Data Screening
The first step of the data screening process was to check for missing data. Kang (2013) says that missing data—no matter the amount—can present various problems. It may reduce statistical power (the probability that a test will reject a false null hypothesis); the missing data can cause estimation bias on the parameters, and can also reduce sample representativeness. The only piece of data missing in the data set was the Emotional Self-Efficacy Scale value for identifying and understanding (ESES_Identifying) for participant number 205. This missing data had a significant effect on the total score on the ESES. Therefore, the best thing to do was to delete the entire record.
Before the record was deleted, the sample size was 232. The resultant sample size after the deletion was 231. The data set had two types of demographic variables: gender and age; however, this analysis will use only gender as the demographic variable because it is a grouping variable grouped into two (1 – male, 2 – female) and thus it can be a perfect variable for a parametric test after proving that the data is parametric using Shapiro-Wilk and Kolmogorov-Smirnov (KS) tests of normality. If the test proves normality, the data can be treated as parametric (Cummiskey et al., 2012). If the Shapiro-Wilk significance value is larger than 0.05, the data is considered normal (Bakker & Wicherts, 2014); if the value is below 0.05, there is a significant deviation of the data from the normal distribution (Macdonald, 1999; Wheelan, 2013). Similarly, the significance values of the KS test indicate normality if they are greater than 0.05 (Ghahari et al., 2017). The following table shows the results of the normality test.
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Table 1 Test of Normality
Tests of Normalityb,d,e
Gender
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Mean Mach score
Man
.111
100
.074
.974
100
.044
Woman
.083
130
.084
.987
130
.234
Total score on the ESES
Man
.056
100
.200
.991
100
.717
Woman
.073
130
.087
.990
130
.445
Agreeableness
Man
.072
100
.200
.989
100
.615
Woman
.083
130
.082
.981
130
.072
All the significance values of the Shapiro-Wilk test are greater than 0.05 (an indication of a normal distribution) apart from men’s value for Mean Mach score which shows (p = 0.044) which shows a slight deviation from the normal distribution. All the KS test significance values are greater than 0.05; this means that the values are normally distributed. Therefore, the data can be considered parametric and parametric tests can be used to analyze the data. See Appendix section for further proof of normality by use of histograms and box plots. The distributions in the histograms are bell-shaped.
Table 2 Homogeneity of Variances
Test of Homogeneity of Variances
Levene Statistic
df1
df2
Sig.
Total score on the ESES
Based on Mean
.562
1
228
.454
Mean Mach score
Based on Mean
.907
1
228
.342
Agreeableness
Based on Mean
.134
1
228
.715
Table 2 shows the homogeneity of variances based on the mean. In this table, our primary concern is the significance value: if the significance value is greater than 0.05 (p>0.05), the group variances are considered equal (homogeneity of variances); however, if p<0.05, homogeneity of variances assumption has been violated (Lee, 2010; Noguchi & Gel, 2010). For all three variables, the assumption of homogeneity of variance has been confirmed (Tyrell, 2008).
Descriptive Statistics
These are the descriptive statistics of EI, Mach, and agreeableness presented on a summary table.
Table 3 Mean (SD) scores for Mach, EI, and agreeableness
Mean (SD)
All
Men
Women
Mach
2.62 (0.42)
2.41 (0.45)
2.56 (0.37)
EI
110.07 (18.22)
107.38 (18.18)
112.14 (18.14)
Agreeableness
38.84 (5.57)
36.90 (5.30)
40.35 (5.34)
Inferential Statistics
In this section, the hypothesis testing will be performed. There are three hypotheses in total and each of the hypotheses will use a different test statistic. However, in all the three hypothesis tests, a common level of significance will be used and, in this case, α = 0.05 will be used. The level of significance will determine whether the hypothesis will be rejected or upheld (Sun et al., 2010). The tests will yield significance values (also known as p-values). The general rule of thumb is that, if the p-value is smaller than the level of significance, the null hypothesis is rejected; otherwise, the null hypothesis is upheld (Wheelan, 2013; Wasserman, 2013; Tyrell, 2008). The α = 0.05 does not only help in determining whether to reject or uphold the null hypothesis but also helps in restricting the possibility of rejecting a true null hypothesis (Type I error) to only 5% (Schumm et al., 2013). Furthermore, α = 0.05 helps establish statistically significant differences such that a p-value of less than 0.05 indicates statistically significant differences (Wheelan, 2013).
H1a: There will be significant group differences between men and women on emotional intelligence.
An Independent sample t-test will be used to analyze this hypothesis (Warner, 2012). Also known as the two-sample t-test, it is an inferential test-statistic that helps researchers to determine whether there are statistically significant differences between the means of two groups that are unrelated. According to Yildirim (2012), to conduct a two-sample t-test, the following conditions must be met: there must be an independent categorical variable having two groups or levels and a continuous dependent variable. In this case, the independent categorical variable is gender (1 – male, 2 – female), and the continuous dependent variable is emotional intelligence. The groups are unrelated and paired as promised, meaning that it is not possible for a member of one group to be a member of the other groups at the same time. For example, one can either be male or female and not both.
The following assumptions have to be made during an independent sample t-test: the dependent variable is normally distributed and homogeneity of variance. Table 1 confirms normal distribution and Table 2 confirms homogeneity of variance. Unequal variances can affect the rate of Type I error (Macdonald, 1999; “Assumptions in Parametric Tests,” 2019). Table 4 below shows the results of the two-sample t-test.
Table 4 Independent Sample T-Test
t
df
Sig. (2-tailed)
Total score on the ESES
Equal variances assumed
-1.970
228
.050
Equal variances not assumed
-1.970
212.847
.050
Mean Mach score
Equal variances assumed
2.583
228
.010
Equal variances not assumed
2.535
195.891
.012
There will be no significant group differences between men (M=117.38, SD=18.18) and women (M=112.14, SD=18.14) on emotional intelligence, t(228)= -1.970, p = 0.050.
H1b: There will be significant group differences between men and women on Mach.
Based on the results of Table 4, it can be concluded that there will be significant group differences between men (M=2.71, SD=0.45) and women (M=2.56, SD=0.39) on mean Mach score, t(228)= 2.583, p = 0.010.
H2a: There will be an inverse correlation between emotional intelligence and Mach.
For H2a and H2b the test statistic that will be used will be Pearson’s correlation because the main agenda is to determine the strength and direction of the relationship between emotional intelligence, Mach, and agreeableness. As much as α = 0.05 can be used to reject or uphold a hypothesis statement in a Pearson’s correlation, it is the coefficient of correlation (r) that plays the major role. The correlation coefficient ranges from +1 (perfect positive correlation) through 0 to -1 (perfect negative correlation) (-1≤r≤+1). Generally, a correlation coefficient of 0.1-0.29 signifies a very weak correlation; 0.30-0.49 signifies a weak correlation; 0.50-0.69 signifies a moderate correlation, and a strong correlation is that of r=0.70 and above. r = 0 means that there is no correlation. Positive correlations are direct correlations (both variables are moving in the same direction; an increase in one variable, leads to an increase in another variable) while negative correlations are inverse correlations (an increase in one variable leads to a decrease in another variable) (Warner, 2013; Olive, 2017). Table 5 shows the correlations.
Table 5 Correlations
Correlations
Mean Mach score
Agreeableness
Total score on the ESES
Mean Mach score
Pearson Correlation
1
-.249**
-.249**
Agreeableness
Pearson Correlation
-.249**
1
.415**
Total score on the ESES
Pearson Correlation
-.249**
.415**
1
**. Correlation is significant at the 0.01 level (2-tailed).
The correlation between emotional intelligence and Mach is -.249**. This is a weak negative correlation. Therefore, it can be concluded that there is an inverse correlation between emotional intelligence and Mach. Because the significance values in all the correlations is p<0.01, the hypothesis stays as it is. An increase in emotional intelligence’ leads to a decrease in Mach and an increase in Mach, leads to a decrease in emotional intelligence.
H2b: There will be inverse correlations between agreeableness and Mach.
According to Table 5, the correlation between agreeableness and Mach is -.249**. Therefore, it can be concluded that the correlation between agreeableness and Mach is inverse. An increase in agreeableness, leads to a decrease in Mach; an increase in Mach, leads to a decrease in agreeableness.
H3: Emotional intelligence will show significant contributions to Mach, after controlling for agreeableness as a covariate.
In this hypothesis, the best statistical test is a linear multiple regression. After correlation, the next step is usually to perform a linear regression (Wheelan, 2013). Linear regression is used in predicting the value of one variable using other variables (Warner, 2012). The variable to be predicted is called the outcome variable (dependent variable); the variable used in prediction is called the predictor variable (independent variable) (Tyrell, 2008). In this case, the outcome variable is Mach and the predictor variables are emotional intelligence and agreeableness. The covariate variable is agreeableness; a covariate variable is a measurable variable considered to be correlated with the dependent variable. In this case, the covariate variable acts as a complementary independent variable. Table 6 is the linear regression table.
Multiple regression also uses α = 0.05 to determine the fate of the hypothesis statement (Strizhitskaya, 2019). When p<0.05, the regression model can statistically significantly predict the outcome variable; in other words, the model is a good fit for the data (Olive, 2017).
Table 6 Emotional Intelligence and Agreeableness Predictors of Mach
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B (SE)
Beta
1
(Constant)
3.584 (.207)
17.291
.000
Total score on the ESES
-.004 (.002)
-.176
-2.537
.012
Agreeableness
-.013 (.005)
-.176
-2.535
.012
- Dependent Variable: Mean Mach score
The multiple regression equation is as follows:
The fact that the p-value is less than α = 0.05 on all occasions; therefore, it can be concluded that the regression model can statistically significantly predict the outcome variable and the model is a good fit for the data.
Table 7 Model Summary
Model
R
R Square
Adjusted R Square
1
.297a
.088
.080
- Predictors: (Constant), Agreeableness, Total score on the ESES
The r is .297—moderate correlation. Even though the regression model can statistically significantly predict the outcome variable, only 8.8% of the total variation in Mach can be explained by both emotional intelligence and agreeableness.
Conclusion
The mean Mach score of men and women are significantly different. The inverse correlation between emotional intelligence and Mach means that when one’s emotional intelligence rises, their Mach score decreases; inversely, when one’s Mach score increases, their emotional intelligence drops. The inverse correlation between agreeableness and Mach means that when agreeableness increases, Mach score drops and vice versa. The regression models shows that the predictor variables (emotional intelligence and agreeableness) can statistically significantly (results are unlikely due to chance) predict Mach score and is hence a model fit (new data can be used to make similar conclusions).
References
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Bakker, M., & Wicherts, J. M. (2014). Outlier removal, sum scores, and the inflation of the type I error rate in independent samples t tests: The power of alternatives and recommendations. Psychological Methods, 19(3), 409-427. https://doi.org/10.1037/met0000014
Cummiskey, K., Kuiper, S., & Sturdivant, R. (2012). Using Classroom Data to Teach Students about Data Cleaning and Testing Assumptions. Frontiers in Psychology, 3. https://doi.org/10.3389/fpsyg.2012.00354
Ghahari, S., Farhanghi, Z., & Gheytarani, B. (2017). The effectiveness of teaching positive psychology on dysfunctional attitudes and emotional self-regulation of withdrawing addicts. European Psychiatry, 41, S410. https://doi.org/10.1016/j.eurpsy.2017.01.345
Kang, H. (2013). The prevention and handling of the missing data. Korean Journal of Anesthesiology, 64(5), 402. https://doi.org/10.4097/kjae.2013.64.5.402
Lee. (2010). A Monte Carlo Study of Seven Homogeneity of Variance Tests. Journal of Mathematics and Statistics, 6(3), 359-366. https://doi.org/10.3844/jmssp.2010.359.366
Macdonald, P. (1999). Power, Type I, and Type III Error Rates of Parametric and Nonparametric Statistical Tests. The Journal of Experimental Education, 67(4), 367-379. https://doi.org/10.1080/00220979909598489
Noguchi, K., & Gel, Y. R. (2010). Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives. Journal of Nonparametric Statistics, 22(7), 897-913. https://doi.org/10.1080/10485251003698505
Olive, D. J. (2017). Multiple Linear Regression. Linear Regression, 17-83. https://doi.org/10.1007/978-3-319-55252-1_2
Schumm, W. R., Pratt, K. K., Hartenstein, J. L., Jenkins, B. A., & Johnson, G. A. (2013). Determining statistical significance (alpha) and reporting statistical trends: controversies, issues, and facts1. Comprehensive Psychology, 2(1), Article 10. https://doi.org/10.2466/03.cp.2.10
Strizhitskaya, O. (2019). Perceived Stress and Psychological Well-Being: The Role of The Emotional Stability. https://doi.org/10.15405/epsbs.2019.02.02.18
Sun, S., Pan, W., & Wang, L. L. (2010). A comprehensive review of effect size reporting and interpreting practices in academic journals in education and psychology. Journal of Educational Psychology, 102(4), 989-1004. https://doi.org/10.1037/a0019507
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Warner, R. M. (2012). Applied Statistics: From Bivariate Through Multivariate Techniques: From Bivariate Through Multivariate Techniques. SAGE.
Wasserman, L. (2013). All of Statistics: A Concise Course in Statistical Inference. Springer Science & Business Media.
Wheelan, C. (2013). Naked Statistics: Stripping the Dread from the Data. W. W. Norton & Company.
Yildirim, E. (2012). The Investigation of the Teacher Candidates’ Attitudes Towards Teaching Profession According to their Demographic Variables (The Sample of Maltepe University). Procedia – Social and Behavioral Sciences, 46, 2352-2355. https://doi.org/10.1016/j.sbspro.2012.05.483
Appendix
Test of normality
Tests of Normalityb,d,e
Gender
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Mean Mach score
Man
.111
100
.074
.974
100
.044
Woman
.083
130
.084
.987
130
.234
Total score on the ESES
Man
.056
100
.200
.991
100
.717
Woman
.073
130
.087
.990
130
.445
Agreeableness
Man
.072
100
.200
.989
100
.615
Woman
.083
130
.082
.981
130
.072
*. This is a lower bound of the true significance.
- Lilliefors Significance Correction
- Mean Mach score is constant when Gender = Other. It has been omitted.
- Total score on the ESES is constant when Gender = Other. It has been omitted.
- Agreeableness is constant when Gender = Other. It has been omitted.
Test of Homogeneity of Variances
Levene Statistic
df1
df2
Sig.
Total score on the ESES
Based on Mean
.562
1
228
.454
Based on Median
.566
1
228
.453
Based on Median and with adjusted df
.566
1
223.493
.453
Based on trimmed mean
.572
1
228
.450
Mean Mach score
Based on Mean
.907
1
228
.342
Based on Median
.854
1
228
.356
Based on Median and with adjusted df
.854
1
219.614
.356
Based on trimmed mean
.861
1
228
.354
Agreeableness
Based on Mean
.134
1
228
.715
Based on Median
.137
1
228
.712
Based on Median and with adjusted df
.137
1
226.564
.712
Based on trimmed mean
.126
1
228
.723
Histograms
Box Plots
Independent Sample T-test
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
Total score on the ESES
Equal variances assumed
-1.970
228
.050
-4.75846
2.41489
-9.51683
-.00010
Equal variances not assumed
-1.970
212.847
.050
-4.75846
2.41569
-9.52021
.00329
Mean Mach score
Equal variances assumed
2.583
228
.010
.14201
.05498
.03368
.25034
Equal variances not assumed
2.535
195.891
.012
.14201
.05603
.03151
.25250
Correlations
Correlations
Mean Mach score
Agreeableness
Total score on the ESES
Mean Mach score
Pearson Correlation
1
-.249**
-.249**
Sig. (2-tailed)
.000
.000
N
231
231
231
Agreeableness
Pearson Correlation
-.249**
1
.415**
Sig. (2-tailed)
.000
.000
N
231
231
231
Total score on the ESES
Pearson Correlation
-.249**
.415**
1
Sig. (2-tailed)
.000
.000
N
231
231
231
**. Correlation is significant at the 0.01 level (2-tailed).
Multiple Linear Regression
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
3.584
.207
17.291
.000
Total score on the ESES
-.004
.002
-.176
-2.537
.012
Agreeableness
-.013
.005
-.176
-2.535
.012
- Dependent Variable: Mean Mach score
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.297a
.088
.080
.40055
- Predictors: (Constant), Agreeableness, Total score on the ESES