1. Descriptive Statistics e.g.,frequencies, percentiles, mean, median, mode, ranges, inter-quartile ranges, sds, Zs Describe data Inferential Statistics e.g., t, ANOVA (F), correlations (r), regression weights (ß); variance explained (R 2 ) Allow for inferences about population to be drawn from sample data Types of Statistics

2. Frequencies, percentiles Central Tendency Mean Sum of all observations divided by total number of observations Median After arraying all observations in ascending/descending order, the obs that divides the sample into two For even number of observations take avg of 2 central obs Mode Most frequently occurring observation When would one use means vs. medians? (Economist article) Descriptive Statistics p.396 Sekaran

3. Variability Range Difference between the two most extreme observations Inter-quartile range Divide observations into quarters & use the middle half Standard Deviation Take each observation’s difference from the mean, square it, add all such squared differences, and divide the result by number of observations Variance Square of standard deviation Descriptive Statistics p.397 Sekaran

4. Variability (cont’d) Confidence intervals The range of values in which the mean occurs 95% of the time Typically includes scores that are two standard errors above or below statistic »Standard error: Type of standard deviation (for more see p. 287 Sekaran) Standard scores (Zs) Deviation from the mean divided by standard deviation Mean of all Zs =0, sd=1 Useful for computing interaction scores in regression analyses Descriptive Statistics

5. Categorical Nominal; Ordinal Can compute frequencies & mode for nominal For ordinal variables, carefully interpret descriptive statistics Continuous Interval; Ratio Can compute descriptive statistics Types of Variables

6. MOD. A Copyright © 2003 John Wiley & Sons, Inc. Sekaran/RESEARCH 4E

7. Parametric vs. non-parametric statistics Non-parametric does not assume normal distribution of data T-test ANOVA (F) Correlations (r) Types of Multiple-regression (R) Regression weights (ß); Variance explained (R 2 ) Types of Inferential Statistics p.394 Sekaran

8. Behavioral research explains individual differences in psychological variables Good measures of psychological variables capture individual differences Individual differences in psychological variables are normally distributed Some psychological variables can be ‘transformed’ to be normally distributed Variables with normal distributions have interval properties & allow for computation of commonly used inferential statistics Key Assumptions

9. Inferential Statistics See also p. 405 Sekaran

10. T-test Compares whether means of two groups are different from each other 95% of the time Compares differences on one independent variable Paired t-test= Same group, two different times or measurements Can be used as a post-hoc or planned contrast after conducting ANOVA analyses Beware the number of t-tests done reduces confidence level so use Scheffe’s, Duncan multiple range etc. Tests of Mean Differences

11. ANOVA (F-test) Compares whether means of three or more groups are different from each other 95% of the time Compares two or more independent variables Tests interaction effects: Does the effect of one IV depend on the level of the other IV? Repeated measures ANOVA: Same sample, multiple times/measurements Sparingly conduct T-test to see if pairs of groups are significantly different from each other Tests of Mean Differences

12. Correlation coefficient (r) Assesses whether 2 variables are ‘linearly’ related to each other 95% of the time Reflects the direction and the strength of the relation Varies from –1 to +1. Better measure of the strength of a relation is the amount of explained variance (r 2 ) Ranges from 0 to 100 Difference between r=.3 & r=.4 is not the same as difference between r=.7 & r=.8 Tests of Association

13. Types of Correlations When both variables are continuous: Pearson product-moment When both variables are nominal (categorical) Two categories for each variable: Phi Multiple categories for each variable: Kappa When both variables are ordinal: Spearman rank Significance of r = t-test Tests of Association

14. Tom Cruise Vince Carter Calista Flockhart Julia Roberts r =.76; r 2 = 58%

15. For Male Celebrities: r =.27; r 2 = 7%

16. For Female Celebrities: r =.78; r 2 =61 %

17. Multiple correlation (R) Describe relation between 3 or more variables (e.g., 2 predictors and one criterion) Two different formulae depending on whether or not predictors are correlated with each other Tests non-linear relationships Significance of R =F-test Are variables related to each other 95% of the time? Tests of Association 405-407 Sekaran

18. Difference between r & ß r ß predictor criterion predictor criterion control

19. Difference between R & R 2 criterion control R 2 not explained control predictor R 2 =  R R=multiple correlation unique R 2 explained

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