Statistical Significance

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The Normal Distribution Hypothetical Distribution Mean=Median=Mode Symmetrical Fixed proportion of cases between mean and a distance from the mean

The Normal Curve

An example Suppose the average income were $50K, SD=15,000 Where does a person with income of $80K fall? (80,000-50,000)/15,000= 2 SD above mean

The Normal Curve Previous case- 2 SDs, where does that put us? 50% of curve from - ∞ to mean ~48% of curve from mean to 2 SD Higher than 98 Percent of cases

Sampling Error Mean from a sample is an ESTIMATE of the population parameter Standard Error- estimate of precision of mean

Sampling Error- Example George W Bush Feeling thermometer mean= 56.1, SD=24.9, N=1761 How precise of an estimate is this of population mean? SE=24.9/√1761=.59 95% Confidence Interval- Add and subtract 2SE ~

Hypothesis Testing State Null Hypothesis Choose decision rule (level of significance) Choose appropriate sample test statistic Collect data, put it into SPSS, go get a cup of coffee See if test statistic is meets level of significance

How to tell if groups differ part I Chi Square Question- Suppose we have two groups, how do we tell if they are different on a variable of interest? Χ 2 – Another distribution Works with nominal data Where to use- Crosstabs Compares expected number of cases if no difference between groups with observed number of cases

Chi Square Example

Pres Approval by Party

Do Two Groups Differ- Interval Data Difference of Means T test Do two groups differ? Republicans and Democrats on feeling thermometers

T Tests Can Also Compare Pairs of Variables E.g. do Clinton, Gore, Bush differ?

Anova Limit of T test- can only compare 2 groups/variables Need one continuous, one dichotomous variable Anova works with two continuous variables to see if there is a relationship

Feeling Thermometers and Partisanship NES 7 point Party Scale Captures not only difference between Republicans and Democrats, but also importance of strength No utility in looking at mean for each score on IV

Anova

Comparing Groups, which test when Nominal Data- Chi Square Compare 2 variables-Paired Samples T Test Dichotomous IV, Continuous DV- independent samples T-test 2 continuous Variables- Anova

Statistical Significance and Measures of Association 0= no association Correlations etc have SEs as well Null hypothesis- score equals zero Significance tells us if it differs meaningfully from 0 Sample size and strength of association influence significance Strong Associations Big Samples

Next week Learning SPSS A- McGrath Meet in SSC 27 Tuesday Mickelson-Z on Thursday Day off otherwise, do something productive