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Elementary Quantitative Analysis II

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Elementary Quantitative Analysis II

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Elementary Quantitative Analysis II

A/S 305: Social Research Methods

Sarah Goodrum, Ph.D.

Elementary Quantitative Analysis II

Measures of Association

Inferential Statistics

- tell us the strength and sometimes the direction of an association between 2 variables
- remember . . .

- 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)

- 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)

- to use Pearson’s r:

- 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

- 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

- 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.

- 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)

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)