Getting the statistical relationship between variables is important as it helps the researcher to get more information in regards to the variables involved. Some of the most important relationships that are important in statistics include the correlation and regression analysis in the variables. Correlation refers to the degree of the relationship that exists between two or more variables (Kapadia et al, 2017). If there are two variables to examine their respective relationship then this is known as the bivariate correlation. When there are more than two variables then their correlation may be termed as the partial correlation. It is also important to highlight that the variables, in this case, are known as the dependent and the independent variables. The independent variable is also called the x variable while the dependent variable is also referred to as the y variables. In the case of regression analysis, there are two types of regression model depending on the number of variables present. If there are two variables then it is called the simple regression model while if there are more than two regression model, then it is termed as the multiple regression models (Wackerly, et al, 2007).
The regression model is important since some of the variables may be predicted using it. Other statistical measures that cannot be assumed are the measures of central tendencies and those of dispersion. The different measure central tendencies are the mean, mode, and the median. The means is the average of the data set present; the mode is the most common value that can be observed in the data set while the median is the value that divides the data set into two equal parts. The measures of dispersion that exists include the variance, the standard deviation, range, the interquartile range etc. The variance and the standard deviation measures how precise the data set is. The range is the difference between the minimum and the maximum value. This paper is tasked with the analysis of the IAT score and to get the correlation of the implicit and the explicit attitudes. This will come handy with their respective interpretations.
Data analysis of the IAT score
In this section, we will be concerned in getting the different statistical measure that exists in the IAT scores. As earlier mentioned, this will be centered on the measures of the central tendencies and those of dispersion in the variable. It is important to highlight that this variable is of ratio scale and therefore these measures can easily be computed. The analysis will also involve the graphical representation of the variable. The following are the statistical output of the variables and the associated graphs. However, this will be only for the Japanese category.
Statistic Std. Error
Japanese Mean -.10443036014 .075808018250
95% Confidence Interval for Mean Lower Bound -.26256311522 Upper Bound .05370239494 5% Trimmed Mean -.10619134688 Median -.07366136200 Variance .121 Std. Deviation .347395981913 Minimum -.751525697 Maximum .575706731 Range 1.327232428 Interquartile Range .420476079 Skewness -.022 .501
Kurtosis -.252 .972
The mean of IAT scores of the Japanese category is -0.104 with an associated standard error of 0.076.The median in the category is -0.07.This value indicates the value that divides the data set into two equal parts. The variance and the standard deviation are 0.121 and 0.347 respectively. These values indicate how precise how the data set is and therefore it can be said that the measure of preciseness is as indicated by these values. Another important value to check is the skewness. It explains how skewed the data set is. According to the above table, it can be said that the skewness is -0.022 and therefore the data set of the IAT score of the Japanese scores is negatively skewed. This can also be seen from the stem and leaf plot and the histogram below.
Japanese Stem-and-Leaf Plot
Frequency Stem & Leaf
3.00 -0. 667
10.00 -0. 0001122334
7.00 0. 0001224
1.00 0. 5
Stem width: 1.000000
Each leaf: 1 case(s)
The above stem and leaf plot diagram shows that the data set is negatively skewed.
Below is the histogram associated with the dataset
A keen look at the histogram indicates that it is skewed to the left.
The following are the mean latencies and the standard deviation the Blocks 3, 4, 6, and 7
N Minimum Maximum Mean Std. Deviation
Block3 21 .575468609 1.059227723 .80106465105 .135980135068
Block4 21 .547057274 1.035255876 .70441637719 .130729485517
Block6 21 .614245728 1.460738578 .85216842738 .187424708057
Block7 21 .520310117 1.061968276 .73999252605 .134353208986
Valid N (listwise) 21 The mean of Block 3 is 0.801 while its associated standard deviation is 0.136.The mean of Block 4 is 0.704 and its associated standard deviation is 0.131.The mean of the 6th block is 0.852 and it's 0.187.Finally, the mean of the 7th block is 0.739 and its associated standard deviation is 0.134.It is also important to note that the mean and standard deviation of the 6th block is higher in comparison to the other blocks.
In terms of the differences of the means of the various blocks, the following statistical measures can be derived.
N Minimum Maximum Mean Std. Deviation
Block3and6 21 -.803932083 .252002983 -.05110377629 .210294350280
Block4adn7 21 -.328967965 .271245463 -.03557614886 .143071762721
Valid N (listwise) 21 The mean of the mean difference of the 3rd and the 6th block is -0.051 while its standard deviation is 0.210.The mean of the mean difference of the 4th and the 7th blocks is -0.036 and its standard deviation is 0.143.
Correlation analysis of the implicit and explicit attitudes
As earlier mentioned, correlation refers to the degree of relationship that may exist between different variables. Statistically speaking, a correlation value of 1 indicates that the degree of relationship is strong while if the value is -1 it shows that there is a strong negative correlation in the variables. In correlation, the p-value measures are important to be interpreted since it helps in determining if the variables are significant or not. This will be on the basis of the value of the p values that will be generated. When explaining correlation analysis, the regression analysis cannot be assumed. If the correlation value generated is negative, then it means that the value of the slope of the regression line is also negative. Likewise, if the value of the correlation of the values is positive then the slope of the regression line is also positive. We will determine the correlation coefficient s that exists in the variables on the basis of Questions 1, 2 and 3.These are Likert scales. The IAT score in the different question has been computed and therefore this will assist in determining the correlation that exists in the variables.
The following is correlation tables of the three questions.
Q1 Q2 Q3
Q1 Pearson Correlation 1 1.000** 1.000**
Sig. (2-tailed) .000 .000
N 31 31 31
Q2 Pearson Correlation 1.000** 1 1.000**
Sig. (2-tailed) .000 .000
N 31 31 31
Q3 Pearson Correlation 1.000** 1.000** 1
Sig. (2-tailed) .000 .000 N 31 31 31
**. Correlation is significant at the 0.01 level (2-tailed).
There exists a positive correlation is all the three Likert scales variables. The correlation coefficient is 1 in all the cases. The p values in all the cases are 0.0000 which is less than 0.05.This, therefore, means that the variables are significant and therefore cannot be assumed in getting the regression equation. In getting the regression equation, the IAT scores of the Japanese category will be used as the dependent variable while the there's Likert scale variable studied above will be used as the independent variables.
The following is the statistical output of the regression equation and the associated model.
Model R R Square Adjusted R Square Std. Error of the Estimate
1 1.000a 1.000 1.000 .000000000000
a. Predictors: (Constant), Q3
Model Sum of Squares Df Mean Square F Sig.
1 Regression 2.414 1 2.414 . .b
Residual .000 19 .000 Total 2.414 20 a. Dependent Variable: Japanese
b. Predictors: (Constant), Q3
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta 1 (Constant) .000 .000 . .
Q3 1.000 .000 1.000 . .
a. Dependent Variable: Japanese
The regression model is y=1.00 (Likert of Q3).This model is significant and therefore the p-value is very insignificant and therefore cannot be generated. The F statistics cannot be generated due to the 0 value in the means square error of the residual. The F statistic is generated by the division of the Mean square of the regression and that of the residual. The p-value is generated from the F statistic. The total degrees of freedom are 10.1 and are associated with the regression while 19 is associated with the residual.
Kapadia, A. S., Chan, W., & Moye, L. A. (2017). Mathematical statistics with applications. CRC Press.
Wackerly, D., Mendenhall, W., & Scheaffer, R. (2007). Mathematical statistics with applications. Nelson Education.
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