$
$$1.183673$$
$$-0.469387$$
$$0.220324$$
$$2$$
$$3.285714$$
$$1.183673$$
$$2.102041$$
$$4.418576$$
$$2$$
$$0.285714$$
$$1.183673$$
$$-0.897959$$
$$0.80633$$
$$3$$
$$0.8$$
$$2.16$$
$$-1.36$$
$$1.8496$$
$$3$$
$$2.2$$
$$2.16$$
$$0.04$$
$$0.0016$$
$$3$$
$$3.2$$
$$2.16$$
$$1.04$$
$$1.0816$$
$$3$$
$$2.8$$
$$2.16$$
$$0.64$$
$$0.4096$$
$$3$$
$$1.8$$
$$2.16$$
$$-0.36$$
$$0.1296$$
$$Total$$



$$15.89299$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{from\;above\;table\;we\;get\;SSE\;=\;Total\;=\;}} \mathbf{\color{Red}{15.89299}} \\ \\ SS(total) = SSG+SSE \\ \\ \Rightarrow 3.318343\;+\;15.892990\;=\; 19.211333 \\ \\ \;\mathbf{\color{Red}{Test\;table}} }$$
$$Source$$
$$Degrees\;of\;Freedom$$
$$Sum\;of\;Squares$$
$$Mean\;Square$$
$$F$$
$$p$$
$$Groups$$
$$k-1$$
$$SSG$$
$$MSG=\frac{SSG}{k-1}$$
$$F$$
$$p$$
$$Error$$
$$n-k$$
$$SSE$$
$$MSE=\frac{SSE}{n-k}$$


$$Total$$
$$n-1$$
$$SS(total)$$
$$Sample Variance=\frac{SS(total)}{n-1}$$


$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Where\;k,n\;are\;number\;of\;groups\;and\;overall\;sample\;size}} \\ \\ \mathbf{\color{Green}{k\;=\;3}} \\ \\ \mathbf{\color{Green}{n\;=\;17}} }$$
$$Source$$
$$Degrees\;of\;Freedom$$
$$Sum\;of\;Squares$$
$$Mean\;Square$$
$$F$$
$$p$$
$$Groups$$
$$2$$
$$3.318343$$
$$1.659172$$
$$1.46155$$
$$0.265178$$
$$Error$$
$$14$$
$$15.89299$$
$$1.135214$$


$$Total$$
$$16$$
$$19.211333$$
$$1.200708$$


$$\displaylines{}$$
$$\displaylines{}$$