1.In order to determine the effects of alcohol on reaction time, 40 randomly selected adult male individuals were assigned to four treatment groups of ten subjects each. The first group was asked to consume the alcoholic equivalent of five beers in a two-hour period, the second group three beers, the third group one beer, and the fourth group no beer. Then, the participants were tested for reaction time by being asked to depress a button as soon as the light they were looking at was turned on. The average time over ten trials for each individual was recorded:
G1 G2 G3 G4
.42 .56 .42 .32
.34 .49 .51 .57
.52 .36 .36 .68
.48 .43 .26 .37
.29 .42 .44 .37
.47 .58 .48 .37
.45 .40 .36 .34
.30 .24 .47 .56
.34 .25 .35 .34
.40 .46 .38 .36
State the hypothesis being tested in this ANOVA, ask SPSS to analyze the data, including a Duncan post-hoc analysis, and draw conclusions at the .05 level. Be sure to include a statement to be tested, describe the random variables involved and assumptions about them, level of significance, test statistic, and the critical region. Include the SPSS output on your answer sheet.
The hypothesis being tested in this ANOVA (Analysis of Variance) is whether the mean reaction times in the four treatment groups (G1, G2, G3, G4) are significantly different. In other words, we want to determine if the consumption of different amounts of alcohol (or no alcohol) affects reaction time.
To analyze the data using SPSS and perform a Duncan post-hoc analysis, follow these steps:
Step 1: Enter the data in SPSS. Create four variables (G1, G2, G3, G4) and enter the corresponding reaction time values for each group.
Step 2: Go to "Analyse" in the menu bar, select "General Linear Model", and then choose "Univariate".
Step 3: In the "Dependent Variable" box, enter the reaction time variable. In the "Fixed Factor(s)" box, enter the group variable (G1, G2, G3, G4). Click on the "Options" button.
Step 4: In the "Options" window, select the "Descriptive statistics" and "Means plot" checkboxes. Then, click "Continue".
Step 5: Back in the "Univariate" window, click "OK" to run the analysis.
After running the analysis, SPSS will generate output that includes several sections such as "Descriptive Statistics", "Tests of Between-Subjects Effects", "Multivariate Tests", and "Univariate Tests".
The statement tested is: "There is no significant difference in mean reaction times between the treatment groups (G1, G2, G3, G4)."
The random variables involved are the reaction times of the participants in the four treatment groups.
Assumptions:
1. Independence: It is assumed that the participants' reaction times are independent of each other.
2. Normality: The reaction times should be approximately normally distributed within each treatment group.
3. Homogeneity of variances: The variances of the reaction times should be equal across the treatment groups.
Level of significance: The significance level is given as 0.05 (or 5%).
Test statistic: The test statistic used in ANOVA is the F-statistic.
Critical region: To determine the critical region, you can refer to the output provided by SPSS under the "Tests of Between-Subjects Effects" or "ANOVA" table. Look for the "Sig." (significance) value associated with the "Between Subjects Effect" row. If the significance value is less than 0.05 (0.05 is the significance level in this case), then you can reject the null hypothesis.
To draw conclusions, analyze the results in the output. Look for the "Sig." value in the "Between Subjects Effect" row. If the significance value is less than 0.05, then you can conclude that there is a significant difference in mean reaction times between the treatment groups. Additionally, for post-hoc analysis, refer to the Duncan post-hoc test in the output to identify specific group differences.