Methods of Inferential Statistics

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Parametric inferential statistics is a method of statistics that is based on the assumption that data is derived from probability distribution where us non-parametric inferential statistics method do not use distribution parameters to make interpretations. Parametric methods are based on many assumptions compared to non-parametric methods. Non-parametric methods use parameters which are flexible while parametric methods use parameters which are fixed.


Questions

  1. In which category does chi- square fall under? Is it under parametric or under non-parametric?
  2. When do we use parametric method of statistics inference?
  3. When do we use non-parametric method of statistic inference?

The chi square summarizes the inconsistency between the values expected and the actual values observed in given model. It is used to show the deviation of the actual value obtained from what was expected. Chi square is used to check whether the distribution of an observation differs from the theoretical values.


Questions:

  1. What is the interpretation of the value obtained if positive or negative?
  2. What is meant by the term null hypothesis?
  3. When do we use the two tailed test and the one tailed test?
  4. What is degree of freedom and how is it applicable?

A contingency table is a table of summary that displays the relationship between two or more variables. It is a tabular representation of data with two or more variables where the variables form the column of the table.


Questions

1.      How do you interpret information in the contingency table?

2.      Can the variables be represented as ratios in the contingency table?

3.      What are the uses of a contingency table?


A phi coefficient is also known as the mean square contingency coefficient which measures the degree at which two binary variables are associated.


Questions

  1. Using examples show how two binary variables are positive and negative associated?
  2. How to you show the association of more than two variables?
  3. What are the uses of phi coefficient?

There are four other non parametric tests. This includes: The Mann-Whitney U-test which is used to compare two independent groups on ordered in which observation of the two independent data fall. It gets the difference between the sets of pairs and gives the analysis of the list of the differences. Mann-Whitney is formed under the assumption that responses are continuous and that on e distribution is stochastically grater compared to the other.


The Wilcoxon test method uses ranks instead of scores to compare groups which are correlated. Wilcoxon rank-sum is the sum of each rank. The third method is the Sign test for Matched Samples which is used to test two correlated sample. It uses the sign of pair different ranks. The last method is the Median Test for two or more Independent samples it compares the medians of the groups. The data is classified into two one containing data which is above the mean and the other containing the mean and data below the mean.


Questions

  1. When are the above non-parametric method used?
  2. How is the solution interpreted in each method?
  3. What are the uses of each method?

Reference.

Hettmansperger, T. P.; McKean, J. W. (1998). Robust nonparametric statistical methods.

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