Statistics Test 2

If a 95% confidence interval for a related-samples t-test includes the value of 0 in the interval range, it can be inferred that:

(a) the independent (categorical) variable likely had no effect on the dependent variable.

A related-samples study would not be appropriate for which of the following situations?

(b) A researcher would like to compare individuals from two populations.

If a researcher reports that t(6) = 1.98, p > .05, then (choose the best response from a statistical perspective):

(b) the null hypothesis was not rejected.

What is the pooled variance for the following two samples? Sample 1: n = 6 and SS = 200 Sample 2: n = 10 and SS = 300

(c) 500/14

Which of the following sets of data is most likely to produce a significant t-statistic?

(c) MD = 10 and SS = 10

What is the estimated value of the standard error of the sampling distribution for the following set of difference scores from a related-samples study. Scores: 4, 8, 4, 4

(d) 1

A hypothesis test with a sample of n = 25 participants produces a t-statistic of t = 2.53. Assuming a two-tailed test, what is the correct decision?

(d) Researcher can reject the null hypothesis at α = .05 but not α = .01.

With α = .05 and a sample of n = 12 subjects in a related-samples experiment, the two-tailed critical region for the t-statistic has the boundaries of ___.

(d) t = ±2.20

An independent-samples t-test is appropriate when ___.

(d) there are two separate samples containing different subjects.

The alternative hypothesis for an independent-samples t-test states:

(d) μ1 - μ2 ≠ 0

What does a 95% confidence interval tell you?

A 95% confidence interval is the range of values that has a 95% chance of containing the true population mean for some population for which a sample has been obtained. The sample mean (the best guess as to the true population mean) is usually at the center of the interval.

What is pooled variance?

A weighted average of two sample variances.

At a general level, all t-tests generally have the same underlying equation and logic. What is the general logic of a t-test (i.e., describe this test in words that could apply to any of the types of t-tests you have learned about)?

All t-tests look at the difference between the obtained sample mean and the null hypotheses mean relative to the units of standard error (that is, relative to how much difference we'd expect just by sampling error alone). If the difference is a lot more than we would expect due to sampling error, we conclude that the sample mean did not come from the hypothesized population.

What is the sampling distribution for an independent-samples t-test a distribution of? Be specific (imagine simulating making such a distribution from an actual population).

Assume that you have a single population with an unknown mean. From this population, imagine taking a sample of size n1 and computing its mean and then taking a sample of size n2 and computing its mean and then getting the difference between the two means. If you plotted this difference for all possible samples, you would get the sampling distribution of mean differences.

What does Cohen's d tell you? (It is the measure of effect size, but what does this mean?)

Cohen's d is a measure of effect size. It is a measure of how different the obtained sample mean (which is one's best guess as to the mean of the population the sample came from) is from the population mean associated with the null hypothesis. It is a way of saying how different the obtained mean is from the hypothesized population mean (and thus how big an effect any treatment had), in standard deviation units, without regard for sample size.

What is a one-sample / or related samples t-test sampling distribution a distribution of?

It is a probability distribution showing what the means would be for all the samples of size n drawn from a hypothesized population with a particular mean and standard deviation. In the case of the related samples t-test, the hypothesized population is always one in which the scores are difference scores and the mean of the hypothesized population is 0. So the sampling distribution is what the mean difference scores for all samples of size n will look like if the null hypothesis is correct. (You can use this when you get your own samples difference score to see if it is more extreme than what you would expect due to sampling error alone.)

What is a sampling distribution generally speaking?

It is a probability distribution showing what the means would be for all the samples of size n drawn from a hypothesized population with a particular mean and standard deviation. You can imagine getting it, in the simplest case, by taking each sample of size n from a population, finding its mean, and plotting the mean value on a new graph, and doing this for all possible samples of this size. The resulting plot with be normally distributed with the same mean as the original population and with a standard error that is based on the original standard deviation, sample size, and the nature of the analysis being done (e.g., one-sample vs. independent samples t-test). It is used in hypothesis testing to assess how likely you would be to get a particular sample if the null hypothesis were correct and thus whether your obtained sample is likely to have come from the hypothesized population or not.

Why is the standard error of the sampling distribution for an independent samples t-test so much larger than that for a one-sample t-test?

It is nearly double the size because of how one makes the sampling distribution. Imagine you have a hypothesized population with a particular mean. When you make a sampling distribution for a one-sample t-test, you take samples of size n and plot the means of the individual samples. When you make sampling distribution for an independent samples t-test, you take two samples (of size n1 and n2) at a time from the population, and plot the difference between the means of the two samples for all possible samples. The latter (taking the differences between two means) leads the standard error to be larger. Consider an example of a population distribution with scores ranging from -10 to 10 and samples of size 1 for the sampling distribution. For the one-sample sampling distribution, the sample means will also range from -10 to 10 (because they are samples of size 1). For the two-sample distribution, the plotted mean differences will range from 20 (10 minus -10) to -20 (-10 minus 10), leading to a larger spread.

What can affect Cohen's d?

Just variance/ standard deviation, larger variance produces smaller measures of effect size

The extreme values in what would result in extreme values in t-test?

Larger n and smaller variance (and larger mean difference) always means more likely to see given sample as extreme.

How is standard deviation different from standard error?

Standard deviation refers to the standard or approximately average amount a set of scores vary from their mean. The SD can be used to assess how far a new score is likely to be from the mean. This is the order of magnitude in which scores should be expected to vary. Standard error is a measure of standard deviation as well, but this is the term used in the context of sampling distributions. It is the standard or approximately average amount a set of sample means vary from the hypothesized population mean. The SE can also be used to assess how far a newly collected sample mean is likely to be away from the population mean (if the null hypothesis is true) due to sampling error. So if the hypothesized population mean is 10 and the SE is 20, you would expect that a new sample collected could have a mean around 20 units away (e.g., at -10 or at 30). This does not mean it will be, but just that this is the order of magnitude in which means should be expected to vary when they come from this population.

Define the term standard deviation.

The standard deviation is the standard, or approximately average, distance away from the mean of a set of values in a distribution. It can also be though of as how far, on average, one should expect a new sampled value to be from the mean of the distribution.

Assuming there is a 5-point difference between two sample means, which set of sample characteristics is most likely to produce a significant value for the independent-samples t-statistic?

n1 = n2 = 100 and small sample variances

The null hypothesis for a related-samples t-test is:

μD = 0