Psychology 390

Data in Psychological Research: Lab 5

Due:April 8, 2013 by Noon

A researcher wanted to investigate whether friendship, optimism, academic success, and self worth were predictive of meaning in life in university students. Thirty students who agreed to participate in the study were administered the five measures. The obtained data is below.

  1. Input the following data into SPSS. Create a correlation matrix for the above variables (Include the output). Write up the significant correlations. Which of the variables are significantly correlated with “Meaning”?

Correlations
Meaning / Optimism / Friendship / Success / Selfworth
Meaning / Pearson Correlation / 1 / .563** / .659** / .587** / .074
Sig. (2-tailed) / .001 / .000 / .001 / .699
N / 30 / 30 / 30 / 30 / 30
Optimism / Pearson Correlation / .563** / 1 / .291 / .495** / .163
Sig. (2-tailed) / .001 / .119 / .005 / .388
N / 30 / 30 / 30 / 30 / 30
Friendship / Pearson Correlation / .659** / .291 / 1 / .450* / -.049
Sig. (2-tailed) / .000 / .119 / .013 / .795
N / 30 / 30 / 30 / 30 / 30
Success / Pearson Correlation / .587** / .495** / .450* / 1 / .453*
Sig. (2-tailed) / .001 / .005 / .013 / .012
N / 30 / 30 / 30 / 30 / 30
Selfworth / Pearson Correlation / .074 / .163 / -.049 / .453* / 1
Sig. (2-tailed) / .699 / .388 / .795 / .012
N / 30 / 30 / 30 / 30 / 30
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).

A Pearson’s correlation was performed and several significant correlations were found.

  • Meaning was significantly positively correlated with Optimism, r(28)=.563, p<.002.
  • Meaning was significantly positively correlated with Friendship, r(28)=.659, p<.001.
  • Meaning was significantly positively correlated with Success, r(28)=.587, p<.002.
  • Optimism was significantly positively correlated with Success, r(28)=.495, p<.006
  • Friendship was significantly positively correlated with Success, r(28)=.450, p<.014
  • Success was significantly positively correlated with Self Worth, r(28)= .453, p<.013
  1. Run a multiple linear regression using the “Enter” method . Which, if any, of the predictors are significant? Which, if any of the predictors are not significant? Create a standardized and non-standardized regression equation.Plug the data from the first participant into both equations. How do your predictions compare to the first participant’s “meaning” score? Explain the differences.

Coefficientsa
Model / Unstandardized Coefficients / Standardized Coefficients / t / Sig.
B / Std. Error / Beta
1 / (Constant) / -3.248 / 8.269 / -.393 / .698
Optimism / .669 / .295 / .318 / 2.267 / .032
Friendship / .649 / .189 / .468 / 3.428 / .002
Success / .694 / .477 / .219 / 1.454 / .158
a. Dependent Variable: Meaning

Predictors:

Optimism: Sig – β = .318, p=.032

Friendship: Sig – β = .468, p = .032

Success: Not Sig – β = .219, p = .158

Unstandardized:

Standardized

For the unstandardized equation, the prediction (34.833) is not very far off from the participant’s actual Meaning score (34). This is because our overall model is significant an accounts for 61.6% of the participant’s meaning score. The standardized equation prediction (17.349) is less than half of the participant’s actual score. This is because we put unstandardized data into a standardized equation. The standardized equation is “out of context” of the data.

  1. What is the R2 for the model? Is the overall model significant?

R2=.620, p<.001, therefore the overall model is significant.

  1. What is the effect size of the overall regression? Cohen (1988) suggested that R2values of 0.02, 0.13, and 0.26 correspond to small, medium, and large effect sizes respectively. How would you classify the obtained effect size?

The effect size is .620. This corresponds to a large effect size.

  1. Rerun a multiple linear regression using the “Stepwise” method. Create a standardized and non-standardized regression equation. How do these equations differ from those created in question 2? Plug the data from the first participant into the unstandardized equation. How does your value compare to that of question 2 and to the original Meaning score? Explain the differences.

Coefficientsa
Model / Unstandardized Coefficients / Standardized Coefficients / t / Sig.
B / Std. Error / Beta
1 / (Constant) / 17.970 / 6.580 / 2.731 / .011
Friendship / .913 / .197 / .659 / 4.638 / .000
2 / (Constant) / .016 / 8.121 / .002 / .998
Friendship / .750 / .180 / .541 / 4.176 / .000
Optimism / .852 / .272 / .405 / 3.126 / .004
a. Dependent Variable: Meaning

Unstandardized:

The initial standardized equation was a good estimate of the participant’s meaning score (34.833), however it overestimated the meaning because it included a non-significant predictor. The second regression equation using only significant predictors is a slight underestimation of the participant’s meaning score (31.816) , but does not include non-significant predictors and is therefore, overall, a better model.

Standardized: