Submitted By: Simran Arora

Ans.1

In research statistics, we have 2 categories of tests for the purpose of data analysis and interpretation- one group is based on means and the other group is based on medians. Based on the outcomes of these tests, we accept or reject the hypotheses. The tests which are based on means of the groups are called parametric tests and the tests which are based on medians of the groups are called as non-parametric tests. Let us discuss them in detail.

Parametric tests

Parametric tests are used when the population is normally distributed, i.e. a bell-shaped curve which is symmetrical about the mean and is spread according to the value of standard deviation. Parametric tests are useful when the scales of

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Z-test: It is used to compare two population means when the variance is known and the sample size is large.

2. Independent/Unpaired t-test: It is used to compare the means of two unpaired and independent groups.

3. Paired t-Test: It is used to compare the means of two paired and related groups.

4. One-way ANOVA: It compares the means of three or more independent or unrelated groups.

5. Two-way ANOVA: It compares the mean differences between 2 groups to check whether there is any relation of 2 independent variables with the 1 dependent variable.

Non-Parametric Tests

These tests are in contrast with the parametric test. Non-parametric tests are used when certain assumptions of the focused population are uncertain. For example, in the case when the data is not normally distributed. It uses the median as the central measure. Non-parametrical tests are useful when the scales of measurement used are nominal or ordinal, i.e. the data is to be categorized or ordered in a particular rank-order. These tests may be used with data collected using interval and ratio scales as well but then it simply causes wastage of a large amount of data in such a case. Non-parametric tests have less number of assumptions and less severe as

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If it does not have, the results of the test may stand invalid. This problem is not seen in parametric test. For example, when using 2 sample t-test or ANOVA test, we may assume equal variance before testing. This would be helpful in providing valid results even if the different groups do not have the same data spread.

3) Statistical Power

Parametric tests have a greater ability to discard the null hypotheses when the alternate hypotheses is valid. In other words, parametric test have a better statistical power than non-parametric test.

b) Assumptions of Non-Parametric Tests

In comparison to the parametric tests, the non-parametric tests are based on a less number and less strict assumptions. They are not totally assumption-free.

1. Assumptions are not made about the population, but instead of the data.

2. Non Parametric tests which are used to compare medians of groups assume that the groups must have same dispersion else invalid results may be obtained.

3. The measurement scale that is used should be at least ordinal since bivariate variables are no dependent on each other.

4. No serious effect of outliers is there on ordinal data.

c)