Chi Square Test

What is a chi-square test used for? And What its application?

Chi-square test is used with nominal or category data (minimum two) in the form of frequency counts. It tests whether the frequency counts in the various nominal categories could be expected by chance or, more specifically, whether there is a relationship. One-sample chi-square compares the frequencies obtained in each category with a known expected frequency distribution, whereas a two sample chi-square uses a crosstabulation or frequency table for two variables. This gives the frequencies in the various possible combinations of categories of these two variables.

What is the chi-square in simple terms?

The disparity between the actual frequencies in the data and what the frequencies would be if the null hypothesis were true is at the heart of the calculation. The bigger the disparity, the bigger the value of chi-square and the more one’s findings are statistically significant. When the chi-square table has more than four cells (i.e. combinations of categories), interpretation becomes difficult. It is possible to subdivide a big table into a number of smaller chi-squares in order to facilitate interpretation. This is known as partitioning.

Sometimes data may violate the mathematical foundations of chi-square too much. In these circumstances, the data may have to be modified to meet the mathematical requirements, or an alternative measure such as the Fisher exact test may be employed.

Why chi-square is used for hypothesis testing?

The simplest form of a chi-square test is a two-cell experiment where the outcome of the experiment is that each participant or event falls into only one of the two cells. An experimenter wishes to know whether male deep-sea divers have more female children than male children. The experimenter asks 10 consecutive long-time deep-sea divers who come to a dive store about the gender of their children. The null hypothesis would be that the probability of having a boy is ½ or .5, and the probability of having a girl is ½ or .5, and the sum of the two probabilities is 1.0. Let us say that the 10 divers reported having a total of 25 children: 10 boys and 15 girls. Do these observed values differ from what we expected to be a 50–50 split?

What is the null hypothesis for a chi-square test?

In a chi-square of this experiment, the null and alternative hypotheses would be

H0: pB = pG

Ha: pB ≠ pG

where

pB = the probability of having a boy (B), and

pG = the probability of having a girl (G).

What are the Assumptions for chi-square test?

Although it was stated that the chi-square test makes no assumption about the shape of the underlying population, there are a few important assumptions when using the chi-square test.

What are the conditions for the test?

1. The scores in each cell should be independent of one another. This means that a score in one cell should have no effect on a score in another cell.
2. There should be a minimum of five participants or events in any one cell.
3. The dependent variable in the chi-square test is assumed to be a frequency or count, such as number of participants. It is not appropriate to analyze continuous variables unless they have been dichotomized.

Does chi square test assume normal distribution?

There is no normality assumption for the test.