What is the Chi-square test?
The Chi-Square test is a kind of statistical testing. This kind of testing is done to compare the values that are observed and the data that is expected based on the found hypothesis. It is one of the simplest non-parametric tests among all the commonly used statistical tests. The Chi-Square test is identified with the Greek letter x2. ‘X2’ denotes the magnitude of the discrepancy in the theory and the extent of the observations made in the theory. The Chi-square test also is conducted to find the summary information investigation. It works best with those operations that require minimal measurements. Two important factors of Chi-square testing are- Degree of freedom and the distribution. Among these two operations, Chi-square distribution is commonly used all over the world for hypothesis testing and statistical probability problems.
Types of Variance in Chi-Square Testing
There are primarily three variances in Chi-square testing. These are-
- Goodness to fit
Types of Chi-Square Tests
There are basically two main types of Chi-square tests. They are as follows-
Chi-Square Testing- Goodness to Fit
Goodness to Fit test is primarily conducted with the samples of populations. This type of test verifies the sample data and sees if these are uniform with the hypothesis distribution of the population. Some of the vital conditions that one should meet for conducting successful testing are-
- A sample random sampling method
- A categorically defined Variable
- Sample observations must be equal to or should be more than 5
Chi-Square Test for Independence
The second very popular type of Chi-Square Testing is Chi-Square Testing for Independence. This type of test consists of two variables and along with that the independence between these variables terms are validated. In other words, Chi-square testing for Independence will help the user calculate the distribution of the given two independent variables.
What are the conditions Chi-square testing must fulfill?
There are certain conditions that Chi-Square tests must fulfill to be used in Statistics. These conditions are-
- The total number of frequencies should be more than 50.
- Sample observations must not depend on each other at any time. Items should not be included twice in the given sample.
- Constraints on the cell frequencies should be linear.
- Theoretical frequency should not be too small. If the expected frequency is lesser than the value of x2, then it will get overestimated. This would lead to the rejection of the null hypothesis.
- Every theoretical frequency should be more than 10 and in some exceptional cases, it should be less than 5. If the theoretical frequency is less than 5, x2 cannot be used for testing.
Students who are learning statistics already know how complex the subject is. Chi-square testing adds to the complexity of the subject and only students with analytical minds are able to understand its operations. Students get weekly assignments on Chi-Square testing and writing those becomes tricky especially when the students are not prepared. Basic knowledge is not enough as the problems require advanced skills in the subject. Some of the common Chi-square assignment topics are-
- Exact Sampling Distributions
- Derivation of the Chi-squared distribution
- Moment Generating function of x2 distribution
- Chi-square probability curve
- Fisher’s Theorem
- Composite Hypothesis
- Chi-square test for Population variance
- Non-Central Chi-Square Distribution, etc.
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