|
Treatment 1 |
Treatment 2 |
Treatment 3 |
|
0 |
1 |
6 |
|
1 |
4 |
5 |
|
0 |
1 |
6 |
|
3 |
2 |
3 |
|
T = 4 |
T = 8 |
T = 20 |
|
SS = 6 |
SS = 6 |
SS = 6 |
N = 12 G = 32 ƩX2= 138
1a.
Conduct a single-factor independent-measures ANOVA to test the hypothesis that there are significant differences in the mean scores among the three treatment conditions. Use α = .01.
The alternative hypothesis is
Group of answer choices
a) H1: μ1 ≠ μ2≠ μ3
b) H1: μ1 = μ2= μ3
c) all pairs of means are significantly different from each other
d) There is at least one significant mean difference: At least two means significantly differ from each other
1b.
The Critical F-value is:
Note: Leave the two decimal places after the decimal point
1c).
The F-statistic is
Note: If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point and do not round.
1d)
Your decision is
Group of answer choices
a) Fail to reject the null hypothesis and conclude that there there is at least one significant mean difference
b) Fail to reject the null hypothesis and conclude that there are no significant differences among the three treatment conditions
c) Reject the null hypothesis and conclude that there is at least one significant mean difference
d) Reject the null hypothesis and conclude that there are no significant differences in mean scores among the treatment conditions
1e)
Calculate η2 (eta squared) as a measure of the effect size
η2 is
Note: If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point and do not round.
Applying one way ANOVA from excel: data -data analysis:
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 34.6667 | 2 | 17.3333 | 8.6667 | 0.0080 | 8.0215 |
| Within Groups | 18.0000 | 9 | 2.0000 | |||
| Total | 52.6667 | 11 |
The alternative hypothesis is d) There is at least one significant mean difference:
1b)
The Critical F-value is =8.02
1c). The F-statistic is =8.67
1d) c) Reject the null hypothesis and conclude that there is at
least one significant mean difference
1e)
η2 =SSR/SST =34.6667/52.6667 =0.6582
Tomato weights and Fertilizer (Raw Data, Software Required): Carl the farmer has three fields of tomatoes, on one he used no fertilizer, in another he used organic fertilizer, and the third he used a chemical fertilizer. He wants to see if there is a difference in the mean weights of tomatoes from the different fields. The sample data for tomato-weights in grams is given below. Carl claims there is a difference in the mean weight for all tomatoes between the...
There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. The second table displays results from an ANOVA test on this data with software. Wait-Times in Minutes x Register 1 2.0 2.0 1.1 2.0 1.0 2.0 1.0 1.3 1.55 Register 2 1.8 2.0 2.2 1.9 1.8 2.1 2.2 1.7 1.96 Register 3 2.1 2.1 1.8 1.5 1.4 1.4 2.0 1.7 1.75 ANOVA Results F...
1.Wait-Times: There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. The second table displays results from an ANOVA test on this data with software. Wait-Times in Minutes x Register 1 2.0 2.0 1.1 2.0 1.0 2.0 1.0 1.3 1.55 Register 2 1.8 2.0 2.2 2.6 1.8 2.1 2.2 1.7 2.05 Register 3 2.1 2.1 1.8 1.5 1.4 1.4 2.0 1.7 1.75 ANOVA Results...
The following data were obtained for a randomized block design involving five treatments and three blocks: SST = 490, SSTR = 310, SSBL = 95. Set up the ANOVA table. (Round your value for F to two decimal places, and your p-value to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Blocks Error Total Test for any significant differences. Use α = 0.05. State the null and alternative hypotheses. H0: At...
A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1000 population for people under 25 98 92 119 127 93 123 112 93 125 95 125 117 97 122 127 88 A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old. x2: Rate of hay fever per 1000 population for...
A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample ofn1 = 16locations in region I gave the following information about the number of cases of fox rabies near that location.x1: Region I Data1999788133325146A second random sample ofn2 = 15locations in region II gave the following information about the number of cases of fox rabies near that location.x2: Region II Data223268544422569(i) Use a calculator...
Tomato weights and Fertilizer: Carl the farmer has three fields of tomatoes, on one he used no fertilizer, in another he used organic fertilizer, and the third he used a chemical fertilizer. He wants to see if there is a difference in the mean weights of tomatoes from the different fields. The sample data is given below. The second table gives the results from an ANOVA test. Carl claims there is a difference in the mean weight for all tomatoes...
In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager's lost time due to inappropriate behavior of employees. Consider the following independent random variables. The first variable x1 measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions. x1: 3 5 8 2 2 4 10 The variable x2 measures manager's hours per week lost due to disputes regarding technical workers' superior attitudes that...
In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager's lost time due to inappropriate behavior of employees. Consider the following independent random variables. The first variable x1 measures manager's hours per week lost due to hot tempers, flaming e-mails, and general unproductive tensions. x1: 3 5 8 2 2 4 10 The variable x2 measures manager's hours per week lost due to disputes regarding technical workers' superior attitudes that...
The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made on all these bridge end pillars. (A higher reading means better visibility.) For the orange paint, the mean...