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# Repeated measures anova calculator

ANOVA is analysis of variance. There are many types of ANOVA test. This calculator is one way Repeated measures ANOVA calculator. It is also called a within subjects ANOVA calculator. Every step is provided as if it is solved by hand. You can learn how to calculate a Repeated measures ANOVA by submitting any sample values. F statistic and the p-value is calculated and shown in Table

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

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{H_{0}:\;there\;is\;no\;difference\;in\;means}} \\ \\ \mathbf{\color{Green}{H_{a}:\;At\;least\;2\;means\;differ}} \\ \\ }$$

$$Treatment\;1$$
$$Treatment\;2$$
$$Treatment\;3$$
$$Subject\;Total$$
$$Subject\;1$$
$$1$$
$$1$$
$$3$$
$$5$$
$$Subject\;2$$
$$2$$
$$3$$
$$6$$
$$11$$
$$Subject\;3$$
$$3$$
$$4$$
$$7$$
$$14$$
$$Subject\;4$$
$$4$$
$$4$$
$$1$$
$$9$$
$$Subject\;5$$
$$5$$
$$3$$
$$2$$
$$10$$
$$Treatment\;Total$$
$$15$$
$$15$$
$$19$$
$$49$$
$$\displaylines{}$$
$$\displaylines{Total\;number\;of\;values\;=\;N\;= 15 \\ \\ \mathbf{\color{Green}{From\;the\;table\;we\;get\;Total\;(Bottom\;right)}} \\ \\ Total= 49 \\ \\ \mathbf{\color{Green}{First\;we\;have\;to\;find\;total\;mean}} \\ \\ \bar{x} = \frac{Total}{N} \\ \\ \Rightarrow \frac{49}{15} \\ \\ \Rightarrow 3.266667 \\ \\ \mathbf{\color{Green}{For\;finding\;SS_{subject}\;make\;below\;table.}} }$$
$$\displaylines{\\ \\ }$$
$$Subject\;Name$$
$$Total$$
$$Mean(\bar{x_{s}})$$
$$\bar{x}$$
$$\bar{x_{s}} - \bar{x}$$
$$(\bar{x_{s}} - \bar{x})^{2}$$
$$Subject\;1$$
$$5$$
$$1.666667$$
$$3.266667$$
$$-1.6$$
$$2.56$$
$$Subject\;2$$
$$11$$
$$3.666667$$
$$3.266667$$
$$0.4$$
$$0.16$$
$$Subject\;3$$
$$14$$
$$4.666667$$
$$3.266667$$
$$1.4$$
$$1.96$$
$$Subject\;4$$
$$9$$
$$3.0$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$Subject\;5$$
$$10$$
$$3.333333$$
$$3.266667$$
$$0.066666$$
$$0.004444$$
$$Total$$




$$4.755555$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{From\;table\;}} \sum_{i=0}^{n}(\bar{x_{s}} - \bar{x}) = 4.755555 \\ \\ Total\;number\;of\;treatments\;=\;k\;=\; 3 \\ \\ SS_{Subject} = k* \sum_{i=0}^{n}(\bar{x_{s}} - \bar{x}) \\ \\ \Rightarrow 3*4.755555 \\ \\ \Rightarrow 14.266665 \\ \\ \mathbf{\color{Green}{For\;finding\;SS_{treatment}\;make\;below\;table.}} }$$
$$\displaylines{}$$
$$Treatment\;Name$$
$$Total$$
$$Mean(\bar{x_{t}})$$
$$\bar{x}$$
$$\bar{x_{t}} - \bar{x}$$
$$(\bar{x_{t}} - \bar{x})^{2}$$
$$Treatment\;1$$
$$15$$
$$3.0$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$Treatment\;2$$
$$15$$
$$3.0$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$Treatment\;3$$
$$19$$
$$3.8$$
$$3.266667$$
$$0.533333$$
$$0.284444$$
$$Total$$




$$0.426666$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{From\;table\;}} \sum_{i=0}^{n}(\bar{x_{t}} - \bar{x}) = 0.426666 \\ \\ Total\;number\;of\;subjects\;=\;s\;= 5 \\ \\ SS_{Treatment} = s* \sum_{i=0}^{n}(\bar{x_{s}} - \bar{x}) \\ \\ \Rightarrow 5*0.426666 \\ \\ \Rightarrow 2.13333 \\ \\ }$$
$$\displaylines{ \mathbf{\color{Green}{For\;finding\;SS_{total}\;make\;below\;table.}} }$$
$$x$$
$$\bar{x}$$
$$x - \bar{x}$$
$$(x - \bar{x})^{2}$$
$$1$$
$$3.266667$$
$$-2.266667$$
$$5.137779$$
$$2$$
$$3.266667$$
$$-1.266667$$
$$1.604445$$
$$3$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$4$$
$$3.266667$$
$$0.733333$$
$$0.537777$$
$$5$$
$$3.266667$$
$$1.733333$$
$$3.004443$$
$$1$$
$$3.266667$$
$$-2.266667$$
$$5.137779$$
$$3$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$4$$
$$3.266667$$
$$0.733333$$
$$0.537777$$
$$4$$
$$3.266667$$
$$0.733333$$
$$0.537777$$
$$3$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$3$$
$$3.266667$$
$$-0.266667$$
$$0.071111$$
$$6$$
$$3.266667$$
$$2.733333$$
$$7.471109$$
$$7$$
$$3.266667$$
$$3.733333$$
$$13.937775$$
$$1$$
$$3.266667$$
$$-2.266667$$
$$5.137779$$
$$2$$
$$3.266667$$
$$-1.266667$$
$$1.604445$$
$$Total$$


$$44.933329$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{From\;table\;}} \sum_{i=0}^{n}(x - \bar{x}) = 44.933329 \\ \\ SS_{Total} = \sum_{i=0}^{n}(x - \bar{x}) \\ \\ \Rightarrow 44.933329 }$$
$$\displaylines{ \mathbf{\color{Green}{SS_{within}\;=\;SS_{total}\;-\;SS_{treatment}\;-\;SS_{subject}}} \\ \\ \Rightarrow 44.933329-2.13333-14.266665 \\ \\ \Rightarrow SS_{within} = \mathbf{\color{Red}{28.533334}} \\ \\ \mathbf{\color{Green}{Now\;make\;ANOVA\;table\;like\;below}} }$$
$$Source\;of\;Variation$$
$$Sum\;of\;Squres$$
$$df$$
$$MS$$
$$F$$
$$Between\;Subjects$$
$$SS_{subject}$$
$$s-1$$


$$Between\;treatments$$
$$SS_{treatment}$$
$$k-1$$
$$MS_{treatment}$$
$$F$$
$$Within$$
$$SS_{within}$$
$$(s-1)(k-1)$$
$$MS_{within}$$

$$Total$$
$$SS_{total}$$
$$sk - 1$$


$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Where,\;s\;=\;number\;of\;subjects}} = \mathbf{\color{Red}{5}} \\ \\ df\;is\;Degrees\;of\;Freedom \\ \\ MS\;=\;Mean\;of\;Squares \\ \\ \mathbf{\color{Green}{k\;=\;number\;of\;treatments}} = \mathbf{\color{Red}{3}} \\ \\ MS_{treatment} = \frac{SS_{treatment}}{k-1} = \frac{2.13333}{2} = \mathbf{\color{Red}{1.066665}} \\ \\ MS_{within} = \frac{SS_{within}}{(s-1)(k-1)} = \frac{28.533334}{8} = \mathbf{\color{Red}{3.566667}} \\ \\ F = \frac{MS_{treatment}}{MS_{within}} = \frac{1.066665}{3.566667} = \mathbf{\color{Red}{0.299065}} \\ \\ p\;value\;is\;\;\mathbf{\color{Red}{0.749452}} \\ \\ }$$
$$Source\;of\;Variation$$
$$Sum\;of\;Squres$$
$$df$$
$$MS$$
$$F$$
$$p\;value$$
$$Between\;Subjects$$
$$14.266665$$
$$4$$



$$Between\;treatments$$
$$2.13333$$
$$2$$
$$1.066665$$
$$0.299065$$
$$0.749452$$
$$Within$$
$$28.533334$$
$$8$$
$$3.566667$$


$$Total$$
$$44.933329$$
$$14$$



$$\displaylines{}$$
$$\displaylines{\alpha\;=\;0.05 \\ \\ p\;is\;more\;than\;\alpha\;.\; So,\;Failed\;to\;Reject\;H_{0} \\ \\ }$$