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Statistical Analysis SC504/HS927 Spring Term 2008

Statistical Analysis SC504/HS927 Spring Term 2008. Week 18 (1st February 2008): Revision of Univariate and Bivariate. Levels of measurement. Nominal e.g., colours numbers are not meaningful

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Statistical Analysis SC504/HS927 Spring Term 2008

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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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