Statistical Analysis Of Educational Studies

• In order to predict the length of the jump of a student with the help of height of the student, regression analysis will be conducted as regression analysis is the technique which is used to predict the future values of variable using the past data of the variable.
• The assumptions that has to be met before conducting a regression analysis are listed as follows:
• Normality:The residuals of the model are distributed normally.
• Linearity:Associations between explanatory variable (height) and response variable (length of jump) are linear.
• Homoscedasticity:The variability in the response variable is the same at all levels of the explanatory variable.
• Independence: The observations are not correlated to each other.
• Multicollinearity: In cases, where there are more than one explanatory variable involved in the model, the explanatory variables must be independent of each other.  

• The statistical test that has been used to find out whether the attitude towards English before and after using newspapers in education has been enhanced is paired t-test.
• The assumptions that should be met before conducting the paired t-test are given as follows:
• The dependent variable involved in the test must be a continuous variable.
• The observations involved in the study must be independent to each other.
• The dependent variable involved in the study must be distributed normally.
• There should not be any outliers in the dependent variable.
• Let be the true mean difference between the posttest and the pretest scores.

Null Hypothesis: The average of the post test scores are not enhanced significantly.

• Alternative Hypothesis:The average of the post test scores are enhanced significantly

• From table 2, it can be seen that the significance value is less than 0.05, which is the default level of significance. Thus, the null hypothesis is rejected. Hence, it can be said that the attitude towards English has been enhanced when the students were taught to use newspapers in education.

• The statistical test that has been used to test the logical reasoning ability of male and female undergraduates is the independent two sample t test.
• The null hypothesis for this test can be stated as:

There is no significant difference in the logical reasoning ability of male and female undergraduates.

• The p-value has been found to be 0.0005 (< 0.05, the level of significance). Thus, the null hypothesis is rejected and it can be concluded that the logical reasoning ability of females are significantly higher than that of men.

• The statistical tests that has been used in this analysis has been used to test for the normality of the scores of male and female.
• Kolmogorov Smirnov test is used to test the normality of two groups where the population mean and variance are specified whereas the Shapiro Wilk test is used to test the normality of two groups where the population mean and variance are not specified.
• Both the Kolmogorov-Smirnov test and the Shapiro-Wilk test shows that the sig. values are less than 0.05. This indicates that the male and the female scores are not distributed normally.  

• The answers to the following questions have been provided from table 1.
• A research question that can be framed for this study is:

Was the program equally successful in benefitting the students in each of the groups of beginner, intermediate and advanced students?

• The average of the study skills for each of three groups of beginners, intermediate and advanced students were to be evaluated. ANOVA is the most appropriate technique to test the difference in the means of more than two groups.
• From the above table, it can be concluded that there are significant differences in the skills of the beginner, intermediate and advanced group of students of English as the significance value is 0.021 which is less than the level of significance (0.05).
• The assumptions for one-way ANOVA are given as follows:
• The variables selected for the study must be distributed independently and identically
• The dependent variable must be homoscedastic.
• The dependent variable must be distributed normally.
• The following answers are provided from table 2:
• From the table it can be seen that the average skill set of the students in the beginner group is higher than that of the students in the intermediate or advanced group. There is no significant difference in the skill sets of the intermediate and the advanced group of students but there is difference in the average skill set of the beginner group of students with the intermediate or the advanced group of students. It can also be said from the table with 95 percent confidence that the average study skills of the beginner group is between 25.02 to 29.38 and the average study skills of the intermediate and advanced group is overlapping.
• From the table. It can be seen that the standard deviation of each of the three groups of students are not much different from each other and are very less. This indicates that are not much deviation in the skill set of the students in each of the groups from the average skill set.
• The 95% confidence interval for mean indicates that there is a 95% change that the mean of the variable will lie within that interval.
• The following answers are provided from table 3:
• Multiple comparison indicates pairwise comparison of the levels of an attribute.
• From table 3, it can be said that study skill of beginner group is significantly higher than intermediate or advanced group. The study skill of intermediate group is not significantly different from that of advanced group.
• From the analysis conducted so far, it can be said that the program was not equally successful in benefitting students belonging to the beginners, intermediate and advanced groups.

• Three research questions for this study can be listed as follows:
• Is there any association between spatial reasoning and all the other attributes such as memory, metacognition, mathematical ability and verbal reasoning?
• Is there any association between memory with metacognition, mathematical ability and verbal reasoning?
• Is there any association between mathematical ability and verbal reasoning?
• From this study, it can be seen that there is a positive association between all the attributes. Among them, a strong positive association has been observed between metacognition and spatial reasoning, metacognition and memory and verbal reasoning with mathematical ability. A moderate positive association exists between memory and spatial reasoning, mathematical ability and spatial reasoning, mathematical ability and metacognition. A weak association exists between verbal reasoning and spatial reasoning.

The three different research objectives that can be constructed from the given case study is listed as follows:

• To estimate differences in the stress tolerance level between males and females.
• To estimate differences in the optimism level between males and females.
• To estimate differences in the emotional self-awareness level between males and females.

• There are no significant differences in the emotional intelligence between male and female students.
• There are no significant differences in the socioeconomic status of the group of students.
• There are no significant differences in the emotional intelligence of the students in the rural and urban schools.

• To test hypothesis (i), a two independent samples t-test has to be conducted
• To test hypothesis (ii), one-way analysis of variance (ANOVA) technique has to be performed.
• To test hypothesis (iii), a two independent samples t-test has to be conducted

For the independent two sample t-test, the following assumptions are considered:

• The variable emotional intelligence must be a continuous variable.
• The observations involved in the study must be independent to each other.
• The dependent variable emotional intelligence must be distributed normally.
• There should not be any outliers to emotional intelligence.

For the one-way Analysis of Variance (ANOVA) test, the following assumptions are considered:

• The variables selected for the study must be distributed independently and identically
• The dependent variable emotional intelligence must be homoscedastic.

The dependent variable emotional intelligence must be distributed normally.