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In the analysis of data using the independent-samples t-test, the data must meet the following six assumptions for the analysis using the SPSS to generate valid results.
- The dependent variable must be in the form of a continuous scale, which is in a ratio or an interval scale.
- The independent variable must be in the form of categorical scale with only two categorical variables, which are independent (Jackson, 2011).
- Between the two categories, there must be an independence of observation.
- The dependent variable must not have any significant outliers as they reduce the validity of results.
- The dependent variable in each category must follow the normal distribution.
- The dependent variable should exhibit homogeneity of variances.
The dependent variable is the duration of eating Big Mac specials in seconds.
The independent variable is weight classification, overweight and normal weight individuals.
H0: The difference in the duration of eating Big Mac specials between overweight and normal weight individuals is not statistically significant.
H1: The difference in the duration of eating Big Mac specials between overweight and normal weight individuals is statistically significant.
|Weight classification||N||Mean||Std. Deviation||Std. Error Mean|
|Time spent eating Big Mac specials in seconds||overweight||10||589.00||42.615||13.476|
The descriptive table above shows that the total number of individuals is 40 (N = 40) where overweight individuals are 10 while normal individuals are 30. From the descriptive table, the duration that normal and overweight individuals take when eating Big Mac specials are different as the means portray.
The mean of the duration taken by the normal weight individuals (M = 698.40, SD = 15.14) is longer than the mean of duration taken by overweight individuals (M = 589.00, SD = 42.62). Thus, to establish whether the difference in the mean of duration is significant, independent-simple test is necessary.
|Independent Samples Test|
|Levene’s Test for Equality of Variances||t-test for Equality of Means|
|F||Sig.||t||df||Sig. (2-tailed)||Mean Difference||Std. Error Difference||95% Confidence Interval of the Difference|
|Time spent eating Big Mac specials in seconds||Equal variances assumed||2.745||.106||-3.975||38||.000||-109.400||27.522||-165.116||-53.684|
|Equal variances not assumed||-5.397||30.828||.000||-109.400||20.272||-150.754||-68.046|
Since the independent-samples t-test assumes equality of variances, at 95% confidence level, the upper and lower confidence intervals are -53.68 and -165.12 accordingly. Essentially, confidence intervals provide a range of values where a true mean occurs at a certain confidence level. Sheskin (2003) states that 95% confidence interval shows that one is 95% confident that a computed mean reflect a true mean of the population.
Additionally, as the assumption of the equal variances is applicable in the independent-samples test, analysis of the data indicates that the p-value is significant, t(38) = -3.98, and p = 0.00. According to Kirk (2006), a p-value that is less than 0.05 is significant while a p-value that is greater than 0.05 is insignificant. Hence, given that the p-value is less than 0.05 (p<0.05), it rejects the null hypothesis and accepts the alternative one.
Statistically, the independent samples t-test indicates that the difference in the duration of eating Big Mac specials between overweight individuals (M = 589.00, SD = 42.62) and normal weight individuals (M = 698.40, SD = 15.14) is statistically significant, t(38) = -3.98, p = 0.00.
In this view, the alternative hypothesis states the difference in the duration of eating Big Mac specials between overweight and normal weight individuals is statistically significant. This implies normal weight individuals take longer time to eat Big Mac specials than overweight individuals do.
Jackson, S. (2011). Research Methods and Statistics: A Critical Thinking Approach. New York: Cengage Learning.
Kirk, R. (2006). Statistics: An introduction. New York: Cengage Learning.
Sheskin, D. (2003). Handbook of Parametric and Nonparametric Statistical Procedures (3rd ed.). Third Edition. New York: CRS Press.