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# Mann Whitney U test calculator

Mann-Whitney U test is a type of nonparametric test which use rank for test. Both U and Z are considered as test statistic for the Mann-Whitney U test. Every step is provided like it is solved by hand. You can learn how to calculate a Mann-Whitney U test by submitting any sample values. U 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

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{H_{0}:The\;two\;populations\;are\;equal}} \\ \\ \mathbf{\color{Green}{H_{a}:H_{0}\;is\;false}} \\ \\ }$$
$$Sample\;1$$
$$Sample\;2$$
$$1$$
$$1$$
$$2$$
$$3$$
$$3$$
$$4$$
$$4$$
$$4$$
$$5$$
$$3$$
$$-$$
$$7$$
$$-$$
$$4$$
$$\displaylines{}$$
$$\displaylines{\\ \\ \mathbf{\color{Green}{Now\;we\;have\;to\;create\;rank\;of\;each\;value}} \\ \\ \mathbf{\color{Green}{If\;2\;or\;more\;values\;are\;equal.\;Take\;average\;and\;give\;equal\;rank}} \\ \\ }$$
$$Values$$
$$Sample$$
$$rank$$
$$1$$
$$Sample\;1$$
$$1.5$$
$$2$$
$$Sample\;1$$
$$3.0$$
$$3$$
$$Sample\;1$$
$$5.0$$
$$4$$
$$Sample\;1$$
$$8.5$$
$$5$$
$$Sample\;1$$
$$11.0$$
$$1$$
$$Sample\;2$$
$$1.5$$
$$3$$
$$Sample\;2$$
$$5.0$$
$$4$$
$$Sample\;2$$
$$8.5$$
$$4$$
$$Sample\;2$$
$$8.5$$
$$3$$
$$Sample\;2$$
$$5.0$$
$$7$$
$$Sample\;2$$
$$12.0$$
$$4$$
$$Sample\;2$$
$$8.5$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Now\;replace\;original\;value\;with\;rank}} \\ \\ }$$

$$Sample\;1$$
$$Sample\;2$$

$$1.5$$
$$1.5$$

$$3.0$$
$$5.0$$

$$5.0$$
$$8.5$$

$$8.5$$
$$8.5$$

$$11.0$$
$$5.0$$

$$-$$
$$12.0$$

$$-$$
$$8.5$$
$$R_{i}$$
$$29.0$$
$$49.0$$
$$n_{i}\;$$
$$5$$
$$7$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Where,\;R_{i}\;is\;sum\;of\;all\;ranks\;in\;a\;sample}} \\ \\ \mathbf{\color{Green}{n_{i}\;is\;total\;number\;of\;values\;in\;a\;treatment}} \\ \\ U_{1} = R_{1}- \left\{\frac{n_{1}(n_{1}+1)}{2} \right\} \\ \\ \Rightarrow 29.0 - \left\{\frac{5(5+1)}{2} \right\} \\ \\ \Rightarrow 14.0 \\ \\ U_{2} = R_{2}- \left\{\frac{n_{2}(n_{2}+1)}{2} \right\} \\ \\ \Rightarrow 49.0 - \left\{\frac{7(7+1)}{2} \right\} \\ \\ \Rightarrow 21.0 \\ \\ U\;=\;minimum\;of\;U_{1},U_{2} \\ \\ \Rightarrow min \left\{14.000000,21.000000 \right\} \\ \\ \Rightarrow 14.0 \\ \\ \mu = \frac{n_{1}*n_{2}}{2} \\ \\ \Rightarrow \frac{5*7}{2} \\ \\ \Rightarrow 17.5 \\ \\ \sigma = \sqrt{\frac{n_{1}*n_{2}*(n_{1}+n_{2}+1)}{12} } \\ \\ \Rightarrow \sqrt{\frac{5*7*(5+7+1)}{12} } \\ \\ \Rightarrow 6.157651 \\ \\ Z= \frac{U-\mu+C}{\sigma} \\ \\ \mathbf{\color{Green}{C\;is\;continuity\;correction,}} \\ \\ \mathbf{\color{Green}{when\;U\;>\;\mu:\;C\;=\;-0.5,\;when\;U\;<\;\mu:\;C\;=\;0.5}} \\ \\ Z= \frac{14.000000-17.500000+0.500000}{6.157651} \\ \\ \Rightarrow -0.487199 \\ \\ \mathbf{\color{Green}{From\;z\;table\;we\;get\;p}} \\ \\ p= 0.626117 }$$