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Statistical Analysis SC504/HS927 Spring Term 2008 Week 18 (1st February 2008): Revision of Univariate and Bivariate

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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.

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

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Mode – value or category that has the highest frequency (count) agefrequency (count) sexfrequency (count) 16-2512male435 26-3520female654 36-4532 46-5527 56+18

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Median – value that is halfway in the distribution (50 th percentile) age12141821364142 median age121418213641 median=(18+21)/2=19.5

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

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Which One To Use? ModeMedianMean Nominal Ordinal Interval

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Measures of dispersion –Range= highest value-lowest value – variance, s 2 = –standard deviation, s (or SD)= The standard error of the mean and confidence intervals –SE

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Bivariate relationships Asking research questions involving two variables: –Categorical and interval –Interval and interval –Categorical and Categorical Describing relationships Testing relationships

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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

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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)

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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)

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

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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.

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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

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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

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

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