In order to determine the effects of alcohol on reaction time, 40 randomly selec
ID: 3360233 • Letter: I
Question
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
.31 .34 .37 .34
.29 .42 .48 .34
.29 .34 .37 .42
.23 .40 .38 .41
.31 .38 .40 .38
.23 .39 .49 .51
.24 .35 .36 .47
.35 .44 .35 .42
.37 .42 .51 .40
.30 .35 .35 .34
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.
please explain in the most simplest way for my own understanding .... thank you
Explanation / Answer
Solution:
Here, we have to use one way analysis of variance or ANOVA F test for checking whether there is any significant difference in the average reaction times for effects of alcohol on four treatment groups.
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no any statistically significant difference in the average reaction times for effects of alcohol on four treatment groups.
Alternative hypothesis: Ha: There is a statistically significant difference in the average reaction times for effects of alcohol on four treatment groups.
H0: µ1 = µ2 = µ3 = µ4
Ha: H0 is not true. (At least one pair differs.)
We are given a level of significance = = 0.05
The SPSS output for this ANOVA test is given as below:
One way ANOVA
Descriptive statistics
Reaction time
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
Group 1: consume the alcoholic equivalent of five beers
10
.2920
.04780
.01511
.2578
.3262
.23
.37
Group 2: Consume three beers
10
.3830
.03683
.01165
.3567
.4093
.34
.44
Group 3: Consume one beer
10
.4060
.06240
.01973
.3614
.4506
.35
.51
Group 4: No consumption of beer
10
.4030
.05677
.01795
.3624
.4436
.34
.51
Total
40
.3710
.06853
.01084
.3491
.3929
.23
.51
ANOVA
Reaction time
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
.086
3
.029
10.701
.000
Within Groups
.097
36
.003
Total
.183
39
The p-value for this test is given as 0.00 which is less than given level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any statistically significant difference in the average reaction times for effects of alcohol on four treatment groups.
There is sufficient evidence to conclude that there is a statistically significant difference in the average reaction times for effects of alcohol on four treatment groups.
Post hoc test for above test is given as below:
Post Hoc Tests
Homogeneous Subsets
Reaction time
Duncan
Group
N
Subset for alpha = 0.05
1
2
Group 1: consume the alcoholic equivalent of five beers
10
.2920
Group 2: Consume three beers
10
.3830
Group 4: No consumption of beer
10
.4030
Group 3: Consume one beer
10
.4060
Sig.
1.000
.357
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 10.000.
Statistically significant difference in the average reaction times for effects of alcohol is observed for given four treatment groups.
Descriptive statistics
Reaction time
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
Group 1: consume the alcoholic equivalent of five beers
10
.2920
.04780
.01511
.2578
.3262
.23
.37
Group 2: Consume three beers
10
.3830
.03683
.01165
.3567
.4093
.34
.44
Group 3: Consume one beer
10
.4060
.06240
.01973
.3614
.4506
.35
.51
Group 4: No consumption of beer
10
.4030
.05677
.01795
.3624
.4436
.34
.51
Total
40
.3710
.06853
.01084
.3491
.3929
.23
.51
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