Manuals/calci/CHITEST

CHITEST(actualrange,expectedrange)

• $actualrange$ is the array of observed values
• $expectedrange$ is the array of expected values

Description

• It is test for independence.
• This function gives the value from the chi-squared distribution and the appropriate degrees of freedom. 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:

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

• $observed_{ij}$ is the array of the observed values in a given set of values
• $expected_{ij}={\frac {(column_{i}total)*(row_{j}total)}{grandtotal}}$
• 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 $observed_{ij}=expected_{ij}$ 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 if $r>1$ and $c=1$, then $df=r-1$.

If $r=c=1$ then this function will give the error result

• The obtained result is entered in the Chi square distribution table with the obtained degrees of freedom.
• This returns the test for independence (probability).

ZOS Section

• The syntax is to calculate CHITEST in ZOS is $CHITEST(actualrange,expectedrange)$.
  • where $actualrange$is the array of observed values.
  • $expectedrange$is the array of expected values.
• For e.g;chitest([60,72,86,45],[57.08,75.10,87.1,42.45])

Chi-Squared Distribution

Examples

A student investigated the chance of getting viral fever in a school for a period that took vitamin tablets every day. The total number of students 880. In that 639 students didn't get viral fever and 241 students got fever .But the expected ratio is 1:3
Answer

• If the ratio is 1:3 and the total number of observed individuals is 880, then the expected numerical values should be: 660 will not get fever and 220 students will get fever.

	No Fever	Get Fever
Observed Values	639	241
Expected Values	660	220
${\frac {(oi-ei)^{2}}{ei}}$	0.668	2

• The $\chi ^{2}$ value is 2.668
• Now $df=(r-1)(c-1)=(2-1)(2-1)=1$
• From the Chi Squared Distribution probability table with $df$ is 1, the $\chi ^{2}$ value of 2.668 is 0.10.
  

CHITEST(or,er) = 0.10

See Also

• CHIDIST

References

CHI-SQUARE Distribution