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# Elementary Quantitative Analysis II PowerPoint PPT Presentation

Elementary Quantitative Analysis II. A/S 305: Social Research Methods Sarah Goodrum, Ph.D. Elementary Quantitative Analysis II. Measures of Association Inferential Statistics. Measures of Association. tell us the strength and sometimes the direction of an association between 2 variables

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

### Measures of Association

• tell us the strength and sometimes the direction of an association between 2 variables

• remember . . .

### 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)

### 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)

### 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

### 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

### 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.

### 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)

### 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)