The following data represent the results of a repeated-measures study comparing different viewing distances for a 42-inch-high-definition television. Four viewing distances were evaluated, 9 feet, 12 feet, 15 feet, and 18 feet. Each participant was free to move back and forth among the four distances while watching a 30-minute video on the television. The only restriction was that each person had to spend at least 2 minutes watching from each of the four distances. At the end of the video, each participant rated the all off of the viewing distances on a scale fro
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The following data represent the results of a repeated-measures study comparing different viewing distances for a 42-inch-high-definition television. Four viewing distances were evaluated, 9 feet, 12 feet, 15 feet, and 18 feet. Each participant was free to move back and forth among the four distances while watching a 30-minute video on the television. The only restriction was that each person had to spend at least 2 minutes watching from each of the four distances. At the end of the video, each participant rated the all off of the viewing distances on a scale from 1 (very bad, definitely need to move closer or father way) to 7 (excellent, perfect viewing distance).
Use a repeated-measures ANOVA with alpha = 0.05 to determine whether there is significant difference among the four viewing distances.
Test Hypotheses:
There are 3 groups of viewing distances. Denote the true average of the four groups of viewing distances 9-feet, 12-feet, 15-feet and 18-feet as μ1, μ2, μ3, and μ4, respectively.
The hypotheses to be tested are:
Null hypothesis:
H0: μ1 = μ2 = μ3 = μ4.
That is, the mean of all the four groups of viewing distances are equal.
Alternative hypothesis:
Ha: At least one of the mean of four viewing distance groups differs from the other.
Evidently, the test is for equality of 4 means. The means take numerical values.
Now, a one-way ANOVA of repeated measures is the most suitable for testing the equality of several means, provided the assumptions of independence of observations, normality of residuals and homogeneity of variances are satisfied.
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