To check the similar distribution of 2 samples drawn from population. If these samples are normal, we can use

**T-test**, but if they are not normal, we need to use**KS-test**. KS-test is a non-parametric test.Null hypothesis (): "

*Two samples drawn from population with the same distribution*."👉 Read more about p-value. We use this value to evaluate the true/false of above null hypothesis.

The difference (in use) of

**T-test**(need an assumption of nomality) and**KS-test**(don't need),- Two samples have the same mean & standard deviation ⇒ p-value is high ⇒ cannot reject (not true)

- KS-test can detect the variance ⇒ p-value is low ⇒ we can reject ⇒ 2 samples are not the same distribution!!! (yep!)

If the

**KS statistic is small**or the**p-value is high**, then we**cannot reject**the hypothesis that the distributions of the two samples are the same.`1from scipy import stats`

```
1# one-sample KS test
2stats.kstest(x, 'norm')
```

```
1# two-sample KS test
2stats.ks_2samp(x, y)
```

**Matthew E. Clapham**-- 10: Kolmogorov-Smirnov test (video)

- An example of why we need to use EMD instead of Kolmogorov–Smirnov distance (video).