PSY300 WEEK 2 Hierarchical Regression AND Mediation Review Notes PDF

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PSY300 Advanced Methods in Psychology Week 2 Hierarchical Regression and Mediation Review Notes....

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TUTORIAL 2: HIERARCHICAL REGRESSION AND MEDIATION REVIEW - Assignment predominantly hierarchical regression, but also includes mediation (*mediation will not be run but the output will be provided).

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Assignment - Important Advice Do not change the data at all at any time and perform all operations on the data as provided. Follow the assignment instructions very closely - do not deviate or do anything additional. Do not conduct any assumption testing. Section A (80%) Students will be provided with a data file, a research question and hypotheses. Requirements: - Conduct hierarchical regression using SPSS - Write up a results section - Report on the hypotheses Section B (20%) Students will be provided with full SPSS output for a mediation (students will not need to run the mediation themselves). Requirements: - Produce one APA/figure for the mediation - Complete a fill in the blank exercise for the mediation Key Steps in Hierarchical Regression Analysis Many of the steps discussed also apply to other research designs (e.g., various ANOVA’s), in particular steps related to data preparation/cleaning and assumption testing. This is highly relevant for conducting own research (fourth-year project). Standard multiple regressions effectively use the same approach. NOTE: the assignment does not require all the steps discussed below - providing context for those who plan to conduct research and to enhance learning. Step 1 - Before Data Collection Calculate required sample size - Typically use GPower but sometimes Tabachnick and Fidell rule (or both). Test assumptions: are the variables suitable to the proposed method of data analysis e.g., dependent variable should be continuous and two (or more); independent variable should be continuous or categorical (not required in assignment).

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Further info on assumptions for multiple regression (not required for assignment but potential interest): http://statistics.laerd.com/spss-tutorials/multiple-regression-using-spss-statistics.php Step 2 - Data Preparation/Cleaning and Assumption Testing Check out-of-range scores e.g., if using a Likert Scale (1-7), a score of 8 would be out-of-range, Remedies include replacing value with correct value and making a missing value (not required in assignment). Check for missingness: missing data can be a major problem. Remedies include Listwise case deletion, Pairwise case deletion and Data imputation (where we replace score with estimate). - Not required in assignment. Check for univariate outliers. Remedies include: deletion, transformation and imputation. - Not required in assignment. Check for multivariate outliers. Typical remedy is deletion but imputation is possible. Not required in assignment. Check for multicollinearity (IV should be highly correlated) tolerance is an indicator. Remedies include combining variables or deleting variables - Not required in assignment. Check for linear relationship between each IV and the DV - Not required in assignment. Check residuals for normal distribution, linear, exhibit, homoscedasticity that are independent - Not required assignment. What is a residual? Residuals Regression revolves around a line of best fit. The regression may actually pass through some of the data points but most of the data points are typically not on the line. The regression line represents the predicted value per data point. The difference between the predicted and actual value for a data point is the residual. Regression between predicted and actual values on the left hand side. Takes the average line of best fit that runs through the middle of data points. Right hand side is the predicted value at each and x and y point.

Interpreting Effect Size 1 - In this assignment, use the Pearson correlation (r) to interpret effect size, r-squared (r2) is used to calculate the percentage of variance explained. - This applies to all correlation coefficients in the regression, including R, R2 adjusted R2, zero-order correlation (r), partial correlation and semi-partial correlation (sr). *USING r TO INTERPRET EFFECT SIZE AND USING R2 TO CALCULATE THE PERCENTAGE OF VARIANCE EXPLAINED.

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Cohen (1992) - if (Pearson) r correlation is: - .1 - effect size is small - .3 - effect size is medium - .5 - effect size is large (Use these values as thresholds i.e. the value must be at least .3 to qualify as medium). Anything below .1 may be labelled as “very small” - Example: a semi-partial correlation (sr) is .7. The effect size is large and 49% of variance is explained.

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The Tutorial Study Research questions: does interviews on local radio stations and candidates policies predict the number of votes received in local elections? Does adding the variable “number of advertisements in the local press’ improve the model? Does reputation mediate the relationship between number of advertisements and votes received? Identify the IV’s/DV and formulate hypotheses for a hierarchical regression. Essential to formulate hypotheses for the model/s as whole and for the individual predictors. - Questions 1 & 2 answer - 3 IV’s (I.e., interviews on local radio stations, candidates policies and number of advertisements in the local press) 1 DV (I.e., votes received in local election). - Question 3 answer - Reputation as a mediator, number of advertisements is the IV and number of votes received is the DV. Variables Advertisements - number of advertisements in the local press. Range: 0 to open. Interviews - number of interviews on local radio stations. Range: 0 to open. Reputation - Range 1-10, with 1 being the lowest. Votes - number of votes in local elections. Range 0 to open. Policies - rating of candidate policies, ranging from 0 (low) to 20 (high). Research Hypotheses It was hypothesised that the number of interviews on local radio stations and the policies of the candidate would predict the number of votes received in local elections. It was hypothesised that the addition of advertisements would improve the predictive efficiency of the model. It was hypothesised that interviews on local radio would make a significant positive contribution to the model [Hierarchical regression].

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It was hypothesised that the policies of the candidate would make a significant positive contribution to the model. It was hypothesised that advertisements would make a significant positive contribution to the model. It was hypothesised that reputation would mediate the relationship between advertisements and the number of votes received.

Diagram for Mediation 1. Independent variable to the dependent variable giving the standardised beta and the P value. 2. Independent variable to mediator to dependent variable - First arrow is the a path - Second arrow is the b path - C path at bottom is the effect Hierarchical Regression 1. Analyse 2. Regression 3. Linear 4. Next (Next x as many times as needed for each variable 35 minute mark on tute 2 lecture 5. Statistics (want r2 change and part and partial correlations) 6. Output 7. Go to ANOVA and check significance level 8. Then go to Model Summary 9. Go to R (use to interpret the effect size) 10. Sig F change (model 2 is important as it informs of the significance of the second variable [whether significant or not]). 11. Look at significance then betas. 12. Beta tells TASK 2 WRITE UP

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Results Present evidence relevant to your hypothesis and succinct details about cleaning/assumption testing. Succinct, focused and precise writing. Do not speculate here or write in a general vague style. You are describing data - avoid getting into the actual hypothesis testing this is done in Discussion). Ok to mention the hypothesis in passing but no more. You may introduce the section briefly but also ok to begin with an intro to the table.

- Remember to introduce a table before it appears e.g., table 1 shows. *always introduce Important to - Do some research of your own - look for research articles using multiple regression but bear in mind that the assignment has specific requirements. - For the assignment, no citations are required. When writing a formal report one will cite. Result of Study Example 1 (Excerpt from intro section) - A hierarchical multiple regression analysis was conducted to assess whether the risk perception model consisting of emotion, social norms and world view would significantly predict attitude to environmental risk. Table 1 shows unstandardised (b) coefficients and 95% confidence intervals (95% CI), standardised (β) coefficients, semi-partial correlations (sr2) and related p-values (note: you will not be showing these in your assignment table). *Extremely important to add tables and graphs at honours level. Results of Study Example 2 (Excerpts from write-up about models) - The multiple regression model was found to explain significant variance in reported energy conservation behaviour F(3,95) = 5.33, p < .001 with a medium effect size and accounted for 14.3 of the variance in perceived climate change risk. Adding self-confidence to the multiple regression model explained an additional 0.1% of the variance in reported climate change risk perception but this change in R2 was not significant, F(1.82) = 0.17, p = .609. The expanded model remained significant with a medium effect size, accounting for 14.4% of the variance explained in perceived climate change risk . *Results of the first model. **What happens when an additional variable is introduced and report on the expanded model. Results of Study Example 3 (Excerpts from write-up about single predictor) - There was considerable variation in the impact of individual predictors on the model as a whole, with neuroticism (β = .62) accounting for more variance than the other three predictors combined. Neuroticism made a significant (p< .001) positive contribution to the model with a large effect size (sr = .8), explaining 64% of the variance in the dependent variable. *Using two-tailed regression....