parametric and non parametric test

parametric and non parametric test

In this tutorial, we will discuss parametric and non parametric test in research.

Key Points:

1. Parametric Test ?

2. Non Parametric Test ?

3. Difference between parametric and non parametric test ?

1.Parametric

1.Parametric Test

✰ Parametric tests usually assume certain properties of the parent population from which we draw samples. ✰ The value assumed about population(eg mean, standard deviation, mode, etc) is called ‘population parameter’. ✰ Data are normally distributed in the case of parametric tests.

Parametric test are used when:

Parametric test are used when:

Parametric test are used when:

✔ Population parameter is known. ✔ Measurement scale is interval or ratio. ✔ Population data is normally distributed.

the main example of parametric tests are following:

the main example of parametric tests are following:

the main example of parametric tests are following:

✔ T-test. ✔ Z-test. ✔ ANOVA. ✔ Correlation Coefficient.

Parametric test in research

Z-Test

Z-Test

✰ Z-Test is based on the normal probability distribution. Z- value is calculated with population parameters such as the population mean and population variance. ✰ Z- test is used when: ⟹The sample size is greater than 30 ⟹Large population ⟹Population Standard deviation is known Where, μ = Population mean σp = Standard deviation of population n = Number of observations

T-Test

T-Test

F-test (ANOVA)

✰ Like Z-test, the T-test is also based on the normal probability distribution. ✰ A T-test is a form of the statistical test to find out the p-value (Probability value) which can be used to accept or reject the Null hypothesis. ✰ It is also called student’s T-distribution test. ✰ It is used to compare the difference between the means of two samples in the case of small sample(s) when population variance is not known. ✰ T- test is used when: ⟹The sample size is less than 30. ⟹Small population. ⟹ Population Standard deviation is unknown. Where, μ = Population mean. s = standard deviation of sample. n = number of observations.

F-test (ANOVA)

✰ F- test is used to compare two population variance. ✰ The variance ratio = S12/S22 ✰ F- test is used when: ⟹The sample can be any size. ⟹Sample must be independent. Where, σ1 = variance of first sample σ2 = variance of second sample

2.Non Parametric Test

2.Non Parametric Test

✰ Non-parametric tests do not depend on any assumption about the parameters of the parent population. ✰ Non- parametric tests are ‘distribution-free’ tests. ✰ In a non-parametric test, skewness, and kurtosis may deviate a lot from the normal distribution.

Non parametric test are used when:

Non parametric test are used when:

✔ Population parameter is unknown. ✔ Measurement scale is nominal or ordinal.

the main example of parametric tests are following:

the main example of parametric tests are following:

✔ Chi-square test. ✔ Friedman test. ✔ Mann-Whitney test. ✔ Spearman rank Correlation.

Non-parametric test in research

Chi-Square test

Chi-Square test

✰ It is non parametric test. ✰ Making inferences about 2 or more 2 populations. ✰ Making inferences about population variance. ✰ Chi-square is one-tailed test(right). ✰ Conducting goodness to fit the test, the extent to which observed data matches with expected data. Example: suppose the expected marks of a student in an exam is 90+. Then chi-square test is used to see the extent to which observed data matches with expected data.

3. difference between parametric and non parametric test

3. Difference between parametric and non parametric test:

3. Difference between parametric and non parametric test:

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