Statistical Analysis SC504/HS927 Spring Term 2008

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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 AnalysisSC504/HS927Spring Term 2008

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

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
• Measures of central tendency
• Mean=
• Median= midpoint of the distribution
• Mode= most common value

age 12 14 18 21 36 41 42

median

age 12 14 18 21 36 41

median= (18+21)/2 =19.5

• What most people call the average
• Mean: ∑x / N
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
• Asking research questions involving two variables:
• Categorical and interval
• Interval and interval
• Categorical and Categorical
• Describing relationships
• Testing relationships
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)
• 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
• 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)
E.g.
• Are the proportions within employment status similar across the sexes?
• Could also think about it the other way round
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
• 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
• 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

r = -.095, p>0.05

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