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Understanding Measures of Association and Inferential Statistics in Social Research

This course module delves into measures of association and inferential statistics as crucial elements of social research methods. It explains the significance of Lambda, Gamma, and Pearson's r in determining the strength and direction of relationships between variables. Key concepts such as statistics, parameters, normal distribution, standard deviation, confidence intervals, sample size, and sampling error are also introduced. The distinctions between univariate and bivariate statistics, especially regarding tests of significance like Chi-square, are covered to facilitate informed decision-making in research.

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Understanding Measures of Association and Inferential Statistics in Social Research

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  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)

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