Capstone Project

Distribution-free Methods

Amna RiazDepartment of StatisticsUniversity of Gujrat

Non Parametric Methods

Nonparametric method refers to a type of statistic that does not require that the population being analyzed meet certain assumptions, or parameters. Parametric methods provide valid information about the data being analyzed only if the underlying population meets certain assumptions. One of the most common assumptions is that the population data have a "normal distribution."

Parametric & Non Parametric Methods

Nonparametric statistics do not require that the population data meet the assumptions required for parametric statistics. Nonparametric statistics refer to a statistical method in which the data is not required to fit a normal distribution.

Parametric & Non Parametric Methods

Nonparametric statistics, fall into a category of statistics sometimes referred to as distribution-free. Often nonparametric methods will be used when the population data has an unknown distribution, or when the sample size is small.

Parametric & Non Parametric Methods

Nonparametric statistics are typically used on nominal or ordinal data. Nominal variables are variables for which the values have not quantitative value. Common nominal variables include gender, whose possible values are discrete categories, "male" and "female."' Other common nominal variables iare race, marital status, educational level, and employment status (employed versus unemployed).

Type of Data

Ordinal variables are those in which the value suggests some order. An example of an ordinal variable would be if a survey respondent asked, "On a scale of 1 to 5, with 1 being Extremely Dissatisfied and 5 being Extremely Satisfied, how would you rate your experience with the cable company?"

Type of Data

Statistical Analysis

The Mann-Whitney U test is used to compare differences between two independent groups when the dependent variable is either ordinal or continuous but not normally distributed, and independent variable should consist of two categorical, independent groups.

Mann-Whitney U Test

Mann-Whitney U Test

Problem statement & Statistical Analysis

The concentration of cholesterol (a type of fat) in the blood is associated with the risk of developing heart disease, such that higher concentrations of cholesterol indicate a higher level of risk, and lower concentrations indicate a lower level of risk.

Problem statement & Statistical Analysis

To investigate whether an exercise or weight loss intervention was more effective in lowering cholesterol levels, a random sample of inactive males that were classified as overweight. This sample was then randomly split into two groups: Group 1 underwent a calorie-controlled diet and Group 2 undertook an exercise-training programme. In order to determine which treatment programme was more effective, cholesterol concentrations were compared between the two groups at the end of the treatment programmes.

Mann-Whitney U Test in SPSS

The table above is very useful because it indicates which group can be considered as having the higher cholesterol concentrations, overall; namely, the group with the highest mean rank. In this case, the diet group had the highest cholesterol concentrations.

Results & Discussions

Test Statistics table provides the test statistic, U statistic, as well as the asymptotic significance (2-tailed) p-value. From this data, it can be concluded that cholesterol concentration in the diet group was statistically significantly higher than the exercise group (U = 110, p = .014).

The Kruskal-Wallis H test (sometimes also called the "one-way ANOVA on ranks") is a rank-based nonparametric test that can be used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable.

Kruskal-Wallis H Test

Problem statement & Statistical Analysis

According to medical researchcertain anti-depressive drugs can have the positive side-effect of lowering neurological pain in those individuals with chronic, neurological back pain, when administered in doses lower than those prescribed for depression. To investigate it, 3 well-known, anti-depressive drugs Drug A, Drug B and Drug C identified, and a group of 60 individuals with a similar level of back pain and randomly assigns them to one of three drugs for a 4 week period. To compare the levels of pain experienced by the different groups at the end of the drug treatment period Kruskal-Wallis H test was run

Results & Discussion

The mean rank or each drug treatment group can be used to compare the effect of the different drug treatments. And the Test Statistics table which presents the result of the Kruskal-Wallis H test showed that drug treatment groups have different pain scores .

Thanks for your attention

Any questions?