Patrick Barlow and Tiffany Smith Descriptive Statistics Parametric Statistics Non-Parametric Statistics Null Hypothesis Alternative Hypothesis Mean Standard Deviation Correlation Confidence Interval Fit the statistics to the research question, not the other way around! First, ask yourself, Am I interested in. Describing a sample or outcome? Looking at how groups differ? Looking at how outcomes are related? Looking at changes over time ? Creating a new scale or instrument? Assessing reliability and/or validity of an instrument? Second, How am I measuring my outcomes? Descriptive Statistics Parametric Statistics Common tests of relationships Pearson r Linear/multiple regression Common tests of group differences Independent t -test Between subjects analysis of variance (ANOVA) Common tests of repeated measures Dependent t -test Within subjects ANOVA Tests of categorical data Odds Ratio / Chi Square Logistic Regression Common Psychometric tests Cronbachs Alpha Principal Components and Factor Analysis Numbers used to describe the sample They do not actually test any hypotheses (or yield any p -values) Types: Measures of Center - Mean Median Mode Measures of Spread - Quartiles Standard Deviation Range Variance Frequencies Most powerful type of statistics we use Researchers must make sure their data meets a number of assumptions (or parameters) before these tests can be used properly. Some key assumptions Normality Independence of observations In research, you always want to use parametric statistics if possible. Pearson r correlation Linear/Multiple Regression What is it? A statistical analysis that tests the relationship between two continuous variables. Commonly Associated Terms: Bivariate correlation, relationship, r -value, scatterplot, association, direction, magnitude. Strong Relationship: r >.50 Weak Relationship: r |.10| 10 No Relationship: r |.00| Moderate Relationship: r |.30| 11 Anscombe, F.J., Graphs in Statistical Analysis, American Statistican, 27, Each has a Pearson Correlation of r =.82, is & is statistically significant What you read: Study found a relationship between GPA and sense of belonging, r =.35, p =.03. What to interpret: Results show r =.35, p =.03, R 2 =.12 How to interpret: There is a weak, significant positive relationship between college GPA and students sense of belonging to the university. As sense of belonging increases, GPA also increases. 13 What is it? A statistical analysis that tests the relationship between multiple predictor variables and one continuous outcome variable. Predictors: Any number of continuous or dichotomous variables, e.g. age, anxiety, SES Outcome: 1 Continuous variable, e.g. ER visits per Month Commonly Associated Terms: Multivariate, beta weight, r 2 -value, model, forward/backward regression, sequential/hierarchical regression, standard/simultaneous regression, statistical/stepwise regression. Independent t -test Between Subjects Analysis of Variance (ANOVA) What is it? Tests the difference between two groups on a single, continuous dependent variable. Commonly associated terms: Two sample t-test, students t-test, means, group means, standard deviations, mean differences, group difference, confidence interval, group comparison. What to interpret? p -values ( 1: For every unit increase in the independent variable, the odds of having the outcome increase by (OR) times after controlling for the other predictor variables. Odds Ratio = 1 or CI crosses 1.0 or p >.05: You are no more or less likely to have the outcome as a result of the predictor variable after controlling for the other predictor variables. (this would be non-significant) Does age, male sex, and time spent playing video games, increase the odds of being on academic probation? Predictor Variables: age (scale), sex (M/F), Gaming (ordinal, 0hrs, 1- 3hrs, 4-6hrs, etc.) DV: Probation (Y/N) What you read: The ORs (95% CI) for each predictor variable are: Age: OR=1.40 (95% CI=0.88 to 6.90), ns Sex male : OR=3.00 (95% CI=2.22 to 5.20), p