Administrators at Parday University asked researchers to study differences in average sleep hours among freshmen, sophomores, juniors, and seniors, controlling for gender. The researchers hypothesized there would be a significant difference in sleep hours between freshmen at the beginning and end of the semester after accounting for gender. An analysis of covariance (ANCOVA) was conducted with year in school as the independent variable, average sleep hours as the dependent variable, and gender as the covariate. The ANCOVA results showed a significant difference in average sleep hours among years in school after removing the effect of gender, but gender was not a significant covariate.

1. One-Way ANCOVA - Example
The Study: Administrators at Parday University are concerned about their poor student
achievement and are examining all possible causes. They ask you to conduct a study into the
amount of sleep students get. You have been asked to find out if there is a difference in the
average number of hours slept among students based on year in school (Freshmen,
sophomore, junior, senior) while controlling for the effect of gender.
Decision Path:
 Inferential/ Difference / Scaled Data / Normal Distributions/ 1 DependentVariable / 1
Independent Variable/ 2 levels / Non-Repeated / Covariate = One-Way Analysis of
Covariance (ANCOVA).
Other Paths to ANCOVA:
 Inferential/ Difference / Scaled Data / Normal Distributions/ 1 DependentVariable / 1
Independent Variable/ 3 levels / Non-Repeated / Covariate = One-Way Analysis of
Covariance (ANCOVA).
 Inferential/ Difference / Scaled Data / Skewed Distributions/ 1 DependentVariable / 1
Independent Variable/ 2 or 3 levels / Non-Repeated / Covariate = One-Way Analysis of
Covariance (ANCOVA).

2. The Hypothesis: There is a statistically significant difference betweenthe amounts of sleep
freshmen get at the beginning compared to the end of the semester after controlling for the
effect of gender.
The Null-hypothesis: There is no statisticallysignificant difference between the amounts of
sleep freshmen get at the beginning compared to the end of the semester after controlling for
the effect of gender.
Question: Do we have enough evidence to reject the null hypothesis?
The Decisionrule: If the probability that we are wrong is .05 or 5 out of 100 times we will
reject the null-hypothesis in other words, accept the hypothesis.

7. This is the
Dependent Variable

9. This is the
Independent Variable

11. This is the Covariate

13. There is a statistically
significant difference among
years in school after taking
out the effect of gender in
terms of average hours slept.
Gender is not a significant
Covariate

14. Result: A one-way between subjects ANCOVA was calculated to examinethe effect of year in
school on hours of sleep controlling for the effect of gender. Gender was not significantly
related to hours of sleep F(1, 115) = .715, p = .400. Year in school did show significant
difference in terms of hours of sleep F(3, 115) = 9.085, p = .000 after eliminating the effect of
gender
Go to the next page to see where these numbers came from:

15. Result: A one-way between subjects ANCOVA was calculated to examine the effect of year in school on
hours of sleep controlling for the effect of gender. Year in school did show significant difference in terms
of hours of sleep F(3, 115) = 9.085, p = .000 after eliminating the effect of gender. Gender was not a
significant covariate F(1, 115) = .715, p = .400.