Statistical Techniques Used for Exploring Relationships:1) Correlation: Explores relationship among two continuous variables (e.g. age and depression scale). a. Partial correlation: Controls for one continuous variable while explores for a relationship among two continuous variables. Example: After controlling for the effects of socially desirable responding, is there still a significant relationship between optimism and life satisfaction scores (three continuous variables) 2) Multiple regression: Predicts. One continuous dependent variable & 2 or more continuous independent variable. It can be seen as an extension of correlation and is used when you want to explore the predictive ability of a set of independent variables on one continuous dependent measure. Example: How much variance in life satisfaction scores can be explained by the following set of variables: self-esteem, optimism and perceived control? Which variables is a better predictor of life satisfaction. All variables here are continuous. 3) Chi Square: Explores relationships among two categorical variables (e.g. sex and exercise—exercise is categorized as either (Yes or No). Example: Is there a relationship between sex (Males and Females) and exercise (Yes vs. No)?4) Spearman’s Rank Order correlation: two variables that are either ordinal, interval or ratio. Exploring Differences Between Groups (interval scales): Parametric tests: the data is required to fit a normal distribution. 5) T-tests are used when you have 2 groups or two set of data (before & after) and when you wish to compare the mean scores on some continuous variable. Example: Are males more optimistic than females?One categorical independent variables with two groups and one continuous dependent variable. a) Independent sample t-test: Used when there are 2 different independent groups and you want to compare their scores. One categorical independent variable with only 2 groups& one continuous dependent variable.b) Paired sample t-test: Same participants are tested on 2 separate occasions. One categorical independentvariable (e.g. Time 1 & Time 2) & one continuous dependentvariable. Example: Does ten weeks of meditation training result in a decrease in participant level of anxiety? Is there a change in anxiety levels from Time 1 (pre intervention) to time 2 (post intervention)? One categorical independent (Time 1/Time 2) & One continuous dependent variable (anxiety score). 6) One sample between groups analyses (ANOVA): Used to compare 2 or more groups and compare their mean scores on a continuous variable. One categorical independentvariables with 2 or more groups & one continuous dependentvariable. Example: Is there a difference in optimism scores for people who are under 30, between 31-49 and 50 years and over. 7) Two way between groups ANOVA: Test the impact of two categorical independent variables and one continuous dependent variable. This test allows the possibility of testing for interaction effect. This is when the effect of one independent variable is influenced by another. Example: What is the effect of age on optimism scores for males and females. 8) Mixed between-within ANOVA: One between groups independent variable (intervention such as math skills and confidence building) and one within group’s independent variable (Time 1, Time 2, Time 3) & one continuous dependent variable. 9) Multivariate ANOVA: One categorical independent variable & ≥ 2 continuousdependent variables. 10) ANCOVA: One categorical independent variable & one continuous dependentvariable & one or more continuous covariates.Nonparametric tests: the data is not required to fit a normal distribution.Data that is often ordinal,meaningit does not rely on numbers, rather a ranking or order of categories.11) Wilcoxon Signed-Rank test: is the nonparametric test equivalent to the repeated measures t-test. *Converts scores to ranks and compares these at Time 1 and at Time 2. 12) Mann-Whitney U: Non parametric measure; tests difference between 2 independent groups. 13) Kruskal–Wallis one-way analysis of variance: The non-parametric option for one-way ANOVA. It is used for comparing two or more independent samples of equal or different sample sizes. It extends the Mann–Whitney U test when there are more than two groups.a. Post hoc analyses are conducted to find out which groups are significantly different from one another. 14) McNemar’s Test: Tests 2 variables, the first recorded at time 1 and the second recorded at time 2. Both of these variables are categorical. a. E.g. Question: Is there a change in the proportion of the sample diagnosed with clinical depression prior to and following intervention. 15) Cochran’s Q Test: If you have 3 or more time points. All three are categorical variables measuring the same characteristics at 3 points in time. a. Example: Is there a proportion of participants diagnosed with clinical depression across the three time points (a) prior to the program (b) three months’ post program. Research Objective Type of DV Type of IV Covariates Test Analysis Goal Test associations or relationships Explore associations nominal (categorical) variables nominal (categorical) variables Chi Square Is there an association between the IV+DV Explore associations and strengths Continuous Continuous Correlation Is there an association between the IV+DV Explore associations and strengths Continuous Continuous one or more Partial correlation Is there an association between the IV+DV controlling for 1 or more variables Explore associations and strength between two ranked variables Continuous Continuous Spearman Rank Order correlation (non-parametric) Is there an association between the IV+DV Differences between groups tests: Explore differences between groups (Before or After) AND Compare the mean scores on some continuous variable Continuous One nominal (categorical) variables with 2 groups T-tests (Parametric) Do differences exist between groups. Explore the differences between independent groups to compare their scores Continuous One nominal (categorical) variable with only 2 groups Independent sample T-test (Parametric) Do differences exist between these two groups. Explore the differences between the same participants on two separate occasions to compare their scores Continuous One nominal (categorical) variable (Time 1 & Time 2) Paired Sample t-test (Parametric) Test the same participants on two separate occasions (Time 1 & Time 2) Research Objective # and type of DV # and type of IV Covariates Test Analysis Goal Explore the differences between ≥2 groups and compare their mean scores on a continuous variable Continuous Categorical with ≥2 groups ANOVA Do differences exist between ≥2 groups on one DV Test the main and interaction effects of categorical variables on a continuous dependent variable, controlling for the effects of selected other continuous variables, which co-vary with the dependent. One continuous Categorical with ≥2 groups one or more additional ANCOVA Do differences exist between ≥2 groups on one DV after controlling for the covariates Explore the differences between ≥2 groups on multiple DVs ≥2 groups (continuous) Categorical with ≥2 groups one or more additional MANOVA Do differences exist between ≥2 groups on multiple DVs Explanation or prediction tests: How much variance in the DV is accounted for by linear combination of the IVs 1 continuous ≥2 Dichotomous Continuous Multiple regression How strongly related to the DV is the beta coefficient for each IV What is the odds or the probability of the DV occurring as the values of the IVs change? 1 dichotomous 1 or more Categorical or continuous Logistic regression What are the odds or the probability of the DV occurring as the values of the IVs change Practice exercise Research Objective # and type of DV # and type of IV Covariates Test Analysis Goal