Statistical Tools
- 1. Polytechnic University of the Philippines Graduate Studies – College of Education Sta. Mesa, Manila STATISTICAL TOOLS RSH 731 Dissertation 2 Kathleen C. Abaja DEM Student Dr. Milagrina A. Gomez Course Specialist
- 2. SEQUENCE OF PRESENTATION DEFINITION OF STATISTICS CORRELATION HYPOTHESIS CHI-SQUARE TEST OF INDEPENDENCE REGRESSION ANALYSIS FACTOR ANALYSIS REFERENCES • Hypothesis : Alpha • Hypothesis : Beta
- 3. Statistics Defined Statistics is the science and practice of developing human knowledge through the use of empirical data expressed in quantitative form. It is based on statistical theory which is a branch of applied mathematics. Within statistical theory, randomness and uncertainty are modelled by probability theory. (Wikipedia Encyclopaedia) What is statistics? The collecting, summarizing, and analysing of data. The term also refers to raw numbers, or “stats”, and to the summarization of data. Example: Frequencies
- 4. Correlation
- 5. Correlation • Correlation is Positive when the values increase together, and • Correlation is Negative when one value decreases as the other increases.
- 6. Hypothesis
- 9. Chi-Square Test of Independence • The test is applied when you have two qualitative variables from a single population. • It is used to determine whether there is a significant association between the two variables. • For example, in an election survey, voters might be classified by gender (male or female) and voting preference (BJP, Congress or AAP). – We could use a chi-square test for independence to determine whether gender is related to voting preference Voting Preferences Row total BJP Congress AAP Male 200 150 50 400 Female 250 300 50 600 Column total 450 450 100 1000
- 10. Chi-Square Test of Independence
- 12. Regression analysis Illustration of linear regression on a data set.
- 13. Factor Analysis
- 14. Factor Analysis Variables Factor 1 Factor 2 Income 0.65 0.11 Education 0.59 0.25 Occupation 0.48 0.19 House value 0.38 0.60 Number of public parks in neighborhood 0.13 0.57 Number of violent crimes per year in neighbourhood 0.23 0.55 Indicators of wealth, with six variables and two resulting factors.
- 15. Factor Analysis • The variable with the strongest association to the underlying latent variable. Factor 1, is income, with a factor loading of 0.65. • Since factor loadings can be interpreted like standardized regression coefficients, one could also say that the variable income has a correlation of 0.65 with Factor 1. This would be considered a strong association for a factor analysis in most research fields. • Two other variables, education and occupation, are also associated with Factor 1. Based on the variables loading highly onto Factor 1, we could call it “Individual socioeconomic status.” • Notice that the variable house value also is marginally important in Factor 1 (loading = 0.38). This makes sense, since the value of a person’s house should be associated with his or her income.
- 16. References • http:// dss.princeton.edu/online_help/analysis/regression_intro.htm • http://stattrek.com/chi-square-test/independence.aspx • http:// www.statsoft.com/Textbook/Principal-Components-Factor-An • http://www.theanalysisfactor.com/factor-analysis-1- introduction/ • http://mathworld.wolfram.com/HypothesisTesting.html • https://www.mathsisfun.com/data/correlation.html