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Define Parametric and Non parametric test. When these tests are used? Also define their sub types along with examples

Explanation:


Parametric tests=
It is the Procedure of hypothesis which explains that the variables of interest are measured on at least an interval scale. It is parameters defining properties of the population distribution from which one's data are drawn,
Uses of Parametric Tests

1: uses in skewed and non-normal distributions=Parametric tests can be used with continuous data that are non-normal if you satisfy these sample size guidelines. For example sample t test (each group should be greater than 15) and in ANOVA (if you have 10 -12 groups then each group should be greater than 20).

2: uses for when spread of each group is different= For nonparametric tests data for all groups must have the same spread (dispersion). If your groups have a different spread, the nonparametric tests might not provide valid results. In parametric tests you’re good to go even when the groups have different spreads.

3: uses as a Power=Parametric tests usually have more statistical power than nonparametric tests. Thus, you are more likely to detect a significant effect when one truly exists.
Some of the following tests of parametric tests are: t test, t statistic, t distribution
t test= is used when the sample size is small and the standard deviation is unknown.
t statistic=This test is used when variable has a symmetric bell-shaped distribution, the mean is known or assumed as known and the population variance is estimated from the sample.
t distribution= it is the symmetric bell-shaped distribution that is useful for small sample [n<30] testing, when the mean is known and the population variance is estimated from the sample.

Example: Market share for a new product will exceed 15 percent; at least 65% of customers will like a new package design; 80% of the dealers will like the new pricing policy. These statements can be translated to null hypothesis that can be tested using a one sample t test.

Nonparametric tests=
It is the Procedure of hypothesis which explains that the variables are measured on a nominal ordinal scale. a non-parametric test makes no such assumptions it is essentially a null category, since virtually all statistical tests assume one thing or another about the properties of the source population.
Non-parametric tests are distribution free methods based on observations.

Uses of Nonparametric Tests
1: uses for representing the median=The use of median for non parametric tests can be understood by the given example For example, the center of a skewed distribution, like income, can be better measured by the median where 50% are above the median and 50% are below. If you add a few millionaires to a sample, the mathematical mean increases although the income for the typical person doesn’t change. For these two distributions, a random sample of 100 from each distribution produces means that are significantly different, but medians that are not significantly different.

2: uses in small samples=If you have a small sample size you should use a nonparametric test instead of parametric tests. When you have a really small sample, you might not even be able to ascertain the distribution of your data because the distribution tests will lack sufficient power to provide meaningful results.

3: uses in outliers=Parametric tests can only assess continuous data and the results can be affected by outliers. Some nonparametric tests can manage ordinal data, ranked data, and cannot be affected by outliers. But it depends upon the assumptions for the nonparametric test because each one has its own data requirements.
Some of the following tests of non-parametric tests are following:
Kruskal Wallis= is the non-parametric method which has to be used in case the assumption of normality.
Mann-Whitney= in non-parametric corresponds to the pooled t test in parametric.
Chi-square= chi-square in non-parametric test is used for testing frequencies in categories; chi-square can also be used for testing goodness of fit, independence and homogeneity.
Example: Nominal or ordinal scale data demand the use of non-parametric methods and in the case of interval and ratio scale data where we cannot assume population normality then again non-parametric methods are suitable for this.

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