Energy Intake and Physical Exercise - Statistics Project Example

The interest of the study is to test if there is any significant difference between the energy intake before and after the exercise session.

The most appropriate test for this study is the paired sample t-test. The test determines if there is a significant difference between the average values of measurements taken from a sampling unit under two different conditions (Park, 2009). The test is based on the paired difference between the two measurements.

Assumptions in paired T-test

1. The paired difference follows a standard normal distribution under the null hypothesis (Weaver, 2004). This assumption will be tested by use of a normal Q-Q plot and the Shapiro-Wilk test.
2. The two populations must have equal variance
3. The difference score must be independent of all other scores.

With, the test hypothesis is

H0: There is no statistically significant difference between energy intake before and after exercise sessions

H1: There is a statistically significant difference between energy intake before and after exercise sessions

This can be expressed as

The test statistics for comparing the two means is

i.e. the mean differences

 is the standard deviation of the differences

 is the number of observations in each sample.

The criterion is to reject it for  degrees of freedom

This is a two-tailed test where both variables are dependent, i.e. pre and post-test variables. The power and post hoc testing for this study will be Bonferroni and Turkey’s tests. Bonferroni is the simplest post hoc test because of its flexibility and ability to be used as a correction test (Pavlidis, n.d). Bonferroni calculates the new pairwise alpha to be compared with the initial alpha. Bonferroni alpha is calculated as

Where is the initially accepted error?

 is the new alpha to be used in determining the significance of the Bonferroni test in each statistical test.

 is the number of statistical tests.

The analysis

Satisfying the assumption

Test of Normality on pre-test data

Test of Normality on post-test data

Pretesting and possessing data both seem to be normally distributed. The conclusion is supported by the Shapiro-Wilk test for normality. This test was chosen since it works best for a smaller sample size of less than 50. The results were as follows;

Tests of Normality

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

Pretesting

.129

20

.200*

.972

20

.803

Posttesting

.112

20

.200*

.968

20

.712

Table 1: Test of Normality

*. This is a lower bound of the true significance.

a. Lilliefors Significance Correction

From Shapiro wilk test, both pretesting and post-testing data were normally distributed. The significance values 0.803 and 0.712 are both greater than alpha 0.05. This test confirms that the data is appropriate for a paired t-test.

Paired sample t-test output

SPSS output for paired sample t-test has three main parts; descriptive statistics, the correlation between the paired variables, and inferential statistics.

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Posttesting

5304.00

20

1518.826

339.620

Pretesting

6650.70

20

1495.704

334.450

Table 2: Descriptive statistic for pretesting and post-testing data

In this study, there were 20 people whose energy intake was examined before and after going to the gym. The average energy intake before the exercise sessions was 6650.7 with a standard deviation of 1495.704 while the energy intake after the session was 5304 with a standard deviation of 1518.826. The last column gives the standard error of the mean for each of the tests.

To check for correlation, the hypothesis to be tested was

H0: The population correlation coefficient is equal to zero

H1: The population correlation coefficient is not equal to zero

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Posttesting & Pretesting

20

.969

.000

Table 3: correlation between the paired variables

This output also shows that there were 20 pairs of observation in the study. The correlation between variables is given in column three i.e. The fourth column shows the p-value for the correlation coefficient. With an the p-value is less than the alpha level. This implies that we reject the null hypothesis that the population correlation coefficient is equal to zero. It follows that there is a significant association between the measurements taken before the exercise session and after the exercise session.

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Posttesting - Pretesting

-1346.700

375.700

84.009

-1522.533

-1170.867

-16.030

19

.000

Table 4: Inferential statistics on paired sample t-test

The second column labeled mean is the mean of the differences between the two data sets, i.e. -1346.7. The third column gives the standard deviation of the difference between the two data sets which is 375.7. The column labeled t gives the calculated t-value which is -16.03 at 19 degrees of freedom. The column labeled Sig. (2-tailed) gives the p-value associated with the test. In this study, the p-value is 0.000.

Since the p-value is less than, the implication is we reject the null hypothesis. This implies that there is a statistically significant difference between energy intake before and after exercise sessions.

Therefore, a paired sample t-test reveals that there exists a reliable statistical difference between the mean of pretesting of individuals attending exercise sessions (M= 6650.70, s= 1518.826 ) and possessing of individuals attending exercise sessions (M= 6650.7, s=1495.704). t(19)= -16.030, p=0.00, . With significant results, the post hoc test could not run since both data tests' error terms had 0 degrees of freedom.