Survey Ch. 9 Review
When does the phrase "free to vary" referring to a number of scored in a given sample, mean for statisticians?
"Free to Vary" refers to the number of scores that can take on different values if we know a given parameter
Why do we modify the formula for calculating standard deviation when using t-test and divide by (N-1)?
The alteration of the formula accounts for some level of error and a more accurate standard deviation`
How is the critical t value affected by sample size and degrees of freedom?
-As sample size increases t distribution becomes closer to the z distribution -Relationship between degrees of freedom and critical value determine statistical significance: - lower degrees of freedom means further apart; SD is small - higher degrees of freedom means closer; SD is greater
What do we mean when we say we have a distribution of mean differences
A distribution of mean differences is constructed by calculating the difference scores for a sample of individuals and then averaging those differences.
Why do the t distributions merge with the z distribution as sample size increases
As the sample size increases, we can feel more confident in the estimate of the variability
Why is a confidence interval more useful than a single-sample t test or a paired-samples t test?
As with other hypothesis tests, the conclusions from both the single-sample t test or paired-samples t test and the confidence interval are the same, but the confidence interval gives us more information-an interval estimate, not just a point estimate
How is paired-samples t test similar to to a single-sample t test
Both requires hypothesis testing Single sample: compare sample mean to population mean (between) Paired sample: compare two sample means (within)
Why is the population mean almost always equal to 0 for the null hypothesis in two-tailed, paired-samples t test?
For a "paired-samples" test, you always assume that null hypothesis is that the the two samples are equal. Or put another way, the "difference" between the two samples will have a mean equal zero.
If we calculate the confidence interval around the sample mean difference used for a paired-samples t test, and it includes the value of 0, what can we conclude?
If the confidence interval around the mean difference score includes the value of 0, then 0 is a plausible mean difference. If we conduct a hypothesis test for these data, we would fail to reject the null hypothesis
When do we use a paired-sample t test
Paired sample t- test, to compare two means for a within groups design, a situation in which every participant is in both samples
When should we use a t-distribution?
To decide how confident we can be when we want to know if we can generalize what we have learned about once sample to a larger population
How is paired-sample t tests different from a single-sample t test
Unlike a single sample t test, in the paired-samples t test we have two scores for every participant, we take the difference between these scores before calculating the sample mean difference that will be used in the t test
Explain the distinction between the terms independent samples and paired samples as they relate to t tests
paired=samples: used to describe a test that compares an individuals scores in two conditions; it is also called a paired-samples t test independent=samples: refers to groups that do now overlap in anyway, including membership; the observations made in one group in no way relate or depend on the observations made in another group
Define the symbols for the t-statistic: t= (M-um) ------------------ sm
t stands for the t statistic, M is the sample mean, um is the mean of the distribution of means, and sm is the standard error as estimated from a sample.
Explain what each part of the following statistical phrase means, as it would be reported in APA format: t(4)= 2.87, p= 0.032
t= statistical symbol 4= degrees of freedom 2.87= t statistic value 0.032= p value
Explain why the standard error for the distribution of sample means smaller than the standard deviation of sample scores
the t statistic which is the standard error for distribution of sample mean is not as extreme as the z statistic, making the t statistic more conservative
When is it appropriate to use a single-sample t test?
when we compare one sample to a population for which we know the mean, but not the standard deviation
How is the calculations of standard error different for a t-test than a z-test?
z-test: the population standard deviation is calculated with N in the denominator t-test: the standard deviation for the population is estimated by dividing the sum of squared deviations by (N-1)
