How do you find the pooled standard deviation in an ANOVA table?

Ratuiszt
2022-09-30
Answered

How do you find the pooled standard deviation in an ANOVA table?

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Cullen Kelly

Answered 2022-10-01
Author has **7** answers

Note that a pooled standard deviation assumes that the population variances are equal. Now, there are two formulas for pooled standard deviation depending if the factors tested in ANOVA have the same group size.

For same group size, the pooled standard deviation can be computed as

$SD=\sqrt{\frac{(S{D}_{1}^{2}+S{D}_{2}^{2})}{2}}\phantom{\rule{0ex}{0ex}}$

where $S{D}_{1}$ is the standard deviation of the first group and $S{D}_{2}$ is thestandard deviation of the second group.

For unequal group size, the pooled standard deviation can be computed as

$SD=\sqrt{\frac{({n}_{1}-1)S{D}_{1}^{2}+({n}_{2}-1)S{D}_{2}^{2}}{{n}_{1}+{n}_{2}-2}}\phantom{\rule{0ex}{0ex}}$

where

$S{D}_{1}$ is the standard deviation of the first group.

$S{D}_{2}$ is the standard deviation of the second group.

${n}_{1}$ is the group size of the first group.

${n}_{2}$ is the group size of the seconf group.

For same group size, the pooled standard deviation can be computed as

$SD=\sqrt{\frac{(S{D}_{1}^{2}+S{D}_{2}^{2})}{2}}\phantom{\rule{0ex}{0ex}}$

where $S{D}_{1}$ is the standard deviation of the first group and $S{D}_{2}$ is thestandard deviation of the second group.

For unequal group size, the pooled standard deviation can be computed as

$SD=\sqrt{\frac{({n}_{1}-1)S{D}_{1}^{2}+({n}_{2}-1)S{D}_{2}^{2}}{{n}_{1}+{n}_{2}-2}}\phantom{\rule{0ex}{0ex}}$

where

$S{D}_{1}$ is the standard deviation of the first group.

$S{D}_{2}$ is the standard deviation of the second group.

${n}_{1}$ is the group size of the first group.

${n}_{2}$ is the group size of the seconf group.

asked 2022-07-22

Comparison between two diets in obese children, one low-fat and one low-carb 8 week intervention with the outcome of weight loss. Based on a similar study in adults, 20% of the children will not complete the study. For a 95% confidence interval with a margin of error of no more than 3 lbs., how many children should be recruited? In the adult trial, the low-fat and low-carb groups had a standard deviations of 8.4 and 7.7, respectively and each group had 100 participants.

A. Calculate the pooled standard deviation (Sp).

B. Calculate the number of children will need to be recruited for the trial if all finish the study use the Sp calculated for the standard deviation?

C. How many children would be needed to account for 20% attrition.

A. Calculate the pooled standard deviation (Sp).

B. Calculate the number of children will need to be recruited for the trial if all finish the study use the Sp calculated for the standard deviation?

C. How many children would be needed to account for 20% attrition.

asked 2022-09-25

Which is greater: the sample standard deviation or the population standard deviation? Explain.

asked 2022-08-11

Consider the data with analysis shown in the following computer output:

$\begin{array}{|cccc|}\hline \text{Level}& \text{N}& \text{Mean}& \text{StDev}\\ \text{A}& 4& 10.500& 2.902\\ \text{B}& 5& 16.800& 2.168\\ \text{C}& 6& 10.800& 2.387\\ \hline\end{array}$

$\begin{array}{|cccccc|}\hline \text{Source}& \text{DF}& \text{SS}& \text{MS}& \text{F}& \text{P}\\ \text{Groups}& 2& 125.07& 62.54& 10.34& 0.002\\ \text{Error}& 12& 72.55& 6.05\\ \text{Total}& 14& 197.62\\ \hline\end{array}$

What is the pooled standard deviation? What degrees of freedom are used in doing inferences for these means and differences in means?

Round your answer for the pooled standard deviation to two decimal places.

The pooled standard deviation is =

degrees of freedom =

$\begin{array}{|cccc|}\hline \text{Level}& \text{N}& \text{Mean}& \text{StDev}\\ \text{A}& 4& 10.500& 2.902\\ \text{B}& 5& 16.800& 2.168\\ \text{C}& 6& 10.800& 2.387\\ \hline\end{array}$

$\begin{array}{|cccccc|}\hline \text{Source}& \text{DF}& \text{SS}& \text{MS}& \text{F}& \text{P}\\ \text{Groups}& 2& 125.07& 62.54& 10.34& 0.002\\ \text{Error}& 12& 72.55& 6.05\\ \text{Total}& 14& 197.62\\ \hline\end{array}$

What is the pooled standard deviation? What degrees of freedom are used in doing inferences for these means and differences in means?

Round your answer for the pooled standard deviation to two decimal places.

The pooled standard deviation is =

degrees of freedom =

asked 2022-07-22

A two sample (independent-sample) study with n = 6 in each sample, produces a sample mean difference of 4 points and a pooled variance of 12. What is the value for the sample t score?Group of answer choices

A)1

B)2

C)4/6

D)4/8

A)1

B)2

C)4/6

D)4/8

asked 2022-09-30

can you write out this formula in the form of a sentence ?

$ES=\frac{\overline{{X}_{1}}-\overline{{X}_{2}}}{s}$

$ES=\frac{\overline{{X}_{1}}-\overline{{X}_{2}}}{s}$

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Assume that n= 20 and P =0.80 what is the standard deviation

asked 2022-07-09

How would actuarial science refer to the idea that the premium should increase as number of insured entities decreases.

In other words, what is the technical term for the intuition that I would charge a higher premium per car to insure just one car than to insure 1000 cars, if such intuition is even justified.

As a sketch of my thinking on this, I have defined risk-adjusted premium as the total premium to cover losses divided by the standard deviation of the total loss on the portfolio of policies. I believe both the numerator and the denominator can be deduced from the law of large numbers.

In other words, what is the technical term for the intuition that I would charge a higher premium per car to insure just one car than to insure 1000 cars, if such intuition is even justified.

As a sketch of my thinking on this, I have defined risk-adjusted premium as the total premium to cover losses divided by the standard deviation of the total loss on the portfolio of policies. I believe both the numerator and the denominator can be deduced from the law of large numbers.