Question

In: Math

Differentiating pooled variance and the estimated standard error of the difference in sample means

 Differentiating pooled variance and the estimated standard error of the difference in sample means 

For the independent-measures t test, which of the following describes the pooled variance (whose symbol is sp2 )? 

The difference between the standard deviations of the two samples 

The variance across all the data values when both samples are pooled together 

A weighted average of the two sample variances (weighted by the sample sizes) 

An estimate of the standard distance between the difference in sample means (M1 - M2) and the difference in the corresponding population means (μ1 - μ2) 


For the independent-measures t test, which of the following describes the estimated standard error of M1 - M2 (whose symbol is S(M1 - M2)_)? 

The difference between the standard deviations of the two samples 

A weighted average of the two sample variances (weighted by the sample sizes) 

An estimate of the standard distance between the difference in sample means (M1 - M2) and the difference in the corresponding population means (μ1 - μ2) 

The variance across all the data values when both samples are pooled together


Aa Aa E 5. Differentiating pooled variance and the estimated standard error of the difference in sample means For the indepenSuppose you conduct a study using an independent-measures research design, and you intend to use the independent-measures t t



Solutions

Expert Solution

Result:

In calculating the test statistic, you typically first need to calculate the standard error . The standard error is the value used in the denominator of the t statistic for the independent measure t test.

size

DF

mean

sd

sum of squares

sample 1

21

20

27.6

4.5

405

sample 2

11

10

21.5

5.5

302.5

SS1 = 20*4.5^2 =405

Sd2 = sqrt(302.5/10) =5.5

Pooled variance = (405+302.5)/30 = 23.5833

Standard error of M1-M2 = sqrt(23.5833*(1/21+1/11)) = 1.8075

t statistic = ( 27.6-21.5)/1.8075 = 3.3748

Degrees of Freedom = 30


Related Solutions

a. Describe the Pooled variance assumption. How does it change the standard error? What impact does...
a. Describe the Pooled variance assumption. How does it change the standard error? What impact does it have on a test statistic? What impact does it have on a p-value? How do you justify making the assumption? HTML EditorKeyboard Shortcuts b. Republican Democrat Libertarian Support 18 24 8 Don't Support 14 12 5 The above contingency table was created by asking a sample of people in a given area if they support a measure taken by the government.   If The...
How do I calculate variance for sample of different scores, estimated standard error for the mean...
How do I calculate variance for sample of different scores, estimated standard error for the mean difference and repeated measure T statistic
Explain the difference between the standard error of a sample proportion and the margin of error...
Explain the difference between the standard error of a sample proportion and the margin of error of a confidence interval for a population proportion.
Use the formula to find the standard error of the distribution of differences in sample means,...
Use the formula to find the standard error of the distribution of differences in sample means, x1 - x2. (there are lines above both x's but my computer won't transcribe it) Samples of size  45 from Population 1 with mean  3.4 and standard deviation  1.5 and samples of size  45 from Population 2 with mean  1.9 and standard deviation  1.4
What is the difference between the standard deviation and the standard error? Is the standard error...
What is the difference between the standard deviation and the standard error? Is the standard error a standard deviation?
Hypothesis Test: Difference Between Means Sample A: 35 Observations, Mean = 10.255, Variance=0.310 Sample B :...
Hypothesis Test: Difference Between Means Sample A: 35 Observations, Mean = 10.255, Variance=0.310 Sample B : 20 Observations, Mean= 9.004, Variance= 0.831 H0: μA – μB= 0 H1: μA – μB ≠ 0 alpha=0.05 Can you run a hypothesis test for the difference between two means?
Std. Err (standard error): The average deviation of sample means from the hypothesized population mean of...
Std. Err (standard error): The average deviation of sample means from the hypothesized population mean of 4.73 drinks is about 0.44 drinks. T-stat (T-score): The observed sample mean of 3.93 drinks is 1.8 standard errors below the hypothesized population mean of 4.73 drinks. P-value: If the population mean is 4.73 drinks, there is a 7.2% chance that sample means will have an error larger than that observed in our sample (observed error = 4.73 – 3.93 = 0.8 drinks) when...
Question 2 What is the difference, if any, between the standard deviation of the sample means...
Question 2 What is the difference, if any, between the standard deviation of the sample means and the standard error of the sample means? Discuss
Describe the difference between standard deviation and standard error.
Describe the difference between standard deviation and standard error.
6.    The analysis of variance methodology will show that there really is a difference between the means...
6.    The analysis of variance methodology will show that there really is a difference between the means of several groups when:    a.    the variance within groups is significantly larger than the variance between groups. b.    the variance between groups is significantly larger than the variance within groups.             c.         the sum of squares within groups is large relative to the sum of squares total. d.    the sample means across the treatment groups are identical and equal the grand mean.             e.         none of the above. 7.    If all of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT