Module 1 Case Study

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Liberty University *

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520

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Statistics

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Jan 9, 2024

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EXSC 520 C ASE S TUDY : C ORRELATION AND B IVARIATE R EGRESSION T EMPLATE I. Correlation Research question: “ Is mean heart rate during exercise correlated to body weight? ” Assumptions Testing 1. Data level of measurement – what was the level of measurement for the data used in this case study (ratio, interval, etc.)? Both variables were in the ratio level of measurement category. 2. Would the amount of skewness and kurtosis in these variables affect the analysis? How do you know? Give numerical values to support your conclusion. The skewness value was 0.714 and the kurtosis value was 0.523. Both values are between 1.96 and -1.96 therfore there was no effect on the variabels in the analysis. Table 1. Table with skewness and kurtosis Paste table below: Page 1 of 12

EXSC 520 3. Was the assumption of normality met and how do you know? The assumption of normality was met for mean heart rate (bpm) at p = 0.621 which is higher than 0.05, however the assumption of normality was not met by the body weight (kg) at p = 0.008 which is less than 0.05. Table 2. Tests of normality Paste table below: Figure 1. Histogram with normal curve for each variable Paste figure below: Page 2 of 12

EXSC 520 Figure 2. Normal Q-Q plot for each variable Paste figure below: Page 3 of 12

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EXSC 520 4. Were there any outliers; how do you know? There was one outlier, number 2, shown in the Box-and-Whiskers plot for body weight (kg) where it is 2 standard deviations above the mean. Table 3. Box-and-Whiskers plot for each variable Paste table below: Page 4 of 12

EXSC 520 Statistical Analysis Table 4. Descriptives statistics table Paste table below: Table 5. Correlations table Paste table below: Page 5 of 12

EXSC 520 Write-up- Use these questions as a guide to write an abstract (paragraph). Use past tense. Include the following items: 1. What was the research question? 2. What was the Pearson correlation value (r), and was it statistically significant? (Use “sig” reported in SPSS. That is the p -value, and compare to alpha to determine significance) 3. Was there a positive or negative relationship between the two variables, and how did you come to that conclusion? Was this a strong correlation? (use r/Pearson) 4. What are your thoughts on the finding of this analysis, and what are the practical application(s) of this finding? Elaborate on what the study means, why, how you know, and relate the findings to exercise physiology knowledge. Use references if needed. (Hint- does this study “make sense?” What could influence results?) The research question for this data set was, “is mean heart rate during exercise correlated to body weight?” The Pearson correlation value (r) was -0.411 and was not statistically significant with a p value of 0.72 which is greater than 0.05. The relationship between the two variables was negative due to the negative r value and it was a weak correlation due to the r value being less than 0.7. The findings of this study produced a weak, inverse, not statistically significant relationship between mean heart rate (bpm) and body weight (kg). This analysis makes sense because while typically as body weight increases so does resting heart rate but these individuals are exercising. However, I would have expected to see a more positive relationship between the two variables but the fitness level and the time of the exercise session is unknown. Both of these factors could have effected the data and the relationship between variables. II. Bivariate Regression Research question: “ Can heart rate during exercise be predicted by using body weight as a predicting variable and creating a linear regression equation?” (THIS SECTION USES the SAME DATA and will replicate results from above, other than the REGRESSION Section) Assumptions Testing 1. Data level of measurement- what was the level of measurement for the data used in this case study (ratio, scale etc.)? Both variables were in the ratio level of measurement category. 2. Would the amount of skewness and kurtosis in these variables affect the analysis? How do you know? Give numerical values to support your conclusion. The skewness value was 0.714 and the kurtosis value was 0.523. Both values are between 1.96 and -1.96 therfore there was no effect on the variabels in the analysis. Page 6 of 12

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EXSC 520 Table 1. Table with skewness and kurtosis Paste table below: 3. Was the assumption of normality met and how do you know? The assumption of normality was met for mean heart rate (bpm) at p = 0.621 which is higher than 0.05, however the assumption of normality was not met by the body weight (kg) at p = 0.008 which is less than 0.05. Table 2. Tests of normality Paste table below: Figure 1. Histogram with normal curve for each variable Page 7 of 12

EXSC 520 Paste figure below: Figure 2. Normal Q-Q plot for each variable Page 8 of 12

EXSC 520 Paste figure below: 4. Were there any outliers; how do you know? Page 9 of 12

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EXSC 520 There was one outlier, number 2, shown in the Box-and-Whiskers plot for body weight (kg) where it is 2 standard deviations above the mean. Table 3. Box-and-Whiskers plot for each variable Paste table below: Statistical Analysis Page 10 of 12

EXSC 520 Table 4. Descriptives statistics table Paste table below: Table 5. Correlations table Paste table below: Table 6. The model summary table Paste table below: Table 7. The ANOVA table Paste table below: Table 8. The coefficients table Page 11 of 12

EXSC 520 Use this table to type out the regression equation for this data. Paste table below: Write-up- Use these questions as a guide to write an abstract (paragraph). Use past tense. Use the following questions as a guide: 1. What was the research question? 2. What was the Pearson correlation value (r), and was it statistically significant? (Use “sig” reported in SPSS. That is the p -value, and compare to alpha to determine significance) 3. Was the relationship positive or negative and what was the (magnitude) strength of the relationship (use r/Pearson)? 4. What was the regression equation for these data? Consider y=mx + b where y = HR. 5. What are your thoughts on the finding of this analysis, and what are the practical application(s) of this finding? Elaborate on what the study means, why, how you know, and relate the findings to exercise physiology knowledge. Use references if needed. (Hint- does this study “make sense?” What could influence results?) The research question for this data set was, “ Can heart rate during exercise be predicted by using body weight as a predicting variable and creating a linear regression equation?” The Pearson correlation value (r) was -0.411 and was not statistically significant with a p value of 0.72 which is greater than 0.05. The relationship between the two variables was negative due to the negative r value and it was a weak correlation due to the r value being less than 0.7. The regression formula used for this data set was, Body weight(kg) = (Mean heart rate) (-.324)+128.806. The findings of this study produced a weak, inverse, not statistically significant relationship between mean heart rate (bpm) and body weight (kg). This analysis makes sense because while typically as body weight increases so does resting heart rate but these individuals are exercising. However, I would have expected to see a more positive relationship between the two variables but the fitness level and the time of the exercise session is unknown. Both of these factors could have effected the data and the relationship between variables. Page 12 of 12

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Module 1 Case Study

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