The following data were obtained in a study using three separate samples to compare three different treatments. Conduct an analysis of variance with α=0.05α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments.
Treatment A | Treatment B | Treatment C |
---|---|---|
24 | 23 | 24 |
25 | 21 | 28 |
23 | 21 | 26 |
24 | 23 | 26 |
F-ratio =
p-value =
Conclusion:
- These data do not provide evidence of a difference between the treatments
- There is a significant difference between treatments
η2=
The above data was changed by increasing the variance within each sample (note below how the data sets have changed).
Before you begin the calculation, predict how the changes in the data should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the F-ratio from above?
Treatment A | Treatment B | Treatment C |
---|---|---|
24 | 24 | 23 |
26 | 20 | 29 |
22 | 21 | 26 |
24 | 23 | 26 |
F-ratio =
p-value =
Conclusion:
- These data do not provide evidence of a difference between the treatments
- There is a significant difference between treatments
η2=
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- treatment conditions. a. Treatment 1 0 0 0 3 0 0 T=3 SS = 7.5 Treatment 2 2 3 1 3 2 1 T = 12 SS=4 Treatment 3 4 2 4 3 4 4 G=36 SStotal = 42 T = 21 SS = 3.5 Use an analysis of variance with a = .05 to determine whether these data indicate any significant mean differences among the treatments. Please organize all of your work on a source table E Carrow_forwardThe following data summarize the results from an independent-measures study comparing three treatment conditions. Treatment I II III N = 12 3 5 6 G = 60 5 5 10 ∑X2 = 392 3 1 10 1 5 6 x̅1 = 3 x̅2 = 4 x̅3 = 8 T1 = 12 T2 = 16 T3 =32…arrow_forward6) The following data summarize the results from an independent-measures study comparing three treatment conditions. Treatment II 3. 6. N= 12 10 G = 60 1 10 EX = 392 1 5. 6. M = 3 M = 4 M= 8 T= 12 T= 16 T= 32 SS = 8 SS = 12 SS = 16 a) Use an ANOVA with a = .05 to determine whether there are any significant differences among the three treatment means. b) Calculate n² to measure the effect size for this study. c) Write a sentence demonstrating how a research report would present the results of the hypothesis test and the measure of effect size. 3.arrow_forward
- The following data represent the results from an independent-measures experiment comparing three treatment conditions. Use StatCrunch to conduct an analysis of variance with a = 0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments. Treatment A Treatment B 6 F-ratio= p-value = 4 5 LO 5 5 8 6 7 4 Treatment C 9 7 11 10 13arrow_forwardDevise a hypotheses for the research question: Is there singificant correlation between students height and typical amount of sleep a student gets per night? Identify the appropriate statistical test using alpha = 0.05. Perform the statistical test. Use descriptive statistics to describe the variables both numerically and graphically. Height (whole inches) Sleep (minutes) 60 360 62 400 66 420 68 440 68 540 70 480 72 320 75 440 66 360 63 420 69 420 75 390 69 360 67 480 69 360 73 360 69 480 70 420 68 360 63 480 69 270 68 360 71 420 71 360 62 420arrow_forwardThe following data represent the results from an independent-measures study comparing two treatment conditions. Treatment I II 10 7 N = 16 8 4 G = 120 7 9 ∑X² = 1036 9 3 13 7 7 6 6 10 12 2 M = 9.000 M = 6.000 T = 72 T = 48 SS = 44 SS = 56 Use an independent-measures t test with α = .05 to determine whether there is a significant mean difference between the two treatments. (Use three decimal places; subtract MIIII from MII.) t-critical = ± t = t Distribution Degrees of Freedom = 21 -3.0-2.0-1.00.01.02.03.0t Conclusion: Fail to reject the null hypothesis; there are significant differences between the two treatments. Reject the null hypothesis; there are significant differences between the two treatments. Fail to reject the null hypothesis; there are no significant differences between the two treatments. Reject the null hypothesis; there are…arrow_forward
- The following data represent the results from an independent-measures experiment comparing three treatment conditions. Conduct an analysis of variance with α=0.05α=0.05 to determine whether these data are sufficient to conclude that there are significant differences in the means for the treatments. Treatment A Treatment B Treatment C 16 16 17 15 16 21 15 15 19 15 19 23 14 14 20 F-ratio (F-test statistic) = p-value = Conclusion: There is a significant correlation in the treatments I was able to show the treatments are independent The data does not provide evidence of a significant correlation for the treatments The data does not provide evidence of a significant difference in the means for the treatments I was unable to show the treatments are independent There is a significant difference in the means for the treatments The results obtained above were primarily due to the mean for the third treatment being noticeably different from the other two sample means.…arrow_forwardThe following data represent the results from an independent-measures experiment comparing three treatment conditions. Conduct an analysis of variance with α=0.05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments. Treatment A Treatment B Treatment C 8 10 16 10 9 12 9 10 14 9 8 15 9 13 13 F-ratio = p-value = Conclusion: There is a significant difference between treatments These data do not provide evidence of a difference between the treatments The results obtained above were primarily due to the mean for the third treatment being noticeably different from the other two sample means. For the following data, the scores are the same as above except that the difference between treatments was reduced by moving the third treatment closer to the other two samples. In particular, 3 points have been subtracted from each score in the third sample.Before you begin the calculation, predict how the…arrow_forwardThe following data represent the results from an independent-measures experiment comparing three treatment conditions. Conduct an analysis of variance with α=0.05α=0.05 to determine whether these data are sufficient to conclude that there are significant differences in the means for the treatments. Treatment A Treatment B Treatment C 6 4 13 4 6 11 4 9 7 6 6 10 5 5 9 F-ratio (F-test statistic) = p-value = Conclusion: The data does not provide evidence of a significant difference in the means for the treatments There is a significant difference in the means for the treatments I was unable to show the treatments are independent The data does not provide evidence of a significant correlation for the treatments I was able to show the treatments are independent There is a significant correlation in the treatments The results obtained above were primarily due to the mean for the third treatment being noticeably different from the other two sample means. For the…arrow_forward
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