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Revision of Univariate and Bivariate Statistical Analysis Levels and Techniques

This document provides an overview of the fundamental concepts in univariate and bivariate statistical analysis. It covers levels of measurement—nominal, ordinal, interval, and ratio—with examples. Univariate analysis is explored through measures of central tendency such as mean, median, and mode, as well as measures of dispersion including range, variance, and standard deviation. Bivariate analysis focuses on relationships between variables, incorporating techniques like t-tests for means comparison and Chi-square tests for categorical data, along with Pearson’s correlation for interval data.

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Revision of Univariate and Bivariate Statistical Analysis Levels and Techniques

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  1. Statistical AnalysisSC504/HS927Spring Term 2008 Week 18 (1st February 2008): Revision of Univariate and Bivariate

  2. Levels of measurement • Nominal e.g., colours numbers are not meaningful • Ordinal e.g., order in which you finished a race numbers don’t indicate how far ahead the winner of the race was • Interval e.g., temperature equal intervals between each number on the scale but no absolute zero • Ratio e.g., time equal intervals between each number with an absolute zero.

  3. Univariate analysis • Measures of central tendency • Mean= • Median= midpoint of the distribution • Mode= most common value

  4. Mode – value or category that has the highest frequency (count)

  5. Median – value that is halfway in the distribution (50th percentile) age 12 14 18 21 36 41 42 median age 12 14 18 21 36 41 median= (18+21)/2 =19.5

  6. Mean – the sum of all scores divided by the number of scores • What most people call the average • Mean: ∑x / N

  7. Which One To Use?

  8. Measures of dispersion • Range= highest value-lowest value • variance, s2= • standard deviation, s (or SD)= The standard error of the mean and confidence intervals • SE

  9. Bivariate relationships • Asking research questions involving two variables: • Categorical and interval • Interval and interval • Categorical and Categorical • Describing relationships • Testing relationships

  10. Categorical (dichotomous) and interval • T-tests • Analyze – compare means – independent samples t-test – check for equality of variances • t value= observed difference between the means for the two groups divided by the standard error of the difference • Significance of t statistic, upper and lower confidence intervals based on standard error

  11. E.g. (with stats sceli.sav) • Average age in sample=37.34 • Average age of single=31.55 • Average age of partnered=39.45 • t=7.9/.74 • Upper bound=-7.9+(1.96*.74) • Lower bound=-7.9-(1.96*.74)

  12. Categorical and Categorical • Chi Square Test • Tabulation of two variables • What is the observed variation compared to what would be expected if equal distributions? • What is the size of that observed variation compared to the number of cells across which variation could occur? (the chi-square statistic) • What is its significance? (the chi square distribution and degrees of freedom)

  13. E.g. • Are the proportions within employment status similar across the sexes? • Could also think about it the other way round

  14. Interval and interval • Correlation – Is there a relationship between 2 variables? • To answer this we look at whether the variables covary • Variance: how much deviation from the mean there is on average • If the 2 variables covary then you would expect that when 1 variable deviates from its mean the other variable will deviate from its mean in the same, or directly opposite way.

  15. Pearson’s Correlation Coefficient • There are many different types of correlation (see your SPSS class handout for more examples) but when both variables are interval level data we will carry out a Pearson’s Correlation Coefficient (r) • The r (correlation coefficient) ranges from -1 to +1 • A negative association indicates that as one variable increases the other decreases • A positive association indicates that as one variable increases so does the other variable

  16. Example • Children’s age and height – as the child gets older they get taller • This is a positive association • The older your car the less money it is worth • This is a negative association

  17. SPSS output r = -.095, p>0.05 There is no relationship between age and scores on the General Health Questionnaire

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