On the pages below are a series of tables and figures that you might consider using in your report. You should feel free to edit these if you want. There are also a few notes in red font to give you some idea of my thought processes during the analysis of the data. This is the first time we have done this practical exercise, so it has been a learning process for me too. I took the following approach to the analysis of the data-set: I first wanted to know something about the characteristics of the sample. This is important because, in any analysis, you must be able to consider the extent to which your observations and conclusions are generalizable to a population. These data are presented in Tables 1 and 2. Table 1 presents the categorical variables and Table 2 presents the continuous variables. How generalizable do you think this sample is to the wider population? For continuous variables I chose to use the standard deviation as my measure of dispersion because, unlike the standard error of the mean, this is largely independent of the sample size. Consequently, the standard deviations can be compared between the various categories, even though some of the sample sizes within each factor vary widely. The next step was to partition the data according to gender (Table 3; Figure 1), diet (Table 4; Figure 2) and level of physical activity (Table 5; Figure 3). This enabled me to test the hypothesis that the continuous variables differed according to these categorical factors. Note that this analysis does not tell us anything about causality. You should also consider whether you find the tables or the figures more useful for presentation of the data. You should include one or the other in your report, not both. One of the rules of scientific presentation is that you should not present the same data in tables and figures. You should make a decision about which of these modes of delivery will be most effective in your report. I then moved to considering the relationship between body mass index and cardiovascular function (Figure 4). My first step for this was to generate scatterplots. I then performed regression analysis to ascertain whether arterial pressure and heart rate vary with body mass index. I calculated the line of best fit both by ordinary least-squares (OLS) regression analysis and ordinary least-products (OLP) regression analysis. Note that the two methods give different lines of best fit. Why do you think this is the case? Which do you think is better? Why? I used two variables to determine the strength of the relationship, r2 and P (Table 6). The P value tests the null hypothesis that the slope of the relationship is zero (i.e. that there is no linear relationship between the two variables). The Pearson product moment correlation coefficient (r2) quantifies the proportion of the variance in the dependent variable (i.e. the one on the y-axis) that can be explained by the (OLP) linear relationship with the independent variable (body mass index). Do you think arterial pressure and heart rate differ according to body mass index? How strong do you think the relationship is? I also present the intercepts and slopes of these relationships in Table 6. What do the slopes tell us about the relationships between body mass index and haemodynamic function? The next step was to consider whether the three categorical variables (gender, diet and level of physical activity) influence the relationships between body mass index and arterial pressure and heart rate. For this, I used analysis of covariance (Table 7). I chose not to do the analysis for diet because the very small sample size of vegetarians would invalidate the statistical test. You will see three sets of P values. PBMI tests the hypothesis that, independent of gender or level of physical activity, there is a linear relationship between body mass index and the four haemodynamic variables. Note the consistency between the PBMI values here and the P values in Figure 4. That is, they seem to support the idea that systolic pressure, diastolic pressure and mean arterial pressure vary with body mass index, but maybe heart rate does not. PGender tests the hypothesis that the haemodynamic variables differ by gender, independently of body mass index. PActivity tests the hypothesis that the haemodynamic variables differ by level of physical activity, independently of body mass index. The data seem to indicate some relationship between gender and systolic pressure, and between activity and heart rate. Contrast these P values with those presented in Tables 3 and 5, which test slightly different hypotheses. Can you explain this slight difference? PGender*BMI and PActivity*BMI are what we call ‘interaction terms’. They test the hypotheses, respectively, that the slope of the relationships between body mass index and the haemodynamic variables differ according to gender or level of physical activity. Note that none of these P values is ≤ 0.05, so it would not be reasonable for us to reject the null hypothesis in any case. That is, it seems unlikely that gender or level of physical activity affect the way in which BMI appears to alter haemodynamic function (assuming there is causality). Finally, I present scatterplots of the data with the two genders (Figure 5) and the four levels of physical activity (Figure 6) shown in different colours. In cases where the analysis of covariance (Table 7) provides evidence that the relationships between body mass index and the haemodynamic variables are dependent on the categorical variable (gender or level of activity), I present the individual regression lines. Hopefully, this will get you thinking about the nature of these apparent effects. I suspect the negative slope for the relationship between body mass index and heart rate, for those of you who do not exercise at all, is a spurious finding. It probably reflects the relatively small sample size, but this is pure speculation. Please download the attached file.
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