# Correlation and Regression: Assertiveness and Anger

## Correlations

### Relationship between assertiveness and the tendency to express anger openly

What are the means and standard deviations of the two variables, “rath” and “about”?

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For a total of 65 subjects, the mean for “rath” is 3.3902 with a standard deviation of.4330. On the other hand, 63 subjects had a mean of 2.1071 for “axout” with a standard deviation of.4276 (Table 1).

What is the Pearson r?

The Pearson correlation r between “rath” and “axout” is r =.286.

What is the p-value (“significance level”)? What does this p-value mean?

The 2-tailed significance value for this Pearson r is.023, which is less than.05, indicating that there is a significant relationship between “rath” and “axout”. It is therefore evident that there is a statistically significant relationship between assertiveness and the tendency to express anger openly (Table 2).

How does the n (sample size) of this sample affect the r and p values?

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Field (2009) explains that the larger the sample size, the more true the reflection of the strength of the relationship between two variables. As such, a larger sample size, n, is likely to increase the value of r perhaps to a figure that is greater than.5 thus indicating a strong relationship between “rath” and “axout”. At the same time, the p-value is deemed to reduce further below the significance level of.05, thus indicating a more statistically significant relationship. Reducing the sample size on the other hand reduces r and is likely to increase p values thus giving a false reflection of the relationship between the two variables.

## Regression

### Relationship between assertiveness and whether one holds anger “in”

#### R and it’s meaning

According to Table 4, there is a negative correlation between Crowne-Marlowe and axin, r = -.246. R is the correlation coefficient between the variables, in this case, the correlation between assertiveness and holding anger “in.” The R-value for this model is.246 indicating that there is a negative but weak relationship between the tendency to hold anger “in” and assertiveness. In other words, the correlation between assertiveness and holding anger “in” is.246 (Table 5).

#### R2 and it’s meaning

The R squared value for this model is.061 which indicates that 6.1 percent of holding anger “in” is contributed by the individual’s assertiveness (Table 5). This is because the R squared value is used to determine the proportion of variance explained by the model (predictor).

#### F and it’s meaning

The F-test value for this model is 4.073 and the F-test determines the statistical significance of the model whereby if the F-test is significant, then the model is termed as fit. In this model, the F value is significant p =.048 (Table 6) indicating that an individual’s assertiveness is a significant variable in predicting the individual’s tendency to hold anger “in.”

The F ratio (4.073) means that fitting in the model (i.e. considering assertiveness) leads to a 4.073 increase in the tendency to hold anger “in.” The p-value associated with the F value is.048 i.e. F (1, 63) = 4.073, p =.048). The p-value (significance value) indicates that the F value is statistically significant. In other words, there is a statistically significant change in holding anger “in” as a result of an individual’s assertiveness.

#### Standard coefficient

The standard coefficient for the variable axin is -.246. The standard coefficient for the variable axin is significant because the value is below.05, i.e. p =.048 (Table 7).

Significance means that the variables obtained from the computations can be relied upon to explain the relationship between the variables being examined. In other words, one unit change in axin causes a -.246 change on Crowne-Marlowe.

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The standardized coefficients are the same as the Beta coefficients and it helps in the direct comparison of the strength of one variable against another variable. It is possible to do a comparison of a Beta (standardized) coefficient against another standardized coefficient since they are determined in standard deviations. However, with the unstandardized coefficients, it is impossible to give a direct comparison between two variables since these are not measured in standard deviations. Instead, it is only possible to state that a one-unit change in the predictor variables results in a given unit change in the outcome variable (Siegel, 2011).

#### Confidence interval

The confidence interval (CI) for axin is 95% CI (-.083 -.000) indicating that the value of the regression coefficients in the population falls within -.083 and.000 (Table 7). The confidence intervals values produced for unstandardized regression coefficients help determine the likely value of the regression coefficients in the population.

#### Summary

From the above analyses and interpretations, it can be said that the more an individual is assertive, the less likely the individual is to hold anger “in.” In other words, assertive individuals tend to express anger more openly. Increased assertiveness leads to a decreased tendency to hold anger in.

## References

Field, A. (2009). Discovering statistics using SPSS. California, SAGE Publications Ltd.

## Appendix

Table 1: Mean and SD for “rath” and “axout”.

 Descriptive Statistics Mean Std. Deviation N rath 3.3902 .43300 65 axout 2.1071 .42766 63

Table 2: Pearson Correlation for “rath” and “axout”.

 Correlations rath axout rath Pearson Correlation 1 .286* Sig. (2-tailed) .023 N 65 63 axout Pearson Correlation .286* 1 Sig. (2-tailed) .023 N 63 63 *. Correlation is significant at the 0.05 level (2-tailed).

Table 3: Mean and Standard Deviation for Crowne-marlowe and Axin.

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 Descriptive Statistics Mean Std. Deviation N crowne-marlowe .6850 .07625 65 axin 2.2519 .44825 65

Table 4: Correlation between Crowne-marlowe and Axin.

 Correlations crowne-marlowe axin Pearson Correlation crowne-marlowe 1.000 -.246 axin -.246 1.000 Sig. (1-tailed) crowne-marlowe . .024 axin .024 . N crowne-marlowe 65 65 axin 65 65
 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 axina . Enter a. All requested variables entered. b. Dependent Variable: crowne-marlowe Table 5: Regression Analysis. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .246a .061 .046 .07448

Predictors: (Constant), axin.

 Table 6: ANOVA Test and F-Statistic ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression .023 1 .023 4.073 .048a Residual .349 63 .006 Total .372 64

Predictors: (Constant), axin.

Dependent Variable: crowne-marlowe.

 Table 7: Unstandardized and Standardized Coefficients. Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) .779 .048 16.348 .000 .684 .875 axin -.042 .021 -.246 -2.018 .048 -.083 .000 a. Dependent Variable: crowne-marlowe

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