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# Statistical analysis in SPSS_

Mean, Correlation, Reliability and Hierarchical regression analysis

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### Statistical analysis in SPSS_

1. 1. Statistical analysis Mean, standard deviation, reliability, correlation, and regression
2. 2. Data entry in SPSS • SPSS Statistics is a software package used for logical batched and non-batched statistical analysis. • The data entry in SPSS is crucial for smoother analysis. • Refer to this link for the entry of data in SPSS https://www.youtube.com/watch?v=BvwNPRy6HJU
3. 3. Descriptive analysis • Mean : The mean is the average of all numbers and is sometimes called the arithmetic mean. • Standard deviation : a quantity expressing by how much the members of a group differ from the mean value for the group.
4. 4. Total value
5. 5. • Divide the outcome of mean and standard deviation by the number of items for each scale. • Like: If value given in table for TC is 12.47 and number of items is 5, then 12.47/5 = 2.494 Interpretation: This indicate that respondents considered their training as less helpful as the mean estimate is low on the scale of 7 point Likert scale.
6. 6. Reliability test • Reliability -A test is considered reliable if we get the same result repeatedly. • Cronbach’s alpha, α (or coefficient alpha), developed by Lee Cronbach in 1951, measures reliability, or internal consistency. “Reliability” is how well a test measures what it should. For example, a company might give a job satisfaction survey to their employees. High reliability means it measures job satisfaction, while low reliability means it measures something else (or possibly nothing at all). • Cronbach’s alpha tests to see if multiple-question Likert scale surveys are reliable. These questions measure latent variables — hidden or unobservable variables like: a person’s conscientiousness, neurosis or openness. These are very difficult to measure in real life. Cronbach’s alpha will tell you if the test you have designed is accurately measuring the variable of interest.
7. 7. Interpretation • Reliability above 0.70 is acceptable level to indicate that the scale used to collect data provides consistent results and thus is reliable for further analysis
8. 8. Correlation • Correlation analysis is a method of statistical evaluation used to study the strength of a relationship between two, numerically measured, continuous variables (e.g. height and weight). • Pearson’s product-moment coefficient is the measurement of correlation and ranges (depending on the correlation) between +1 and -1. +1 indicates the strongest positive correlation possible, and -1 indicates the strongest negative correlation possible. • Put all the total values in SPSS
9. 9. Correlation estimates P values
10. 10. • As correlation estimates between each variable is positive and significant (p value <0.001), this indicates all the variables are related to each other. • This gives basis for further regression analysis to understand the causal relationship between variables.
11. 11. Regression analysis • Regression analysis is used to model the relationship between a response variable and one or more predictor variables. • Eg: IV DV
12. 12. Steps 1. Standardize the variable data In statistics, standardized coefficients or beta coefficients are the estimates resulting from a regression analysis that have been standardized so that the variances of dependent and independent variables are 1.
13. 13. Standardized estimates
14. 14. CONTD… 2. Put the data in regression model IV: Independent variable = TC M: Mediator = SE DV: Dependent variable = CAA
15. 15. Mediation analysis • First enter IV in independent variable and mediator as dependent variable • Then, put DV as dependent variable and IV as independent variable. • Then click on ‘next’ • And put mediator as independent variable
16. 16. TC SE CAA H1 H2 H3 HYPOTHESISED MODEL
17. 17. MEDIATOR INDEPEDENT VARIABLE
18. 18. Beta coefficient P value R square estimate
19. 19. Dependent variable Independen variable
20. 20. Mediator Dependent variable
21. 21. R square estimate P value Beta estimate
22. 22. R square estimate • R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression. • R-squared is always between 0 and 100%: • 0% indicates that the model explains none of the variability of the response data around its mean. • 100% indicates that the model explains all the variability of the response data around its mean. • In general, the higher the R-squared, the better the model fits your data.
23. 23. P value • The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable. • Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.
24. 24. Beta coefficient A standardized beta coefficient compares the strength of the effect of each individual independent variable to the dependent variable. The higher the absolute value of the beta coefficient, the stronger the effect. For example, a beta of -.9 has a stronger effect than a beta of +.8. Standardized beta coefficients have standard deviations as their units. This means the variables can be easily compared to each other. In other words, standardized beta coefficients are the coefficients that you would get if the variables in the regression were all converted to z-scores before running the analysis.
25. 25. Interpretation • As R square changed from 0.250 to 0.299, this indicate addition of mediator in equation contributes towards relationship between IV and DV. • As P value is below 0.05, this indicate chances of Type I and type II error is less than 5%.
26. 26. Contd.. • Effect of TC on SE = 0.526, p < 0.05 • Effect of SE on CAA = 0.261, P< 0.05 • Effect of TC on CAA = 0.362, P< 0.05 • As all the relationship is significant, this indicate the SE has a significant mediating role between TC and CAA. TC SE CAA Β = 0.362*** Β = 0.526*** Β = 0.261***
27. 27. • Note that a mediational model is a causal model. • For example, the mediator is presumed to cause the outcome and not vice versa. If the presumed causal model is not correct, the results from the mediational analysis are likely of little value. • Mediation is not defined statistically; rather statistics can be used to evaluate a presumed mediational model.
28. 28. Baron and Kenny mediation steps • The above steps of mediation is based on the four step mediation analysis test proposed by Baron and Kenny (1986), Judd and Kenny (1981), and James and Brett (1984). • Thus, to indicate mediation four steps are to be analyzed- Step 1: Show that the causal variable is correlated with the outcome. Use Y as the criterion variable in a regression equation and X as a predictor (estimate and test path c in the above figure). This step establishes that there is an effect that may be mediated. Step 2: Show that the causal variable is correlated with the mediator. Use M as the criterion variable in the regression equation and X as a predictor (estimate and test path a). This step essentially involves treating the mediator as if it were an outcome variable.
29. 29. Step 3: Show that the mediator affects the outcome variable. Use Y as the criterion variable in a regression equation and X and M as predictors (estimate and test path b). It is not sufficient just to correlate the mediator with the outcome because the mediator and the outcome may be correlated because they are both caused by the causal variable X. Thus, the causal variable must be controlled in establishing the effect of the mediator on the outcome. Step 4: To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for M (path c') should be zero (see discussion below on significance testing). The effects in both Steps 3 and 4 are estimated in the same equation.
30. 30. Final mediation decision • If all four of these steps are met, then the data are consistent with the hypothesis that variable M completely mediates the X-Y relationship, and if the first three steps are met but the Step 4 is not, then partial mediation is indicated. Meeting these steps does not, however, conclusively establish that mediation has occurred because there are other (perhaps less plausible) models that are consistent with the data. Some of these models are considered later in the Specification Error section.