What is the Chi-Square test in statistics?
The Chi-Square test (abbreviation: x²) is a non-parametric statistical test used to compare observed results with the expected results. A low value of X² means that there is a high correlation between the two sets of data.
Assumptions:
- Sample data is randomly picked from the population.
- The data categories are mutually exclusive.
- The data should be in the form of frequencies or counts and not in percentages.
- The observations should be independent of each other.
Formula:
The chi-squared test is done to check if there is any difference between the observed value and expected value. The formula for chi-square can be written as:
Chi-Square distribution table:
The Chi-Square distribution table is a table that shows the critical values of the Chi-Square distribution. To use the Chi-Square distribution table, you only need to know two values:
- The degree of freedom for the Chi-Square test, which is calculated as df = number of categories - 1
- Significance value α
The critical value can be found by using below distribution table (row = df, column = α)
Solved example:
Q) Is there a relationship between the placements of students and their CGPA considering a significance value of 0.05
H0: There is a relationship between the CGPA and the frequency of placed students.
H1: There is no relationship between the CGPA and the frequency of placed students.
