Exercise is known to produce positive psychological effects. Interestingly, not all exercise is equally effective. It turns out that exercising in a natural environment (e.g., jogging in the woods) produces better psychological outcomes than exercising in urban environments or in homes (Mackay & Neill, 2010). Suppose that a sports psychologist is interested in testing whether there is a difference between exercise in nature and exercise in the lab with respect to post-exercise anxiety levels. The researcher recruits n=7 participants who exercise in the lab and exercise on a nature trail. The data below represent the anxiety scores that were measured after each exercise session. Treat the data as if the scores are from an independent-measures study using two separate samples, each with n=7 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. α=0.05, is there a significant difference between the two sets of scores?Now assume that the data are from a repeated measures study using the same sample of n=7 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference, and the repeated-measures t statistic. Using α=0.05, is there a significant difference between the two sets of scores? Anxiety afterExercisingin LabAnxiety afterExercisingin NatureParticipantA328B66685248D4837E5244F48385244

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Exercise is known to produce positive psychological effects. Interestingly, not all exercise is equally effective. It turns out that exercising in a natural environment (e.g., jogging in the woods) produces better psychological outcomes than exercising in urban environments or in homes (Mackay & Neill, 2010). Suppose that a sports psychologist is interested in testing whether there is a difference between exercise in nature and exercise in the lab with respect to post-exercise anxiety levels. The researcher recruits n=7 participants who exercise in the lab and exercise on a nature trail. The data below represent the anxiety scores that were measured after each exercise session.

Treat the data as if the scores are from an independent-measures study using two separate samples, each with n=7 participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. α=0.05, is there a significant difference between the two sets of scores?
Now assume that the data are from a repeated measures study using the same sample of n=7 participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference, and the repeated-measures t statistic. Using α=0.05, is there a significant difference between the two sets of scores?

Anxiety after
Exercising
in Lab
Anxiety after
Exercising
in Nature
Participant
A
32
8
B
66
68
52
48
D
48
37
E
52
44
F
48
38
52
44

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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