Inferential Statistics Inferential Statistics Explore relationships between variables

Inferential Statistics

Inferential Statistics • Explore relationships between variables • Test hypotheses – Research hypothesis: a statement of the relationship between variables. • An increase in the number of stressors as measured by the LE scale will correspond to an increase in the number of illness incidents as measured by self-report. – Statistical hypothesis: mathematical statement implying a relationship between variables – Null hypothesis: mathematical statement implying no relationship

Examples • You are looking the relationship between GPA and gender – Null hypothesis: H 1: f = m – Statistical hypothesis: H 0: f m • You are looking at the relationship between stressors and illness – Statistical hypothesis: H 1: = 1 – Null hypothesis: H 0: 1

Tests • • Crosstab Difference of Means ANOVA Bivariate correlation

Crosstab • Used for 2 categorical variables • Like a sort box, only you are using frequencies instead of objects triangles orange blue circles

• I want to use a crosstab to see if there is a difference in referral patterns by school • SPSS: analyze – descriptive statistics - crosstab This is the raw sorted data. It gives you a sense of what’s Going on, but let’s add percentages…

• To read this table, first search for the 100% and then follow the line up or down. .

• Significance test for a crosstab is the Chi Square ( ²) The p-value for this hypothesis test is 0. 001, therefore you would reject the null hypothesis

• Pearson's chi-square is by far the most common type of chi-square significance test. If simply "chisquare" is mentioned, it is probably Pearson's chisquare. This statistic is used to test the hypothesis of no association of columns and rows in tabular data. It can be used even with nominal data. Note that chi square is more likely to establish significance to the extent that (1) the relationship is strong, (2) the sample size is large, and/or (3) the number of values of the two associated variables is large. A chi-square probability of. 05 or less is commonly interpreted by social scientists as justification for rejecting the null hypothesis that the row variable is unrelated (that is, only randomly related) to the column variable.

Difference of means test • One variable is dichotomous (2 categories only) and the other is continuous • t-test for significance of the difference of means – Can look at means within one sample and means between two samples. • I want to look at the difference in depression symptoms between women who retained custody of their children vs. women who did not after an allegation of child sexual abuse.

• Analyze – compare means – independent samples t test I can choose the p-value of 0. 022 because the standard deviations are close enough to assume equal variances. SPSS also tests this with the Levene’s test for equality of variances in the table above

ANOVA • One variable is categorical with 3 or more categories and the other is continuous • Looks for a difference between and within groups. – Takes into account the mean and the variability • The ANOVA uses the F-test for significance. – F is between-groups mean square variance divided by within-groups mean square variance x x x

Analyze – compare means – one way ANOVA I am trying to find out if the schools serve children of different grades The p-value is less than 0. 001 so I can reject the null hypothesis

Bivariate Correlations • Both variables are continuous • Measure of the association between the two variables • Pearson's r is the usual measure of correlation, sometimes called product-moment correlation. It is a measure of association which varies from -1 to +1, with 0 indicating no relationship (random pairing of values) and 1 indicating perfect relationship, taking the form, "The more the x, the more the y, and vice versa. " A value of -1 is a perfect negative relationship, taking the form "The more the x, the less the y, and vice versa. "

Analyze – correlate - bivariate The pearson r is 0. 205, which shows a weak association between the two variables. The p-value is less than 0. 001 so it is significant. If you remember, variation is r-squared (0. 205²) which means that child age at first abuse explains 4% of the variance in abuse severity

What does the p-value really mean? • Based on the idea of the sampling distribution. – If you have a population and repeatedly sample that population you will end up with a normal distribution of means – If you find a mean that the SPSS program tells you has a p-value of less than 0. 05, that means that if there is no relationship between the variables in the population and you take 100 samples from the population, you will find a relationship as strong as the one SPSS found in less than 5 out of 100 samples.