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# Kolmogorov Smirnov Test Calculator

INSTRUCTION: Use ',' or new line to separate between values

 Enter alpha value:

## You can see a sample solution below. Enter your data to get the solution for your question

* We are using Lilliefors table for p value calculation.
$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{First\;we\;have\;to\;find\;mean\;and\;standard\;deviation}} }$$
$$\displaylines{}$$
$$\displaylines{Mean = \frac{\sum_{i=1}^{n}X1_{i}}{n} \\ \\ \,=\frac{1+2+3+4+5+1+3+4+4+3+7+4}{12} \\ \\ \,=\frac{41}{12} \\ \\Mean = 3.416667 }$$
$$x$$
$$\bar{x}$$
$$x-\bar{x}$$
$$[x-\bar{x}]^{2}$$
$$1$$
$$3.416667$$
$$-2.416667$$
$$5.840279$$
$$2$$
$$3.416667$$
$$-1.416667$$
$$2.006945$$
$$3$$
$$3.416667$$
$$-0.416667$$
$$0.173611$$
$$4$$
$$3.416667$$
$$0.583333$$
$$0.340277$$
$$5$$
$$3.416667$$
$$1.583333$$
$$2.506943$$
$$1$$
$$3.416667$$
$$-2.416667$$
$$5.840279$$
$$3$$
$$3.416667$$
$$-0.416667$$
$$0.173611$$
$$4$$
$$3.416667$$
$$0.583333$$
$$0.340277$$
$$4$$
$$3.416667$$
$$0.583333$$
$$0.340277$$
$$3$$
$$3.416667$$
$$-0.416667$$
$$0.173611$$
$$7$$
$$3.416667$$
$$3.583333$$
$$12.840275$$
$$4$$
$$3.416667$$
$$0.583333$$
$$0.340277$$
$$Total$$


$$30.916662$$
$$\displaylines{}$$
$$\displaylines{Sample \;variance = (\sigma)^{2} = \frac{\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}}{n-1} \\ \\ \Rightarrow \frac{30.916662}{11} \\ \\ \Rightarrow 2.810606 \\ \\ \sigma = \sqrt{variance} \\ \\ \Rightarrow \mathbf{\color{Red}{1.676486}} }$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Green}{Now\;we\;have\;to\;arrange\;in\;order\;and\;find\;rank\;and\;other\;values}} \\ \\ F_{x}\;=\;F(Normal,x,(mean:3.416667,std:1.676486)) \\ \\ D^{+} = \left\{\frac{Rank}{n} \right\} -F_{x} \\ \\ D^{-} = F_{x}- \left\{\frac{Rank-1}{n} \right\} }$$
$$x$$
$$Rank$$
$$\frac{Rank-1}{n}$$
$$\frac{Rank}{n}$$
$$F_{x}$$
$$D^{+}$$
$$D^{-}$$
$$1$$
$$1$$
$$0.0$$
$$0.083333$$
$$0.074721$$
$$0.008612$$
$$-0.074721$$
$$1$$
$$2$$
$$0.083333$$
$$0.166667$$
$$0.074721$$
$$0.091946$$
$$0.008612$$
$$2$$
$$3$$
$$0.166667$$
$$0.25$$
$$0.199049$$
$$0.050951$$
$$-0.032382$$
$$3$$
$$4$$
$$0.25$$
$$0.333333$$
$$0.40186$$
$$-0.068527$$
$$-0.15186$$
$$3$$
$$5$$
$$0.333333$$
$$0.416667$$
$$0.40186$$
$$0.014807$$
$$-0.068527$$
$$3$$
$$6$$
$$0.416667$$
$$0.5$$
$$0.40186$$
$$0.09814$$
$$0.014807$$
$$4$$
$$7$$
$$0.5$$
$$0.583333$$
$$0.636061$$
$$-0.052728$$
$$-0.136061$$
$$4$$
$$8$$
$$0.583333$$
$$0.666667$$
$$0.636061$$
$$0.030606$$
$$-0.052728$$
$$4$$
$$9$$
$$0.666667$$
$$0.75$$
$$0.636061$$
$$0.113939$$
$$0.030606$$
$$4$$
$$10$$
$$0.75$$
$$0.833333$$
$$0.636061$$
$$0.197272$$
$$0.113939$$
$$5$$
$$11$$
$$0.833333$$
$$0.916667$$
$$0.827526$$
$$0.089141$$
$$0.005807$$
$$7$$
$$12$$
$$0.916667$$
$$1.0$$
$$0.983718$$
$$0.016282$$
$$-0.067051$$




$$Max:$$
$$0.197272$$
$$0.113939$$
$$\displaylines{}$$
$$\displaylines{test\;statistic\;D\;=\;max\;of\; (0.197272, 0.113939) \\ \\ \Rightarrow 0.197272 \\ \\ P\;value\;=\; 0.225416 [based\;on\;Lilliefors] }$$