Elementary Quantitative Analysis II

1. Elementary Quantitative Analysis II A/S 305: Social Research Methods Sarah Goodrum, Ph.D.

2. Elementary Quantitative Analysis II Measures of Association Inferential Statistics

3. Measures of Association • tell us the strength and sometimes the direction of an association between 2 variables • remember . . .

4. Measures of Association • Lambda– tells us the magnitude (but NOT the direction) of the relationship b/t the 2 variables; use when one or both variables are nominal. • Gamma– tells us the magnitude and the direction of the relationship b/t the 2 variables; use when variables are ordinal (or above)

5. Measures of Association • Pearson’s r– reveals the magnitude and thedirection of the correlation coefficient (or relationship) b/t 2 interval or ratio level variables • to use Pearson’s r: • it must be assumed that the relationship is linear (i.e., increase in X -> increase in Y; increase in X -> decrease in Y) • need an adequate sample size (n>30)

6. Inferential Statistics • estimate how well your sample statistic reflects the population parameter • this is necessary when we have a sample and want to make generalizations to the population

7. Terms to Know • statistic– summary description of a given variable in the sample • parameter– summary description of a given variable in the population • normal distribution– the normal distribution is symmetric; this shape is produced by random sampling error • standard deviation- the square root of the variance; tells you how much dispersion (or spread) there is in the variable for your sample • confidence intervals – sets the upper and lower limits of your sample statistic; tells you how much confidence can be placed in the sample statistics

8. Terms to Know, Con’t • sample size– as sample size goes up, sampling error goes down • sampling error– degree of error to be expected in probability sampling; the larger the sampling error, the less representative the sample.

9. Types of Inferential Statistics: (1) Univariate • With univariate inferential statistics (e.g., confidence intervals, which are estimated using standard deviation) we move beyond describing the sample to making estimates (or inferences) about the larger population • Three things MUST be established: • Sample drawn from population of interest • Sample must be drawn randomly using simple random, systematic, or stratified random sampling • Inferential statistics tell us about sampling error NOT about non-sampling error (e.g., bad survey question; problematic interviewer)

10. Types of Inferential Statistics: (2) Bivariate: Tests of Significance Tests of Significance- tell us the likelihood that the relationship observed b/t 2 variables in a sample can be attributed to sampling error only • Chi-square– tells us whether we can safely assume that there is a relationship b/t the values in the population; it does not measure the strength or the direction of the association b/t the 2 variables, but indicates whether the association is significant (or due to chance)