EDPS 459 Ch.9 Review
sample size (N)-1
What is the Degree of Freedom for a single-sample t test
2.093
I have an alpha of a = 0.05, and N = 20 Using a two-tailed test, find my tcrit value.
2.228
I have an alpha of a = 0.05, and degrees of freedom df = 10 Using a two-tailed test, find the tcrit value
- confidence in the estimates improves - degrees of freedom increase - critical values for t decrease (making it easier to reach statistical significance) - the t distributions approach the z distribution"
What happens to a t distribution as the sample size increases
Single-sample t test
A(n) _____ is a type of t test in which we compare data from one sample to a population for which we know the mean but not the standard deviation.
[3.92,36.08]
Calculate a 95% confidence interval using the following statistics: df = 15 a = 0.05 (two-tailed) estimated standard error = 7.54 estimated population standard deviation = 8.65 sample mean = 20.00 population mean = 19.67
0.04
Calculate the effect size, Cohen's d, using the following statistics: df = 15 alpha a = 0.05 (two-tailed) estimated standard error of 7.54 estimated population standard deviation of 8.65 sample mean of 20.00 population mean of 19.67
5.21
Calculate the estimated population standard deviation (s) from the following scores: 10 15 20 13 9 5
2.12
Calculate the estimated standard error (sM) from the following scores 10 15 20 13 9 5
when the research hypothesis allows for change in either direction
How can you determine a two-tailed test is being used
through degrees of freedom
How do t tables take the size of the sample into account
1. Draw the t distribution with the confidence interval 2. Indicate the bounds of the confidence interval on the drawing 3. Look up the t statistics for the critical values and mark these on the drawing 4. Convert the t statistics back into raw means 5. Verify that the confidence interval makes sense
Steps to Calculate a Confidence Interval for a Single-Sample t Test
1. Write the symbol for the test statistic- t(df) 2. Write the degrees of freedom in parentheses 3. Write an equal sign and then the value of the test statistic 4. Write a comma and then indicate the p value by writing "p=" (p<0.05= reject null) (p>0.05= fail to reject null)
Steps to writing the APA formate of presenting test statistics
how far the sample mean is from the population mean in terms of estimated standard error
What does the t statistic tell us
- help us specify how confident we can be about research findings - tell us how confident we can be that a sample differs from the larger population
What are t distributions used for in general
if our test statistic falls in the critical region
When do we find a "significant" test statistic using t test
If the difference in means occurs less than 5% of the time due to chance
When do we reject the null hypothesis using t test
- when we don't know the Population σ (Standard Deviation) - hypothesis test in which we compare a sample to a population where we know the mean of the population, but not the population standard deviation - When the sample size is less than 30
When do we use Single-Sample t Test
when comparing two samples and every participant is in only one sample—a between-groups design
When do we use a Independent-Samples T test
when comparing two samples and every participant is in both samples—a within-groups design
When do we use a Paired-Samples T test
when comparing a sample mean to a population mean but do not know the population standard deviation
When do we use a Single-Sample T test
it requires only that we know the population mean (not the population standard deviation)
Why are single-sample t test more useful than a Z test
They would decrease (move closer to the mean)
With α = 0.05 and df = 8, the critical values for a two-tailed test are t = ± 2.306. Assuming that all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t?
