Unit 8 - Parametric Tests, Research and Statistics

Research and Statistics

1. Parametric Tests Unit 8

2. Topic Highlights 1 2 3 4 5 Introduction Choosing Between Parametric and Nonparametric Test Types of Parametric Tests Restrictions of Parametric Test Summary 2 Unit 8 02.11.2024

3. 3 Unit 8 02.11.2024

4. 4 Unit 8 02.11.2024

5. 5 Unit 8 02.11.2024

6. CHOOSING BETWEEN PARAMETRIC AND NONPARAMETRIC TESTS: THE EASY AND HARD CASES 6

7. The Easy Cases Parametric Tests: Sure that data are sampled from a population that follows Gaussian Distribution( also know as Normal Distribution) Nonparametric Tests: The outcome is a rank or a score and the population is clearly not Gaussian Some values are “off the scale”, too high or too low to measure The data are measurements and researcher is sure that the population is not distributed in a Gaussian manner 7 Unit 8 02.11.2024

8. The Hard Cases If researcher collect many data points (over hundreds or so), researcher can look at the distribution of data and fairly obvious if it is Gaussian Distribution. Researcher should look at previous data and what matters is the distribution of overall population not the researcher sample Consider the source of scatter 8 Unit 8 02.11.2024 Researchers Considerations:

9. 9 Unit 8 02.11.2024

10. Correlation Technique used for measuring the degree of relationship between two variables. shows the extent to which values in one variable are linked or related to values in another variable. Two main types of Correlation: 10 Unit 8 02.11.2024

11. Where n = Quantity of Information Σx = Total of the First Variable Value Σy = Total of the Second Variable Value Σxy = Sum of the Product of first & Second Value Σx 2  = Sum of the Squares of the First Value Σy 2  = Sum of the Squares of the Second Value 11 Pearson’s Correlation coefficient is calculated using the formula: =========

12. Multiple Correlation/Regression It is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them . It helps businesses and researchers make informed decisions by predicting outcomes based on historical data. Regression of ‘y’ on ‘x’ 12 Unit 8 02.11.2024 Regression equation Average value of ‘y’ is a function of ‘x’ Y = a* x + b

13. Factor Analysis It is a powerful tool when you want to simplify complex data, find hidden patterns, and set the stage for deeper, more focused analysis. It is also called Dimension Reduction. T he overall objective of factor analysis is data summarization and data reduction.  Types of Factor Analysis 13 Unit 8 02.11.2024 Exploratory Factor Analysis (EFA) - used to discover underlying structure Confirmatory Factor Analysis (CFA) - used to test if the data fit a priority expectation for data structure. - uses structural equations modeling. Principle Component Analysis (PCA) Common Factor Analysis or just Factor analysis Image Factoring Maximum Likelihood Other methods such as Alpha Factoring and Weight Square.

14. 14 Unit 8 02.11.2024 Assumptions in Factor Analysis

15. 15 Unit 8 02.11.2024 Restrictions of Parametric Tests The parametric tests are restricted by their assumptions, especially of normal or near-normal distribution. If the data fail to meet these assumptions and the information about their underlying distributions is not known, the predicted parameters, means and the standard deviation, could be invalid.  When can you not use a parametric test? - The population sample size is too small

16. Thank you