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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

Statistical AnalysisSC504/HS927Spring Term 2008

Week 18 (1st February 2008): Revision of Univariate and Bivariate

levels of measurement
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.
univariate analysis
Univariate analysis
  • Measures of central tendency
    • Mean=
    • Median= midpoint of the distribution
    • Mode= most common value
median value that is halfway in the distribution 50 th percentile
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

mean the sum of all scores divided by the number of scores
Mean – the sum of all scores divided by the number of scores
  • What most people call the average
  • Mean: ∑x / N
measures of dispersion
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
bivariate relationships
Bivariate relationships
  • Asking research questions involving two variables:
    • Categorical and interval
    • Interval and interval
    • Categorical and Categorical
  • Describing relationships
  • Testing relationships
categorical dichotomous and interval
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
e g with stats sceli sav
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)
categorical and categorical
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)
slide13
E.g.
  • Are the proportions within employment status similar across the sexes?
  • Could also think about it the other way round
interval and interval
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.
pearson s correlation coefficient
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
example
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
spss output
SPSS output

r = -.095, p>0.05

There is no relationship between age and scores on the General Health Questionnaire