The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with α=.05 to determine whether there are any significant mean differences among the treatments. The table presented here summarizes data from three different treatment groups, denoted as I, II, and III. Below are the details for each group:- **Treatment I:** - $ n = 8 $: The number of observations in the group. - $ T = 16 $: The sum of the observations. - $ SS = 40 $: The sum of squares for the group.- **Treatment II:** - $ n = 6 $: The number of observations in the group. - $ T = 24 $: The sum of the observations. - $ SS = 24 $: The sum of squares for the group.- **Treatment III:** - $ n = 4 $: The number of observations in the group. - $ T = 32 $: The sum of the observations. - $ SS = 16 $: The sum of squares for the group.Additionally, the table includes aggregate information:- $ N = 18 $: The total number of observations across all groups.- $ G = 72 $: The grand total of all observations.- $ \Sigma X^2 = 464 $: The sum of squares of all observations. This data is often used in statistical analysis, such as ANOVA, to determine if there are significant differences between the treatment groups.

Given: α=0.05 Treatment I: n=8, T=16, SS=40 Treatment II: n=6, T=24, SS=24 Treatment III: n=4, T=32,…

Answered: Treatment II II n 8 n 4 N = 18 T 16 24…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with α=.05 to determine whether there are any significant mean differences among the treatments.

The table presented here summarizes data from three different treatment groups, denoted as I, II, and III. Below are the details for each group:

- **Treatment I:**
- $ n = 8 $: The number of observations in the group.
- $ T = 16 $: The sum of the observations.
- $ SS = 40 $: The sum of squares for the group.

- **Treatment II:**
- $ n = 6 $: The number of observations in the group.
- $ T = 24 $: The sum of the observations.
- $ SS = 24 $: The sum of squares for the group.

- **Treatment III:**
- $ n = 4 $: The number of observations in the group.
- $ T = 32 $: The sum of the observations.
- $ SS = 16 $: The sum of squares for the group.

Additionally, the table includes aggregate information:

- $ N = 18 $: The total number of observations across all groups.
- $ G = 72 $: The grand total of all observations.
- $ \Sigma X^2 = 464 $: The sum of squares of all observations.

This data is often used in statistical analysis, such as ANOVA, to determine if there are significant differences between the treatment groups.

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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