Apply underastanding of the various statistical tests
Data Analysis Assignment
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Data Analysis Assignment
Question 1 – comparing 3 cohorts of students in terms of their self-reported age, gender and programme of study.
- Appropriate statistical methods for comparing age, gender and programme of study
For any statistical test, it is important to understand the data types of the variables.
Age – discrete variable
Gender – categorical variable with 2 levels
Programme of study is a categorical variable with more than two levels
Age and Programme of study
We can use stratified descriptive statistics to understand the distribution of age across the different programmes of study. Mean or median is used as the measure of central tendency based on the distribution shape of the age variable. Therefore, a one-way ANOVA will be appropriate to test whether there are significant differences between average ages across the different categories of the programme of study. If the distribution of age is skewed (not normally distributed), Kruskal Wallis test is used and a non-parametric test Bonferroni used to identify the specific difference if the test is statistically significant.
Gender and programme of study
Both of these variables are categorical variables and the use of contingency tables explains the distribution of gender categories across the different programme groups. A chi-square test is effective in testing for possible dependence between gender and selection of programme of study.
Null hypothesis: There is no statistical difference in mean ages across the study programme groups
Alternative hypothesis: At least one study programme groups have students with a mean age which is statistically significantly different from the others.
Age and programme of study
The histogram of age in years above shows a slight skewness of the age distribution with an average of 29.3 and a standard deviation of 5.8 years. Therefore, we use the one way ANOVA to test the difference in means.
The distribution of a number of students on different programmes varies significantly with most of the doing psychology.
The p-value of the one-way ANOVA test is greater than a 5% significance level. We conclude that there are statistically significant differences in mean ages across the different study programmes.
Gender and programme of study
We used the chi-square test of independence between gender and programme of study
Null hypothesis: Selection of the programme of study does not depend on gender
Alternative hypothesis: Selection of the programme of study depends on gender
In all the study programmes, female (64.72%) is more than the male (35.28%) students.
The chi-square test is not statistically significant which indicates that study programme selection does not dependent on gender.
Question 2 – Level of flourishing and level of perceived stress
- Hypothesis
- Pearson's correlation
- Linear regression
- Any problem with the analysis above
- Redoing the analysis in part A
Null hypothesis: There is no significant association between the level of flourishing and perceived stress
Alternative hypothesis: There is no significant association between the level of flourishing and perceived stress
There is a statistically significant (p-value < 0.001) correlation (0.98) between composite flourishing and perceived stress score.
The linear model of predicting perceived stress level using flourishing score is statistically significant at 95% confidence level. The predictor explains approximately 95% of the variation in the perceived stress score.
First, I investigate the distribution of the response variable to check if it meets the normality assumption.
The graph above shows that the response variable is highly skewed with extreme values of around negative 100. However, we do not expect to have such values because the data is an interval data and negative 100 is out of the bounds. After investigating the data, I found out that negative 99 was coded for missing values and make the definition, which leads solves the problem as shown in the histogram below.
The histogram above shows that the response variable is now normally distributed and it can be used in the linear regression model.
After redoing the correlation test, the results change significantly and they are as shown below.
The new correlation test after defining negative 99 as missing values indicate that there is no significant correlation between flourishing score and stressed score.
Further, the linear regression results also change significantly and as shown below, flourishing score is not a statistically significant predictor of perceived stress score.
Prediction for the flourishing score of 35.
Question 3
- Testing the functionality of random assignment
- Hypothesis
- Examining if there is framing effect
In this case, we have two variables, a categorical and discrete variable. We can use descriptive statistics to understand the distribution of the variable. Therefore, I propose the use of one-way ANOVA to test there significant differences in means between the two categories (Gain and Loss). This is a classical statistical test which assumes that the response variable; in this case, fear of statistics assumes a normal distribution. Therefore, we will use the histogram to understand the distribution before applying the one-way ANOVA. If the normality assumption is violated, we then choose to use the non-parametric version – the Kruskal Wallis test.
The histogram above shows that fear of statistics assumes a normal distribution. Therefore, we will use the parametric test – one-way ANOVA to test for the equality of means.
Null hypothesis: There are no differences in the average fear of statistics between the loss and gain groups
Alternative hypothesis: There are statistically significant differences in an average fear of statistics between the loss and gain groups
The p-value of the test is less than the significance level, we conclude that the means of the two groups are statistically different. Those in the main frame had a higher fear of statistics score compared to those in loss frame.
