data science: chi-square

Data Science Day 3:Chi-square Test

Learning Objectives

1.DefinetheChi-Squaredistribution

2.Explainthe 3Chi-squaretest applications scenario

TheChi- Square distributionis thesum of variance(squared standard normal deviates). The following equation represents a Chi-Square distribution with m degrees of freedom.

 V= X1^2+X2^2+...+Xm^2 

where X1,  X2, ... Xm are m independent random variables having the standard normal distribution.The higher the degree of freedom, the more it approaches to a normal distribution.

The Chi-Square distribution has 3 basicproperties:

Not symmetric, Skewed to the right

No Negative Values

Total area under the curve=1

Three primary Chi-square test applications:

1.Test independence of two categorical variables:

Whether the two categorical variables have a strong association, or whether the two categorical variables are independently distributed in one sample space.

Null hypothesis:Two categorical variables are independent.

Note:There are two categorical variables from one sample space

2*.Test the Goodness of Fit (Pearson):

Whether the sample categorical data are consistent with a hypothesized distribution.

Null hypothesis: Sample data are consistent with a specified distribution

Note:It is one Categorical variable from one sample space

3.Test of Homogeneity:

Whether frequency counts of the categorical variable have the same distribution for different sample spaces.

Null hypothesis: The proportion of the categorical variable is the same in all sample space.

Note:It is one categorical variable from two or more different sample space.

* In Clinical Trials, we use Chi-square log-rank test in survival analysis.

We will show the application examples next time!

Thanks very much to Renee Wu, Ali Motamedi~ 

Happy learning!