When variables are categorical and continuous, and there are “many samples”, then we should not use the t-test. If sample size n>=30, then we can go for z-test. When there are too many samples and the mean/average of multiple groups are to be compared, then ANOVA can be chosen.

When we don’t have many samples and variance is unknown, then we will use the t-test. In a t-test, the expectation is that the sample size is smaller. Typical n<30, where n is the number of observations or sample size.

The t-test and z-test can be defined as follows. There is a very subtle difference between the two. z-test is used for n>=30 and t-test is used for n<30 scenarios mostly.

t-test = (x-bar - mu) / (sd / sqrt(n))

• where x-bar = sample average or sample mean of x
• mu = population average or population mean
• sd = standard deviation of a sample
• n = number of observations, which is sample size

z-test = (x-bar - mu) / (sigma / sqrt(n))

• where x-bar = sample average or sample mean of x
• mu = population average or population mean
• sigma = standard deviation of a population
• n = number of observations, which is sample size

ANOVA is an analysis of variance. For example, let’s SAY we are talking about 3 groups.

Figure ANOVA

In the “Figure ANOVA” above, we can consider ANOVA for analysis as there are more than 2 sample groups. i.e. 3 groups of samples. There can be many rows in each class. We have considered only 10 each for simple understanding.