Setting -
An exercise class with 50 participants were studied for a period of 30 weeks. Represented in the class were an even distribution of male and female participants between the ages of 20 to 60 years of age. At the beginning of the class, participants were weights and again, at the end of the 30 weeks.
Hypotheses -
1. Is age correlated with change in weight? I hypothesize that the younger a person is the greater will be his/her weight loss.
2. Is gender is associated with weight loss? I hypothesize that the women will have lost, on the average, more weight than the men.
Correlation -
1. Describe your subjective impressions from the overall mean weight loss, scatter plot, and regression line.
Overall the average weight loss
of the group was about 6 pounds. The regression line is nearly horizontal and
the data points are widely scattered. Age does not appear to be a determining
factor in weight loss.
2. What is the correlation value?
The correlation value is - .08
What standard are you using to decide if it is significant?
I am using the .05 level of probability as my standard. A significant correlation at the .05 level of probability is .288 (This value is from Table 1, Chapter 8, The Whole Art of Deduction, using 45 degrees of freedom. The degrees of freedom are 48, but 45 is the next smaller increment on the table).
Does it indicate a significant correlation?
Since the obtained value (-.08) is less than my criterion value (.288), I conclude that the correlation is not significant. There is not a significant relationship between age and weight loss.
If the correlation is significant, is the relationship weak, strong or very strong?
Since the correlation was not significant, then there was no relationship present.
3. What is your conclusion about the hypothesis and research question? Are they supported or not?
I conclude that the hypothesis was not supported.
Had the correlation been larger, and negative, then the hypothesis would have been supported. In regard to the research question, given that my hypothesis was not supported, I conclude that there does not appear to be a relationship between age and weight loss.
t-Test -
1. Describe your subjective impressions from the means for men and women, the bar chart and error bars.
The men lost on the average 5.1 pounds and the women lost 6.5 pounds. The bar charts show women with greater weight loss than men, but the men have a larger standard deviation as indicated by the error bars.
2. What is the t-value and its associated probability?
The t-value is 1.95 and the probability is .057
What standard are you using to decide if it is significant?
I am using the .05 level of probability as my standard.
Does it indicate a significant difference between the means for women vs. men on weight loss?
Since the obtained probability (.057) is larger than my standard (.05), I conclude that the t-value does not indicate a significant difference is present between the means.
If the t-test is significant which group lost the most weight?
Since the t-value was not significant, then there was no difference between the means.
3. What is your conclusion about the hypothesis and research question? Are they supported or not?
I conclude that the hypothesis was not supported.
Had the t-test indicated significant differences, and if the mean weight loss were larger for the women, then the hypothesis would have been supported. Had the results of the t-test indicated a significant difference, and the men lost the most weight, then the hypothesis would not have been supported.
In regard to the research question, given that my hypothesis was not supported, I conclude that it does not appear that weight loss is a factor related to gender.
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Susan Quinn |