Statistics question
1 SPSS Multiple Regression Overview The sample analyses in this handout are from the dataset titled “Demo Regression Dataset.” Pirlott and SXU student researchers Abu-Maizur, Elkins, and Torres wondered what predicts disgust toward breastfeeding. Accordingly, they showed participants a series of photos of a woman engaged in various tasks, one of which included breastfeeding. Participants reported their levels of physical disgust to each photo (BF_Disgust; ranging 1 to 9). Participants also provided measures of endorsement of traditional gender roles (TradGenderRole; ranging 1 to 7), political conservatism (Conservatism; ranging 1 to 3), and breastfeeding knowledge (BF_Knowledge; ranging 1 to 7). Outcome variable = disgust toward breastfeeding Predictor variables = endorsement of traditional gender roles, political conservatism, and breastfeeding knowledge Correlation: − First, obtain zero-order conduct correlation analyses between all pairs of variables − Analyze → Correlate → Bivariate − Select all variables used in regression analysis − Under “Options,” select “Exclude cases listwise” Regression: The simplest regression analysis to perform would be to select the outcome variable and all potential predictors in a linear regression analysis: − Analyze → Regression → Linear − Dependent: select your outcome variable − Independent(s): select your predictor variables − Statistics: select your desired statistics. Minimally select “regression coefficient estimates,” “model fit,” and “descriptives.” This will provide your regression estimates, model tests, descriptive statistics, and correlations among variables. 2 Example Abbreviated Output Here, SPSS tells us what predictor variables were entered into the model (BF_Know, TradGenderRole, Conserv_Lib), and what the outcome variable was, i.e., the “dependent variable,” BF_PDis 3 R = the (multiple) correlation between all predictors (knowledge, traditional gender roles, conservatism) and the outcome variable (physical disgust). R2 = proportion of variance in outcome (physical disgust) accounted for by full model (knowledge, traditional gender roles, conservatism) = .103 Significance testing: did full model (knowledge, traditional gender roles, conservatism) explain a significant proportion of variance in outcome variable (physical disgust)? Yes, F(3, 300) = 11.52, p < .001 (Constant): the Y-intercept. Its significance value tests whether its value significantly differs from 0. Unstandardized regression coefficients (b): used in the regression equation Standardized regression coefficients (β): the correlation between the predictor and the outcome variable, controlling for the other predictor variables Sig: indicates whether each predictor significantly predicts the outcome variable, while controlling for the other predictors 4 APA Write-Up Information The style of a regression analysis write-up depends upon the researcher’s goals with the analyses. Minimally, report the following: the R2 for the full model and the corresponding Fstatistic, the intercept, and for each predictor: the unstandardized regression coefficients and their standard error, standardized regression coefficients, and significance for each predictor variable. If there are few predictors, this information can be included in the text. If there are many predictors, this information can be included in a regression table, and then summarize the results in the text. Summarize the relationship between each predictor variable and the outcome variable by stating the direction of the relationship, the significance of the relationship, and the meaning of the relationship. Write-Up Template: − To examine whether the model, which includes [predictor variables] as predictors, accounts for a significant proportion of variance in [outcome variable], we entered the predictor variables into a linear regression analysis predicting [outcome variable]. − The regression model accounted for X% of variance in [outcome variable], (R2 = .XX), which [was/not] significant, [F-statistic]. − Describe the results of each predictor variable’s ability to predict the outcome variable by including: o the regression coefficients in the text (b, SE, β, p) OR refer to reader to a summary table o if the relationship was significant: ▪ that the relationship was significant, whether the relationship was [positive or negative], and what it means in layperson’s terms [e.g., as X goes up, Y goes up; as X goes up, Y goes down]. o if the relationship was not significant: ▪ that the relationship was not significant and what it means in layperson’s terms [e.g., that X and Y are unrelated] − Correlations among all pairs of variables are summarized in Table 1. − A summary of the regression coefficients are summarized in Table 2 (if the regression coefficients were not included in the text). − Discuss whether results support or don’t support your hypothesis and whether you reject or fail to reject the null hypothesis. 5 Correlation Matrix Table. Create a correlation matrix table with the correlations between all pairs of variables used in the analysis (examples on p. 215-216 of the APA Publication Manual). In Word: To create a correlation table: 1. Insert → Table; choose number of columns by number of rows. 2. Type in the correlation coefficients between variables, to two decimal places. 3. * the significant correlations: *** = p < .001, ** = p < .01, * = p < .05. 4. Add a note clarifying the meaning of the variables in the table. 5. Add *** = p < .001, ** = p < .01, * = p < .05 below the note. 6. The only lines to include is the top and bottom of the first row, and the bottom of the last row. 7. Do any final APA Format formatting, see chapter seven in the APA Publication Manual. Regression Coefficient Table. When creating a regression table summarizing the model information of the ability of each predictor variable to predict the outcome variable, include the intercept and predictor variables and their corresponding values each on their own line. Differentiate between the unstandardized and standardized regression coefficients. Include the SE, the t-value, and p-value. See the APA Publication Manual for more details about writing up regression analyses and summarizing the results in tables (see examples on p. 219). In Word: To create a regression coefficient table: 1. Insert → Table; choose number of columns by number of rows. 2. Include the intercept and each predictor variable 3. Enter the b, SE, β, t, and p statistics 4. Add a note clarifying the meaning of the variables in the table. 5. The only lines to include is the top and bottom of the first row, and the bottom of the last row. 6. Do any final APA Format formatting, see chapter seven in the APA Publication Manual. 6 Regression Lab Example Write-Up Angela G. Pirlott Department of Psychology, Saint Xavier University PSYCH 300: Statistics for the Social Sciences Professor Angela G. Pirlott [due date] 7 Regression Lab Example Write-Up Does the model, which includes traditional gender role endorsement, conservatism, and breastfeeding knowledge as predictors, account for a significant proportion of variance in disgust toward breastfeeding? The null hypothesis states that the regression model does not account for a significant proportion of disgust toward breastfeeding, whereas the alternative hypothesis suggests that the regression model accounts for a significant proportion of disgust toward breastfeeding. Results Option #1: Results in Text To examine whether the model, which includes traditional gender role endorsement, conservatism, and breastfeeding knowledge as predictors, accounts for a significant proportion of variance in disgust toward breastfeeding, we entered the predictor variables into a linear regression analysis predicting disgust toward breastfeeding. The regression model accounted for 10% of variance in disgust toward breastfeeding, (R2 = .10), which was significant, F(3, 300) = 11.52, p < .001, therefore we reject the null hypothesis. Breastfeeding knowledge negatively predicted significantly disgust toward breastfeeding, such that as knowledge increased, disgust decreased (b = -0.72, SE = 0.15, β = -.28, p < .001). Conservatism positively predicted disgust toward breastfeeding, such that as conservatism increased, disgust increased (b = 0.55, SE = 0.27, β = .12, p = .039). Traditional gender role endorsement failed to predict disgust toward breastfeeding, suggesting that gender role endorsement and breastfeeding disgust were unrelated, once controlling for the other predictors (b = 0.05, SE = 0.09, β = .03, p = .58). Correlations among all pairs of variables are summarized in Table 1. Results Option #2: Results in Table 8 To examine whether the model, which includes traditional gender role endorsement, conservatism, and breastfeeding knowledge as predictors, accounts for a significant proportion of variance in disgust toward breastfeeding, we entered the predictor variables into a linear regression analysis predicting disgust toward breastfeeding. The regression model accounted for 10% of variance in disgust toward breastfeeding, (R2 = .10), which was significant, F(3, 300) = 11.52, p < .001, therefore we reject the null hypothesis. Breastfeeding knowledge negatively predicted significantly disgust toward breastfeeding, such that as knowledge increased, disgust decreased. Conservatism positively predicted disgust toward breastfeeding, such that as conservatism increased, disgust increased. Traditional gender role endorsement failed to predict disgust toward breastfeeding, suggesting that gender role endorsement and breastfeeding disgust were unrelated, once controlling for the other predictors. Correlations among all pairs of variables are summarized in Table 1, and a summary of the regression coefficients are summarized in Table 2. 9 Table 1 Correlations Among All Variables Tested Breastfeeding Disgust Traditional Gender Role Endorsement .08 Conservatism .17** Breastfeeding -.29*** Knowledge ***p < .001, **p < .01, *p < .05 Traditional Gender Role Conservatism Endorsement .36*** .00 -.13* 10 Table 2 Regression Coefficient Table: Predictors of Disgust Toward Breastfeeding b SE Intercept 3.83 0.86 Traditional Gender Role Endorsement 0.05 0.09 Conservatism 0.55 0.27 β t p 4.45 < .001 .03 0.56 .58 .12 2.07 .039 Breastfeeding -0.72 0.15 -.28 -4.97 < .001 Knowledge Note. b = unstandardized regression coefficient predicting Y; SE = standard error; β = standardized regression coefficient predicting Y; t = t-value; p = p-value. REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT AgePref_3 /METHOD=ENTER Age BFF. Regression Notes Output Created 19-FEB-2024 10:27:22 Comments Input Data /Users/yousefrashad/Do wnloads/Stats_Class_Dat aset (8).sav Active Dataset DataSet1 Filter Weight Split File N of Rows in Working Data File Missing Value Handling Definition of Missing User-defined missing values are treated as missing. Cases Used Statistics are based on cases with no missing values for any variable used. REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT AgePref_3 /METHOD=ENTER Age BFF. Syntax Resources 425 Processor Time 00:00:00.04 Elapsed Time 00:00:00.00 7728 bytes Page 1 Resources Notes Memory Required 7728 bytes Additional Memory Required for Residual Plots 0 bytes Descriptive Statistics Mean Please rate how willing you are to date someone who is: – Five years older than you Std. Deviation N 4.94 1.810 359 Please report your age 21.4318 3.93242 359 How many best friends do you have, not including family members or romantic partners? 2.6267 1.98034 359 Correlations Please rate how willing you are to date someone who is: – Five years Please report older than you your age Pearson Correlation Sig. (1-tailed) How many best friends do you have, not including family members or romantic partners? Please rate how willing you are to date someone who is: – Five years older than you 1.000 .103 .054 Please report your age .103 1.000 -.090 How many best friends do you have, not including family members or romantic partners? .054 -.090 1.000 Please rate how willing you are to date someone who is: – Five years older than you . .026 .152 Please report your age .026 . .044 How many best friends do you have, not including family members or romantic partners? .152 .044 . 359 359 359 Page 2 Correlations Please rate how willing you are to date someone who is: – Five years Please report older than you your age N How many best friends do you have, not including family members or romantic partners? Please rate how willing you are to date someone who is: – Five years older than you 359 359 359 Please report your age 359 359 359 How many best friends do you have, not including family members or romantic partners? 359 359 359 Variables Entered/Removed a Model Variables Entered Variables Removed How many best friends do you have, not including family members or romantic partners?, Please report your age b 1 Method . Enter a. Dependent Variable: Please rate how willing you are to date someone who is: – Five years older than you b. All requested variables entered. Model Summary Model 1 R R Square Adjusted R Square Std. Error of the Estimate .121 a .015 .009 1.802 a. Predictors: (Constant), How many best friends do you have, not including family members or romantic partners?, Please report your age Page 3 ANOVAa Sum of Squares Model 1 Regression df Mean Square 17.139 2 8.570 Residual 1155.512 356 3.246 Total 1172.652 358 F Sig. 2.640 .073 b a. Dependent Variable: Please rate how willing you are to date someone who is: – Five years older than you b. Predictors: (Constant), How many best friends do you have, not including family members or romantic partners?, Please report your age Coefficients a Unstandardized Coefficients B Model 1 Std. Error (Constant) 3.715 .555 Please report your age .050 .024 How many best friends do you have, not including family members or romantic partners? .059 .048 Standardized Coefficients Beta t 6.689
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