Free Essay On Descriptive Statistics

Introduction

The purpose of this analysis is to estimate the degree of relationship between the BMI of that individual and the largest number of drinks that an individual had on any occasion. The health of an individual and specifically their BMI highly depends on the lifestyle of the individual. Apart from eating habits and lack of exercising, it has been established that drinking alcohol is one of the main causes of obesity. The purpose of this analysis is to explore the relationship between the BMI of an individual and the drinking habits. It is approximated that respondents who had a high number of alcoholic drinks on any occasion are frequent drinkers, and their BMI will be higher than that of individuals who have less number of drinks on any particular occasion. The research question we are attempting to answer in this analysis is ‘what is the relationship between the BMI of an individual, and the largest number of drinks the respondent had in the past thirty days?’

The descriptive statistics for the two variables BMI and the MAXDRINKS are included in the table presented below.
The mean number of the variable maximum number of drinks in the past 30 days is 2.9 and the median is 2. This indicates that the average number of alcoholic drinks taken by the respondents in the past 30 days is 3.
'1' represents the number of individuals who took a maximum of 1 alcoholic drink in the past 30 days, this represents 25.8% of the respondents. '2' represents the number of respondents who took a maximum of 2 alcoholic drinks in the past 30 days, this represents 32.2% of the respondents. The percentage of respondents that took three or less alcoholic drinks in the past 30 days was 74.2%, and less than five drinks was 88.8%. This indicates that a higher percentage of the respondents were not heavy consumers of alcohol. The percentages are included in the bar chart given below.
It is worth observing that 94.4% of the respondents took six or less alcoholic drinks in the past 30 days. This shows that a very small percentage of respondents took more than six alcoholic drinks. The small number of alcoholic drinks might be the reason for the unexpected correlation between the variables.
The histogram does not indicate a distribution that is distinctly similar to the normal distribution. It shows that the distribution is skewed to the left, which indicates that a majority of the respondents had less than six alcoholic drinks in the past 30 days.

The computed Body Mass Index

The summary statistics of the variable BMI are included above. The mean is above the median which indicate that there could possibly be outliers which are pulling the mean up.
A plot of the histogram of the BMI of respondents for the different values of MAXDRINKS indicate a concentration of the BMI on the values less than six. This reinforces the observation that had been made earlier which stated that most of the respondents take less than six alcoholic drinks in the 30 day period.
The scatterplot does not indicate a distinct relationship between the variables. It does, however, indicate that there are outliers.

Hypothesis

The test that is being conducted is testing whether the relationship between the variables MAXDRINKS and BMI is significant. This means that the standard regression equation can be used to predict the BMI of an individual if the number of drinks that an individual has taken in the past 30 days.
The null and the alternative hypotheses are testing the presence of a correlation coefficient between the BMI of an individual and the highest number of drinks taken by the individual in the past 30 days.
HO: There is no significant relationship between the BMI of an individual and the highest number of drinks taken on a single occasion in the past 30 days.
Statistical notation of the null hypothesis HO: r = 0
H1: There is a significant relationship between the BMI of an individual and the highest number of drinks taken on a single occasion in the past 30 days.

Statistical notation of the null hypothesis H1: r ≠ 0.

The appropriate significance level to be used is 0.05 significance level. This is because a significance level of 0.05 is considered the best because the probability of making type one error is moderated. That is the probability of rejecting a true null hypothesis, and the probability of accepting a false null hypothesis are moderated.
The p-value is 0.704 which is greater than 0.05 therefore we fail to reject the null hypothesis at 0.05 level of significance. The test is insignificant therefore we fail to reject the null hypothesis that there is no association between the variables BMI and the highest number of drinks that the individual had in the past 30 days. Therefore, the null hypothesis is accepted and it is concluded that there is no significant relationship between BMI and the maximum number of drinks taken in the past 30 days.

Confidence intervals

The significance level used was 0.05 therefore it would be appropriate to use 95% confidence interval so as to ensure conformity in our test criterion. The 95% confidence interval of the slope parameter is (-24.37, 16.48), that is the upper 95% confidence interval is 16.48, and the lower 95% confidence interval is -24.37. The broad interval is because there was no distinct relationship between the two variables as indicated in the scatterplot. There are outliers in the variable BMI, which could be the causing factor in the insignificant relationship and the indistinct relationship as indicated by the scatterplot.

Discussion

The results cannot be generalized to any population because the test to estimate the relationship between the variables was insignificant. There are a number of confounding variables that affect the computed Body Mass Index this includes the Income level of the individual and the satisfaction level. Stress is a great contributor to obesity and income level in most cases determines the lifestyle of the respondents. The results cannot be interpreted as evidence of a ‘cause-and-effect’ relationship because the test was not significant. The results can be interpreted further if the outliers are eliminated, and the confounding factors are considered in the partial correlation coefficient analysis. The results are not surprising because the respondents considered in the analysis were not heavy consumers of alcoholic drinks. 58% of respondents claimed to have consumed two or less alcoholic drinks in the past 30 days, this number of alcoholic drinks is small and is unlikely to affect the health of the respondents.