Theoretical Background of one way analysis and application of One way ANOVA.
One-way analysis of variance: three means
College Students' Seating Choices and Motivation to Achieve
This activity is a revision of an activity found in Real Data: A Statistics Workbook Based on Empirical Data by Z. C Holcomb (1997). Published by Pyrczak Publishing.
Statistical Guide: To determine the significance of a set of differences among two or more means, we use analysis of variance (ANOVA). When ANOVA yields a probability of .05 or less, we usually reject the null hypothesis (the null hypothesis says that the difference among the means were created by sampling-random-error and are not reflective of a true difference in the population means). If the null hypothesis is retained, there is not sufficient reason to reject the hypothesis that the difference among the means is due to sampling error.
In this exercise you will be using ANOVA to compare three means. If the null hypothesis can be rejected based on these results, a further comparison between the groups can be calculated to determine which, if any, of the population means differ from one another. The formulas and explanations of the relevant F and t-tests can be found in chapters 15 and 16 of our text. Finally, a judgment of the effect size of independent variable will be calculated.
Background Notes: The seating positions chosen by college freshmen in three sections of a required course were observed and recorded as either rows 1-2, rows 3-4, or rows 5-6. Students were administered a self-report questionnaire on their achievement motivation (that is, their desire to achieve). The possible range of scores was 0 (very low motivation) to 30 (very high motivation).
Making Predictions: Before examining the data below, predict the results you will obtain. (When scientists make predictions, they are hypothesizing.) Note that your predictions are not right or wrong. Rather, they represent your best guess as to the outcomes you will obtain. After you perform the calculations, you will be able to determine whether the data support your predictions.
Specify confidence intervals for the three protected t-tests and list them here.