Stats Tests

When, ## Why, ### and How. to use different tests in R and python

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Tests of normality

*1. Summary /:The Shapiro–Wilk test tests the normality of a given distribution. Shapiro Wilk effectively compares two estimates of variance;

The null-hypothesis of this test is that the population is normally distributed. Thus, if the p-value is less than the chosen alpha level α, then the null hypothesis is rejected and there is evidence that the data tested are not from a normally distributed population; in other words, the data are not normal.

In R

$ shapiro.test(ItemName) Sample output In PYTHON

from scipy import stats np.random.seed(12345678) x = stats.norm.rvs(loc=5, scale=3, size=100) stats.shapiro(x_array_like) output (0.9772805571556091, 0.08144091814756393) This returns a float, which is the p-value for the hypothesis test.

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Chi Squared

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PCA

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Tests For Variance

varTest

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Tests comparing Variance

When to use this test Comparing two variances is useful in several cases, including: When you want to perform a two samples t-test to check the equality of the variances of the two samples When you want to compare the variability of a new measurement method to an old one. Does the new method reduce the variability of the measure?

Method 1 var.test(values ~ groups, data, alternative = "two.sided") **Method 2 ** var.test(x, y, alternative = "two.sided") Preleminary test to check F-test assumptions

   **F TEST**

F-test is very sensitive to departure from the normal assumption. You need to check whether the data is normally distributed before using the F-test.

Shapiro-Wilk test can be used to test whether the normal assumption holds. It’s also possible to use Q-Q plot (quantile-quantile plot) to graphically evaluate the normality of a variable. Q-Q plot draws the correlation between a given sample and the normal distribution.

If there is doubt about normality, the better choice is to use Levene’s test or Fligner-Killeen test, which are less sensitive to departure from normal assumption Compute F-test

F-test

res.ftest <- var.test(len ~ supp, data = my_data) res.ftest

Example output The p-value of F-test is p = 0.2331433 which is greater than the significance level 0.05. In conclusion, there is no significant difference between the two variances