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# Correlation analysis

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Correlation analysis attempts to study the relationship between variables that are unrelated (Mukaka, 2012). The analysis is based on statistical numbers known as the correlation coefficient, which range from -1 to +1. (Mukaka, 2012). A zero-correlation coefficient indicates that there is no linear relationship between variables. This study will use statistics to analyze the association between two variables on college students. Is there a relationship between a student's mental stability and their total college GPA?

Question for Research

This question generates the following Null (H0) and Alternative (HA) hypotheses: (H0): There is no link between a student's emotional stability and their college GPA.(HA): There is a significant relationship between student’s emotional stability and college GPA

Data used in to address this hypothesis was obtained from the internet via a companion website that contain data sets used in SPSS tutorials. The selected data set was a SPSS file named ‘graduate’ and it contained several variables on college students, from demographics through z-scores to discriminant scores. In the data set, we select the overall college GPA and the student emotional stability variables since they are the focus of our study. Both variables are ratio scales of measurement and the data set has a sample size (N) of 50 observations.

The two variables were observed independently, which means using a correlation coefficient of association would be appropriate. In this study, we will use descriptive statistics (mean, standard deviation, and range) as well as Pearson or Spearman rho correlations (r) depending on violation of the assumptions. The conditions for performing this test include, a normal distribution of variables, 2) independence of observations, 3) linear association, and 4) no extreme bivariate outliers.

These assumptions were tested by performing Shapiro-Wilk test for normal distribution, scatterplots for linear association and box plots for outliers. Table 1 shows that the overall college GPA data was normally distributed while that of student’s emotional stability was not. The normal Q-Q plots showed that the data for both variables are not linearly associated (Figure 1). The overall college GPA data has an outlier (Figure 2) while student emotional stability has no outliers (Figure 3). Due to the violation of several assumption, the study used Spearman correlation rather than the Pearson correlation since its more robust with assumption violation (Moore et al. 593; Hauke & Kossowski, 98). An alpha level of 0.05 will be considered statistical significant.

Table 1. Test for Normality

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

OVERALL COLLEGE GPA

.078

50

.200*

.969

50

.213

STUDENTS EMOTIONAL STABILITY

.155

50

.004

.912

50

.001

*. This is a lower bound of the true significance.

Lilliefors Significance Correction

Figure 1. Scatterplot showing linear association between the two variables

Figure 2. Box plot showing presence of outlier in the variable, overall college GPA

Figure 3. Box plot for variable student’s emotional stability

Results

Descriptive Statistics

The descriptive statistics analysis found a mean score of 3.51±0.26702 for the overall college gpa with data ranging from 2.8 to 3.94 scores. Student emotional stability had a mean score of 6.38±1.677, ranging from 4 to 9 scores (Table 2). The spreads of the data are 0.071 for GPA scores and 2.812 for emotional stability scores. This means that values of the GPA data are close to the mean compared to those of the emotional stability data.

Table 2. Descriptive statistics for the two study variables

Statistic

Std. Error

OVERALL COLLEGE GPA

Mean

3.5100

.03776

95% Confidence Interval for Mean

Lower Bound

3.4341

Upper Bound

3.5859

5% Trimmed Mean

3.5221

Median

3.5500

Variance

.071

Std. Deviation

.26702

Minimum

2.80

Maximum

3.94

Range

1.14

Interquartile Range

.36

Skewness

-.595

.337

Kurtosis

.045

.662

STUDENTS EMOTIONAL STABILITY

Mean

6.38

.237

95% Confidence Interval for Mean

Lower Bound

5.90

Upper Bound

6.86

5% Trimmed Mean

6.37

Median

6.00

Variance

2.812

Std. Deviation

1.677

Minimum

4

Maximum

9

Range

5

Interquartile Range

3

Skewness

.123

.337

Kurtosis

-1.211

.662

The correlation analysis was done to answer the hypothesis of the study. The Spearman’s rho correlation found that a weak correlation between overall college GPA scores and students emotional stability scores that was not statistically significant, r (48) = -.110, p < .05 (two-tailed), r2 =.0.0121). Thus, about 1% of the variance in student’s emotional stability would predict overall college GPA scores; this is a weak negative relationship. the direction of the weak relationship meant that as the student’s emotional score increase, their overall GPA score decrease. However, the null hypothesis ‘there is no significant relationship between student’s emotional stability and college GPA’ was not rejected and, hence student’s emotional stability does not relate to their overall college GPA scores.

Table 3. Spearman rho correlation showing the relationship between the two study variables

Overall College GPA

Students Emotional Stability

Spearman's rho

Overall College GPA

Correlation Coefficient

1.000

-.110

Sig. (2-tailed)

.

.448

N

50

50

Students Emotional Stability

Correlation Coefficient

-.110

1.000

Sig. (2-tailed)

.448

.

N

50

50

Conclusion

Spearman’s rho correlation was able to answer the hypothesis of this study. The analysis showed that there is no significant relationship between overall college gpa scores and students emotional stability. The Spearman rank-order correlation was, therefore, appropriate to address the concerns of this research. The analytical tests are justifiable making the results obtained to be valid for application in the paper to make our conclusion. Other than showing the no linear association between the overall college GPA and student’s emotional stability, the Spearman correlation coefficient predicted the strength of the association indicated by the closeness to zero (0) of the coefficient values. It is, therefore, clear about the importance of examining the requirement of a statistical approach as well as researchers need to justify the use of any particular statistical procedure for the purpose of ensuring accurate interpretation, which will produce highly reliable and valid conclusions. Noticeably, the advantage of this analysis was its ability to report the effect size of the data that showed the strength of the relationship. however, one identifiable limitation was its inability to explain the cause-effect (Rebekić, Lončarić, Petrović, & Marić, 2015).

Work Cited

Moore, David S., ‎ William I. Notz,‎ & Michael A. C. The Basic Practice of Statistics. W. H. Freeman; New Yolk, US.

Mukaka, M. M. ‘A guide to appropriate use of Correlation coefficient in medical research’, Malawi Medical Journal, 24 (3), 2012, 69–71.

Rebekić, A., Lončarić, Z., Petrović, S., & Marić, S. ‘Pearson’s or spearman’s correlation coefficient – which one to use ?’ Poljoprivreda, 21(2), 201, 47–54.

April 06, 2023
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