Solution Found!
Reaction Time In an online psychology experiment sponsored
Chapter 1, Problem 18AYU(choose chapter or problem)
Problem 18AYU
Reaction Time
In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups. Subjects in group 1 were in the simple group. They were required to respond as quickly as possible after a stimulus was presented. Subjects in group 2 were in the go/no-go group. These subjects were required to respond to a particular stimulus while disregarding other stimuli. Finally, subjects in group 3 were in the choice group. They needed to respond differently, depending on the stimuli presented. Depending on the type of whistle sound, the subject must press a certain button. The reaction time (in seconds) for each stimulus is presented in the table.
The researcher wants to determine if the mean reaction times for each stimulus are equal.
(a) State the null and alternative hypotheses.
(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from a normal population.
(c) Test the hypothesis that the mean reaction times for the three stimuli are the same at the α = 0.05 level of significance.
(d) Draw boxplots of the three stimuli to support the analytic results obtained in part (c).
Questions & Answers
QUESTION:
Problem 18AYU
Reaction Time
In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups. Subjects in group 1 were in the simple group. They were required to respond as quickly as possible after a stimulus was presented. Subjects in group 2 were in the go/no-go group. These subjects were required to respond to a particular stimulus while disregarding other stimuli. Finally, subjects in group 3 were in the choice group. They needed to respond differently, depending on the stimuli presented. Depending on the type of whistle sound, the subject must press a certain button. The reaction time (in seconds) for each stimulus is presented in the table.
The researcher wants to determine if the mean reaction times for each stimulus are equal.
(a) State the null and alternative hypotheses.
(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from a normal population.
(c) Test the hypothesis that the mean reaction times for the three stimuli are the same at the α = 0.05 level of significance.
(d) Draw boxplots of the three stimuli to support the analytic results obtained in part (c).
ANSWER:Answer:
Step 1
Participants were randomly assigned to one of three groups. Subjects in group 1 were in the simple group. They were required to respond as quickly as possible after a stimulus was presented. Subjects in group 2 were in the go/no-go group. These subjects were required to respond to a particular stimulus while disregarding other stimuli. Finally, subjects in group 3 were in the choice group. They needed to respond differently, depending on the stimuli presented.
a) We need to determine if the mean reaction times for each stimulus are equal.
The Hypotheses can be expressed as
H0 : (The mean reaction times for each stimulus are equal)
H1 : At least one them is not equal.
b) The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met:
- Response variable residuals are normally distributed (or approximately normally distribution).
- Variances of populations are equal.
- Responses for a given group are independent and identically distributed normal random variables (not a simple random sample (SRS)).
The methods of one-way ANOVA are robust, so that departures from the requirement of normality will not significantly affect the results of the procedure. In addition, the requirement of equal population variances does not need to be strictly adhered to, especially if the sample size for each treatment group is the same. Therefore, it is worthwhile to design an experiment in which the samples from the populations are roughly equal in size. We can verify the requirement of normality by constructing normal probability plots by using excel.
- Start Excel.
- Open the text/data file containing the data you wish to analyze. The data should all be in one column.
- Load the Analysis Toolpak as follows:
- Under the Tools menu, choose Add-ins. From the list select Analysis Toolpak. This will allow you to perform many statistical functions within Excel.
- Create a new column of data adjacent to the original data. The new column can contain any values as long as it has the same number of entries as the original data.
- Under the Tools menu, choose Data Analysis, and then Regression. Follow the directions given in the dialog box.
- Enter values for the Input Y Range. The Input Y Range contains the data for which you want the probability plot.
- Enter values for the Input X Range. These are irrelevant in this case. We are only interested in the Normal Probability Plot option.
- Check the Normal Probability Plots option.
- Click OK
From the above plots, we see that the points on the pattern lie close to the straight line. Hence, All of the normal probability plots are roughly linear. We conclude that the sample data come from populations that are normally distributed.