Experimental+Designs+I


 * ** EDU7006-8 ** ||  ||
 * ** Quantitative Research Design ** || ** 3 Experimental Designs I ** ||
 * Steve: Thanks for your work on this assignment. You are doing a great job on all these calculations and essay questions. Please see my comments below for more details and let me know if you have any questions. Thanks! **
 * Steve: Thanks for your work on this assignment. You are doing a great job on all these calculations and essay questions. Please see my comments below for more details and let me know if you have any questions. Thanks! **

=Experimental Designs I=

Jackson (2012) Chapter Exercises
**#2.** A randomized ANOVA indicates an analysis of variance conducted on data where the subjects were randomly selected for a between-subjects design. A repeated-measures ANOVA is an analysis of variance conducted on data where the subjects are correlated in either a within-subjects or matched-subjects design. Thus, the difference between a randomized versus repeated-measures ANOVA is the underlying design of the research study being analyzed. A one-way ANOVA indicates an analysis of data with a single independent variable. **#4.** When analyzing multiple measures, the probability of a Type I error increases. This probability can be determined by the formula 1 – ( 1 – α ) c . According to the formula, the current probability of a Type I error on at least one of the three conditions is 1 – (1 - .05) 3 = 1 – (.95)3 = 1 - .86 = __.14__. The Bonferroni adjustment used the formula α / k = .05 / 3 = __.017__. **#6.** A post hoc comparison is performed when the ANOVA indicates that at least one of the sample means is statistically different from the other means. The post hoc comparison allows determining which means are statistically different from which other means.* **#8.** In a randomized ANOVA, error variance consists mostly in individual differences between subjects. A repeated-measures ANOVA analyzes data that removes or minimizes individual differences. Since error variance is the denominator in the ANOVA calculation, a smaller value results in more sensitivity and more statistical power. #10a.
 * **SOURCE ** || //**df **// || //**SS **// || //**MS **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">F **// ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Between Groups ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">22.167 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">11.084 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">6.763 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Within Groups ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">9 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">14.750 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.639 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Total ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">11 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">36.917 ||  ||   ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#10b. F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv(.05) = 4.26, F<span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv(.01) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">= 8.02; __F(2,9) = 6.763, //p// < .05__. Stress affects the number of illnesses in at least one group and is statistically significant at the .05 level, but not at the .01 level.* <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#10c. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#10d. In the present study, only the differences between the minimal and high stress conditions is significant at alpha = .05. All other comparison conditions in the study are not statistically significant. Those who have high levels of stress are much more likely to get sick than those with either moderate or low levels of stress.* <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#10e. The effect size eta-squared uses the formula η <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">= SS <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">between <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> / SS <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">total <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">= 22.167 / 36.915 = __0.60__, meaning that approximately 60% of the variance among the illnesses can be attributed to the level of stress. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#10f. [image in Word document] <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#12a. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#12b. F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv(.05) = <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.74, F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv(.01) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">= 6.51; __F(2,14) = 3.974, //p// < .05__. The groups affect the measurement of depression in at least one group and is statistically significant at the .05 level, but not at the .01 level. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#12c. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#12d. In the present study, only the differences between the control group and the drug group conditions is significant at alpha = .05. All other comparison conditions in the study are not statistically significant. The drug decreases the effect of depression over the use of a placebo or no treatment at all. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#12e. The effect size (η <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) = .362, meaning that approximately 36% of the variance in depression score is attributable to application of the drug. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#12f. [Image in Word document] <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#14a. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#14b. F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv(.05) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">= 3.55, F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv(.01) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">= 6.01; __F(2,18) = 74.848, p < .01__. At least one group of types of pizza slices is statistically significant at both the .05 and .01 level. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#14c. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#14d. In the present study, all comparisons are significant at the .05 level, and two comparisons are significant at the .01 level. Subjects preferred thin crust pizza over both hand-tossed and thick crust pizza at a .01 significance level. Subjects preferred thick crust over hand-tossed pizza at a .05 significance level. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#14e. The effect size (η <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) = .881, meaning that approximately 88% of the variance of pizza slice choice is attributable to the type of slice. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">#14f. [Image in Word document]
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Tukey's Post Hoc Test ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.05 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.010 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Q(3,9) ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.950 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">5.430 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">MSwithin ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.639 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.639 ||  ||
 * //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">n **// || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4.000 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">HSD ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2.528 ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.476 ** ||  ||
 * || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Minimal ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Moderate ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">High ** ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Minimal ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Moderate ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">High ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">High ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">SOURCE ** || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">df **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">SS **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">MS **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">F **// ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Between Groups ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1202.313 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">601.157 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.974 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Within Groups ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">14 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2118.000 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">151.286* ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Total ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">44 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3320.313 ||  ||   ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Tukey's Post Hoc Test ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.05 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.010 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Q(3,14) ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.700 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4.890 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">MSwithin ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">151.286 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">151.286 ||  ||
 * //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">n **// || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">15 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">15.000 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">HSD ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">11.750 ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">15.530 ** ||  ||
 * || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Control ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Placebo ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Drug ** ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Control ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2.93 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">12.13 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Placebo ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">9.2 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Drug ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Drug ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">SOURCE ** || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">df **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">SS **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">MS **// || //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">F **// ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Subject ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">9 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2.75 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.306 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Between Groups ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">180.050 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">90.025 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">74.848 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Error ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">18 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">21.650 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.203 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Total ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">29 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">204.450 ||  ||   ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Tukey's Post Hoc Test ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.05 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">0.010 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Q(3,18) ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">3.610 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4.700 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">MSerror ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.203 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.203 ||  ||
 * //**<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">n **// || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">10 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">10 ||  ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">HSD ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.252 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.630 ||  ||
 * || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Hand-tossed ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Thick ** || **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Thin ** ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Hand-tossed ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">1.47 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">5.77 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Thick ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">4.3 ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Thin ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- ||
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Thin ** || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- || <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">- ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Part I Assignment Question Answers
<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is an F-ratio? Define all the technical terms in your answer.** Calculation of the F-ratio is the third and last step in performing an analysis of variance (ANOVA). To get to the third step of an ANOVA several (three or four depending on the type of ANOVA) sums of squares must be calculated in the first step. For a one-way randomized ANOVA these consist of (a) “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">the sum of the squared deviations of each score from the grand mean <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Jackson, 2012, p. 290 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) or total sum of the squares, (b) “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">the sum of the squared deviations of each score from its group or condition mean <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Jackson, 2012, p. 290 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) or within-groups sum of the squares, and (c) “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">the sum of the squared deviations of each group’s mean from the grand mean, multiplied by the number of participants in each group <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Jackson, 2012, p. 292 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) or between-groups sum of the squares. A one-way repeated measures ANOVA adds a between-subjects sum of squares which is “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">the sum of the squared difference scores for the mean of each subject across conditions and the grand mean, multiplied by the number of conditions <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Jackson, 2012, p. 302 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). In the second step, the sums of squares are converted into mean squared deviation scores, which are an estimate of the variance within and between groups. Variance is the capriciousness of data due to error, confounds, differences in subjects, and the manipulation of the independent variable. These variance estimates are calculated by dividing each sum of the squares by the appropriate degrees of freedom. The F-ratio is calculated by dividing the mean square of the between-groups estimate by the mean square of the within-groups estimate. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is error variance and how is it calculated?** In a randomized ANOVA the error variance is reflected by the within-groups sum of squares, and indicates the changeability of measures within each condition and is represented with the formula Σ (X – M <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">g <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">. With human beings, direct causation is rarely identifiable; if participants are treated exactly the same in any given condition the results received will vary to some extent. The error variance is a measure of how much subjects in a given condition, or within-groups, vary. In a repeated-measures ANOVA, the within-groups sum of the squares is split into subject variance and error variance. The error variance in this situation is calculated by subtracting the variance attributable to between-subjects from the within-groups variance to determine the error variance. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Why would anyone ever want more than two (2) levels of an independent variable?** Few conditions in the real world are truly dichotomous. Independent variables with multiple levels give researchers the chance “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">to address more complicated and interesting questions <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Jackson, 2012, p. 281 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). A common experimental design with multiple levels uses control, placebo, and experimental groups to counteract demand characteristics and provides an opportunity to compare differences between no treatment, the expectation that something will occur, and the experimental treatment. An independent variable with more than two levels gives a more complete picture of the relationship between the independent variable and the dependent variables. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**If you were doing a study to see if a treatment causes a significant effect, what would it mean if within-groups variance was higher than between-groups variance? If between-groups variance was higher than within-groups variance? Explain your answer.** The within-groups variance reveals the amount of inconsistency of measures within a given condition or treatment and is indicative of the differences between subjects plus error. The between-groups variance reflects the difference between measures caused by the independent variable, confounding variables, and error. In the situation where the within-groups variance is higher than the between-groups variance, the F-ratio will be closer to one, representing that no or little variation is attributable to the independent variable. In the situation where the between-groups variance is higher than the within-groups variance, the F-ratio will be much greater than 1, indicative that there are differences between the experiment conditions. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is the purpose of a post-hoc test with analysis of variance?** Only when the F-ratio exceeds the value of F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">cv <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> will a post-hoc test be conducted. If the F <span style="font-family: 'Times New Roman',Times,serif; font-size: 80%;">obt <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> exceeds the critical value, differences between at least one pair of conditions is significant. The post-hoc test compares each condition with every other condition to establish “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">which ones differ significantly from each other <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Jackson, 2012, p. 297 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is probabilistic equivalence? Why is it important?** In order to utilize experimental results to determine cause and effect or predict behavior it is important to be able to control the environment such that the manipulation of the independent variable is the only difference between two groups. For many experiments it is either not plausible or possible to use the same subjects in the manipulation groups. Without using the same subjects, a major assumption of an experiment is broken; that the only difference in the environment is the way that the independent variable is manipulated, because different subjects with different characteristics are being compared. Probabilistic equivalence indicates that while two groups may not have the same participants, the chance, as a group, they are different from the population from which they are drawn is very small and predictable ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Trochim & Donnelly, 2008 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). Probabilistic equivalence is obtained through random assignment of participants to groups.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT1] We use it when there are three or more groups that we want to compare. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT2] Don’t forget to write a bit more detail here. For example, you can write that those people who had the highest stress levels had more colds than those people who had the lowest stress levels or something similar. <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;"> [The question asked me if Fobt was significant at alpha = .05 or alpha = .01, not to describe its significance.] <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT3] Right! This is what I meant in Comment 2. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT4] <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">This calculation and your F value are not quite right here! Your F value should be around 11.90 or so. Check the within group df.


 * = References ||
 * * Jackson, S. L. (2012). //Research methods and statistics: A critical thinking approach// (4th ed.). Belmont, CA: Wadsworth Cengage Learning.
 * Trochim, W. M. K., & Donnelly, J. P. (2008). //The research methods knowledge base// (3rd ed.). Mason, OH: Cengage Learning. ||