401077 Introduction To Biostatistics And Assessment Answers

Solution

The researchers used a sample of 4746 middle school and high school students. However, it is not clear how the sampling was done. The researchers have not mentioned the sampling techniques they applied, whether simple random, cluster, systematic or stratified sampling. Sampling used is important to be explained clearly to allow the respondents know whether the results can be generalized.

The researchers I did a good job by giving us the demographic characteristics of the respondents. For instance, they mentioned what proportion was represented by the males and females, the age brackets of the respondents, the ethnicity of the respondents and the socio-economic status of the students.

In terms of control for confounding that might have arose in the course of the study, the researchers have not mentioned to this end. The reader is made to assume that there were no any confounders that should have been controlled to avoid having biased results.

The researchers did not mention or rather highlighted whether they had issues to do with the missing data. Missing data also referred to as missing values, comes to play when there is no any data value stored for one or several variables in an observation. In research, missing data is a common occurrence that can have some significant effect on the results and conclusions made from the data.

When it came to analysis, the researchers conducted parametric tests for the inferential analysis. What is missing is their test of the required assumptions regarding the parametric tests. Parametric tests are not distribution free (they must comply with some assumptions) and violating any of the assumptions may result to biased results being reached at. Some of the assumptions associated with parametric tests include, linearity assumption, normality assumption, homogeneity assumption (also known as equal variances assumption) and independence assumption.

Question 2:

Present the findings of your descriptive analyses

Solution

The aim of this question was to try and answer the research question of whether the logarithm of MVPA predicts GPA after correcting for overweight in the population of Australian university students. We began by looking at the summary statistics of the two variables. For the logMVPA, the average was found to be 0.44 and the median was 0.52 (slightly higher than the mean). The minimum value was -0.52 while the highest value was 1.22 with a range of 1.75. The values of both the skewness and the kurtosis are negative (-0.49 and -0.46) respectively); this could mean negatively skewed data. See figure 1 below.

Figure 1: Histogram for logMVPA

On average, students were found to have a GPA score of 4.76 with a median score of 4.7. The highest GPA score for this group of students was 6.9 while the lowest score was 2.4. The summary statistics also gave the values of the skewness and kurtosis which were -0.08 and -0.44 respectively. With the skewness value close to zero, this implies that the data seems to have come from a normally distributed set. This notion can be confirmed from the histogram shown in figure 2 below.

Figure 2: Histogram for GPA

Present the findings of relevant regression models and inferential analyses (about 150-200 words, 10 marks)

Solution

To check whether logMVPA predicts GPA we ran linear regression model as well as Pearson correlation test.

Correlation

A Pearson correlation test was done and the coefficient between GPA and logMVPA was found to be 0.6648; this implies that there is a moderately strong positive relationship between GPA and logMVPA.

Also presented is the scatter plot of GPA versus logMVPA controlling for the overweight

Figure 3: Scatter plot of GPA and logMVPA

The figure clearly shows that there is a positive linear relationship between GPA and logMVPA.

Regression

Regression analysis was done to come with a model that could predict the GPA score using the logarithm of the MVPA (logMVPA).

To determine the fitness of the model, we had to look at two key aspects of the fit obtained (these are coefficient of determination and significance value of the model). First looking at the goodness of fit for the model we found that the model is indeed fit to predict GPA based on logMVPA at 5% level of significance (p < 0.05). The coefficient of determination (R-squared) is 0.442; this means that 44.2% of the variation in the dependent variable (GPA) is explained by the explanatory variable (logMVPA) in the model. The variable logMVPA was also found to be significant in the model (p < 0.050) with its coefficient being 1.6256, meaning that a unit change in logMVPA would result to a change in the GPA by 1.6256 i.e. if logMVPA increases by one unit, we would expect the GPA to increase by 1.6256. Similarly, if the logMVPA decreases by one unit, GPA would decrease by 1.6256.

The constant intercept was 4.03387

Provide your answer to the research question

Solution

This study sought to understand whether the logarithm of MVPA (logMVPA) predicts GPA after correcting for overweight in the population of Australian university students. Regression models was constructed to answer this question. Results showed that indeed the logMVPA predicts the GPA when the overweight is controlled.