Statistics

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Statistics

Statistics Question # 5
a) The table -1 in the question paper indicates the moral reasoning scores before and after teaching the students. It can be seen in the table that the mean score of the students increased significantly from 18.5 before preparation to 23.86 after preparation. The standard deviation also reduced from 5.33 Statistics before preparation to 4.75 after preparation; the std. error mean also reduced. It can be concluded from the results that the students’ performance improved significantly on the moral reasoning test after the preparation.
b) Null Hypothesis
H0 = There is not a significant difference in the moral reasoning test performance after teaching the students.
c) Alternative Hypothesis
Ha = There is a significant difference in the moral reasoning test performance after teaching the students.
d) Paired Sample t-test
A paired sample t-test is used to analyze whether there is a difference between mean results of the same variable over two different conditions as in this case mean score of students has been analyzed before and after teaching (Zimmerman, 1997).
e) Results of Paired Sample t – test
The table – 2 in the question paper indicates the results of paired sample t-test for the mean score of students. It can be analyzed that the sig. value for the paired sample t-test is 0.000 which shows that the results are statistically significant to reject the null hypothesis and conclude that there is significant difference in the moral reasoning test performance after teaching the students.

Statistics Question # 6
a) Research Question
Which of the three groups i.e. beginners, intermediate and advanced speakers of English benefited most from the teaching program?
b) ANOVA Table
ANOVA is a statistical technique used to analyze the means of three or more variables using the quantitative data. It usually compares the mean of three or more variables or groups for same variable.
c) Conclusion from ANOVA Table
From the table provided, it can be noticed that the sig. level resulting from the analysis is 0.021 which is lower than 0.05. This shows that there is a statistically significant difference between the means of the groups at 95% confidence level.
d) Assumptions for Using One – Way ANOVA
In the view of Dowdy, Wearden & Chilko (2011) One – Way ANOVA is based on the following assumptions:
1. Response variables are normally distributed.
2. All the samples are independent.
3. Populations have equal variances.
4. Response variables are normal random variables and not the simple random variables.
e) Conclusion from Descriptive Table
The descriptive table indicates that the beginners have scored better than the other two groups. The standard deviation of the group is also low which indicates that this group learnt in a better way and scored higher.
f) Standard Deviation
As discussed earlier, the standard deviation of the beginners group is also low; it shows that the variation or deviation from the mean is lower for beginners.
g) The Meaning of 95% confidence Interval Mean
The 95% confidence interval mean shows the range in which the mean significant at 95% confidence level.
h) Multiple Comparison Test
The multiple comparison tests are used to compare the means of different groups with other groups and analyze whether there is a statistically significant difference between the mean of two groups (Hogg, McKean & Craig, 2005).
i) Interpretation of Multiple Comparison Test
The table in the question paper analyzes the difference in mean of three different groups. It has been found that there is a statistically significant difference between beginner and two other groups at 95% confidence level as the sig. value is lower than 0.05 between these groups. Whereas there is not statistically significant difference between intermediate and advanced group at 95% confidence level as indicated by sig. value of greater than 0.05.

Statistics Question # 7
a) Purpose of Tests Used
The statistical tests named Shapiro-Wilk test and Kolmogorov-Smirnov test are used test the normality of data (Razali & Wah, 2011).
b) Difference between two Tests
Despite same purpose of both tests used in this part, Statistics there is a key difference between the two; Shapiro-Wilk test is used to analyze the normality of data when the sample size is between 3 and 50. On the other hand Kolmogorov-Smirnov test is used when the sample size is greater than 50 (Razali & Wah, 2011).
c) Conclusion
It can be analyzed that the sig. value from results of Shapiro-Wilk test and Kolmogorov-Smirnov test is lower than 0.05 so it can be concluded that the data is not normally distributed it is either right or left skewed data.

Statistics Question # 8
a) Research Questions
1. Is there a significant correlation between the spatial reasoning, memory, metacognition,  Statistics mathematical ability and verbal reasoning?
2. Is the relationship negative or positive?
3. What is the extent or coefficient of relationship / correlation?
b) Analysis of Correlations Table
From the table provided, it can be analyzed that there is possible correlation between all the variables studied. Statistics can be noticed that the correlation for different variables varies from 0.3 to 0.7 which shows that there is a moderate to the high positive relationship between the variables studied…