Hypothesis Testing in Data Science

• Other names are AB testing, Confirmative Analysis, and significance testing.

• Generally, population parameters (standard deviation, maximum, minimum, and so on) are unknown in real-time.

• However, we do have hypotheses about what the true values are.

• Hypothesis testing is a bunch of methods to evaluate the hypothesis about the population parameter based on the available sample parameters.

• There are 2 terms in the hypothesis, they are null hypothesis and alternate hypothesis.

Null Hypothesis (H0):

• A general statement about the population parameters which assumed to be true unless strong proof for the opposite statement.

• The default statement is that there is no difference between the measured phenomenon, there is an association among groups.

Alternate Hypothesis (H1 or Ha):

• Just the opposite of the null hypothesis.

• the default statement is that there is a difference between the groups.

Testing types:

T-Test

Also called Student’s T-Test. If the sample size is less than 30 and the population variance is unknown we should use a t-test.

• One-Sample T-Test

• Two sample T-Test

• Paired sample T-Test (Dependant T-Test)

One-Sample T-Test:

 

• To check whether the mean of the population is significantly different from the sample mean or not.

• Here the H0 is “there is no difference” and the H1 is “there is a significant difference”.

• P-value should be less than 0.05 (5%) to accept (failed to reject) the alternate hypothesis.

• To perform one-sample t-test in python we can use scipy.stats.ttest_1samp()

Note: dataset for the following program will be available in https://drive.google.com/file/d/1SD44pF68zADNS-0OuXCn_J_E2andQUV7/view?usp=sharing

• By this result, we can come to the conclusion that the sample data is good and there is no difference between the sample mean and population mean.

Two-Sample T-Test:

• To check if there is any relationship or association between two independent groups or not.

• Here the H0 is “there is no difference”(association is there) and the H1 is “there is a significant difference” (no association).

• P-value should be less than 0.05 (5%) to accept (failed to reject) the alternate hypothesis.

• To perform two sample t-test in python we can use scipy.stats.ttest_ind()

Note: dataset for the following program will be available in https://drive.google.com/file/d/1SD44pF68zADNS-0OuXCn_J_E2andQUV7/view?usp=sharing

• By this result, we can come to the conclusion that the salesprice of 1st and 2nd floor is not related (no relationship between the tested 2 independent variables).

Paired Sample T-Test:

• This test is conducted between to dependent variables to check the difference in data.
• Here the H0 is “there is no difference” and the H1 is “there is a significant difference”.
• To perform paired sample t-test in python we can use scipy.stats.ttest_rel()

• by this result, we can tell that this weight loss program is effective without any doubt.

Z-Test

If the sample size is greater than 30 and population variance is known we should use a z-test. And it is the same as the T-test. Data that is chosen for this z test should have data points that are independent of each other.

• One Sample Z-Test

• Two sample Z-Test

One Sample Z-Test:

• Same as one sample T-Test but here we know the population variance and population standard deviation. And the data size should be more that 30.
• To check whether the mean of the population is significantly different from the sample mean or not.
• Here the H0 is “there is no difference” and the H1 is “there is a significant difference”.
• to perform one sample z-test in python we can use statsmodels.stats.weightstats.ztest()

• By this result, we can come to the conclusion that the sample data is good and there is no difference between the sample mean and population mean.

Two Sample Z-Test:

• Same as two sample T-Test but here we know the population variance and population standard deviation. And the data size should be more that 30.

• To check if there is any relationship or association between two independent groups or not.

• Here the H0 is “there is no difference”(association is there) and the H1 is “there is a significant difference” (no association).

• P-value should be less than 0.05 (5%) to accept (failed to reject) the alternate hypothesis.

• To perform two sample z-test in python we can use statsmodels.stats.weightstats.ztest()

• By this result, we can come to the conclusion that the sales price of the 1st and 2nd floor is not related (no relationship between the tested 2 independent variables).

F-Test

Also called ANOVA test.

• Two sample t-test or two sample z-test can able to validate the hypothesis containing only 2 groups at a time. But if we want to perform with more than 2 groups, there this ANOVA test will give its hand to do that.

• ANOVA determines whether the means of 3 or more groups are different or not.

• It uses F-Test to test the equality of the means.

Note: here the degree of freedom is calculated differently for numerator and the denominator. (df for between groups = no. of groups -1 and df for within groups = Total no. of observations - no. of groups)

One-way ANOVA:

• This test is conducted when we have only one independent variable and other as dependent variables.

• This is implemented in scipy by as f_oneway().

Two-way ANOVA:

• We perform one-way ANOVA between one independent and other dependent variables but in this two-way ANOVA, we will perform between two independent variables and two plus groups.

• It’s the extension of one-way ANOVA.

• It will not tell which variable is dominant. if we want to know about that we can perform Post-hoc testing.