# Correlation and T-Test in Psychological Statistics

## Correlation Test

To establish the nature of correlation that exists between mindfulness and two forms of happiness, namely, subjective happiness and Oxford happiness, Spearman’s correlation test was used. According to Coolican (2014), Spearman’s correlation test is suitable in the analysis of ordinal data because it is a nonparametric test, which assesses the extent of dependence between two variables. Since Spearman’s correlation test ranks measurements before analysing their dependence, it gives an accurate correlation of nonparametric data. As scales, such as subjective happiness scale, mindfulness scale, and Oxford happiness scale, collect data in ordinal form, Spearman’s correlation test is appropriate in analysing their dependence. The Spearman’s correlation test gives a correlation coefficient, which is a value that ranges from -1 to +1. The correlation coefficient gives the nature of dependence or relationship that exists between two variables.

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The hypothesis of the study is that mindfulness has significant positive correlation with subjective happiness and Oxford happiness. The test of the hypothesis using Spearman’s correlation, one-tailed test, indicates that mindfulness has significant positive correlation with subjective happiness, (rs = 0.472, p = 0.001) and Oxford happiness, (rs = 0.590, p = 0.000). The positive correlation between mindfulness and subjective happiness is moderate, whereas the positive correlation between mindfulness and Oxford happiness is very strong. Analysis of correlation coefficients reveals that mindfulness correlates more with Oxford happiness than subjective happiness. However, since the p-values are less than 0.05, the correlation tests show that mindfulness has significant positive correlation with subjective happiness and Oxford happiness.

### Data Analysis: Spearman’s Correlation

Correlation between Mindfulness and Subjective Happiness

 Correlations Five Facet Mindfulness Questionnaire Subjective Happiness Scale Five Facet Mindfulness Questionnaire Pearson Correlation 1 .472 Sig. (1-tailed) .001 N 39 39 Subjective Happiness Scale Pearson Correlation .472 1 Sig. (1-tailed) .001 N 39 39

Correlation between Mindfulness and Oxford Happiness

 Correlations Five Facet Mindfulness Questionnaire Oxford Happiness Questionnaire Five Facet Mindfulness Questionnaire Pearson Correlation 1 .590 Sig. (1-tailed) .000 N 39 39 Oxford Happiness Questionnaire Pearson Correlation .590 1 Sig. (1-tailed) .000 N 39 39

### Descriptive Statistics

 Descriptives Statistic Std. Error Oxford Happiness Questionnaire Mean 4.1370 .09123 95% Confidence Interval for Mean Lower Bound 3.9524 Upper Bound 4.3217 5% Trimmed Mean 4.1529 Median 4.1034 Variance .325 Std. Deviation .56972 Minimum 2.21 Maximum 5.38 Range 3.17 Interquartile Range .72 Skewness -.730 .378 Kurtosis 2.369 .741 Five Facet Mindfulness Questionnaire Mean 118.9744 3.40308 95% Confidence Interval for Mean Lower Bound 112.0852 Upper Bound 125.8635 5% Trimmed Mean 118.9259 Median 117.0000 Variance 451.657 Std. Deviation 21.25223 Minimum 68.00 Maximum 164.00 Range 96.00 Interquartile Range 31.00 Skewness .044 .378 Kurtosis -.155 .741 Subjective Happiness Scale Mean 19.6154 .58388 95% Confidence Interval for Mean Lower Bound 18.4334 Upper Bound 20.7974 5% Trimmed Mean 19.7123 Median 19.0000 Variance 13.296 Std. Deviation 3.64631 Minimum 10.00 Maximum 27.00 Range 17.00 Interquartile Range 6.00 Skewness -.281 .378 Kurtosis -.162 .741

## T Tests Repeated Measure Design. Analyse Comparing Means, Head Samples as Same People Generated

Given that the blindness study consists of four related measurements, the appropriate form of test statistic, which can analyse collected data, is paired-samples t-test. The four related measurements provide different pairs of data, which paired-samples t-test can analyse by comparing means. Weinberg and Abramowitz (2008) state that paired-samples t-test is suitable in comparing the means of two related groups. The related groups in this case are the three pairs of measurements, namely, Q1 and Q2, Q2 and Q3, and Q3 and Q4, which are obtained from the four related measurements in the blind study.

The hypothesis of the blind study is that there are significant differences between means of Q1 and Q2, Q2 and Q3, and Q3 and Q4. The paired-samples t-test indicated that there were significant differences between means of Q1 and Q4 (t(64) = -22.688, p = 0.000), Q2 and Q3 (t(64) = -15.355, p = 0.000), and Q3 and Q4 (t(64) = -13.817, p = 0.000).

### Pairs of Measurements

Pair 1: Q1 and Q4

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Pair 2: Q2 and Q3

Pair 3: Q3 and Q4

### Data Analysis

 Paired Samples Test Paired Differences t df Sig. (2-tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Q1 – Q4 -7906.8516 2809.68083 348.49802 -8603.0564 -7210.6467 -22.688 64 .000 Pair 2 Q2 – Q3 -3043.8971 1598.25131 198.23868 -3439.9244 -2647.8698 -15.355 64 .000 Pair 3 Q3 – Q4 -3057.4225 1784.07109 221.28678 -3499.4937 -2615.3514 -13.817 64 .000
 Paired Samples Correlations N Correlation Sig. Pair 1 Q1 & Q4 65 .758 .000 Pair 2 Q2 & Q3 65 .796 .000 Pair 3 Q3 & Q4 65 .831 .000

## References

Coolican, H. (2014). Research Methods and Statistics in Psychology. New York: Psychology Press.

Weinberg, S., & Abramowitz, S. (2008). Statistics using SPSS: an integrative approach. New York: Cambridge University Press.

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