Manuals/calci/CHITEST

CHITEST(ar,er)

• $ar$ is the array of observed values
• $er$ is the array of expected values

Description

• This function gives the the value from the chi-squared distribution. i.e it calculates $\chi ^{2}$ statistic and degrees of freedom, then calls CHIDIST.

The conditions of $\chi ^{2}$ test is

The table should be 2x2 or more than 2x2
Each observations should not be dependent
All expected values should be 10 or greater. 
Each cell has an expected frequency of at least five.

• The $\chi ^{2}$ test first calculates a $\chi ^{2}$ statistic using the formula:

$\chi ^{2}=\sum _{i=1}^{columns}\sum _{j=1}^{rows}{\frac {(observedij-expectedij)^{2}}{grandtotal}}$

• $observedij$ is the array of the observed values in a given set of values
• $expectedij={\frac {(columnitotal)*(rowjtotal)}{grandtotal}}$
• observed and expected must have the same number of rows and columns and there must be atleast 2 values in each.
• A low result of $\chi ^{2}$ is an indicator of independence.
• From the formula of $\chi ^{2}$ we will get $\chi ^{2}$ is always positive or 0.
• 0 only if $observedij=expectedij$ for each $i$ and $j$.
• CHITEST uses the $\chi ^{2}$ distribution with the number of Degrees of Freedom df.

where $df=(r-1)(c-1),r>1$ and $c>1$.
If $r=1$ and $c>1$, then $df=c-1$ or $ifr>1$ and $c=1$, then $df=r-1$.
If $r=c=1$ then this function will give the error result

	Column1	Column2	Column3	Column4
Row1	45	38	0.000313
Row2	10	23
Row3	12	26
Row4	40.5	49.36
Row5	19.56	16.44
Row6	17.05	17.41

Let’s see an example

B C

45 38

10 23

12 26

40.5 49.36

19.56 16.44

17.05 17.41

CHITEST (a, b)

i.e. =CHITEST (B2; C4, B5:C7) is 0.003