Psy 350: Exam 2

What is the difference between a directional hypothesis and a nondirectional hypothesis?

*We can make predictions that are directional*: H1: μ> 0; H1: μ1> μ2; H1: r> 0 *Or nondirectional*: H1: μ≠ 0; H1: μ1≠ μ2; H1: r≠ 0

What is the connection between Type II error and research design?

*Why wouldn't we find an effect if it's really there?* Sometimes by chance. Often, by design flaws! *It's hard to find an effect -even a real effect -if you have*: A weak manipulation. Unreliable (noisy) measures. Small samples. Confounding variables that counteract the impact of your variables. An overly complicated study design.

What do the four basic steps look like in an independent-samples t-test?

1. H0: μ1-μ2= 0, Both groups will report the same number of correct answers. H1: μ1-μ2≠ 0, One group will report more correct answers than the other. 2. df= (n1+ n2 ) -2 = (8 + 8) -2 = 14. For α= .05, our critical t = 2.145. 3. Sample 1 has M = 8, SS= 60, and s2= 8.57. Sample 2 has M = 12, SS= 66, and s2= 9.43. (60+66)/(7+7)= 9. Then, sqrt of 9/8 + 9/8 is 1.5. 4. (8-12)/1.5= -2.67. So, -2.67 is more extreme than -2.145, so we reject H0.

In class (and your text), we discussed three factors that tend to make it more likely that we will obtain a large test statistic (e.g., z-score) and thus reject the null hypothesis - what are they?

1. Having a larger difference between M and μ. 2. Having a smaller population standard deviation -less real variability overall. 3. Having a larger number of observations (sample size).

What four steps do we go through every time we conduct an inferential test?

1. State your hypotheses 2. Choose your α level and find the critical region. 3. Compute your test statistic. 4. Compare your test statistic to the critical region and make a decision!

As discussed in lecture and your text, what are the four assumptions underlying all of our inference tests?

1. Your sample was random. 2. Your observations are independent-statistically independent, one does not affect the probability of another. 3. The standard deviation in the "unknown population" is the same as in the known population. 4. The distribution of sample means (or other effects) is normal.

What is the definition of an effect size?

A measure of effect size is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.

When would you use a one-sample t-test?

A one-sample t-test is useful when we know or can assume the population mean, but we don't know the population standard deviation.

By default, which hypothesis do we always assume is true unless we have evidence to the contrary?

By default, we assume that the null is probably true until we have evidence that we should reject it.

What are the consequences of Type I error? Why do we worry about it?

Claiming a treatment works when it doesn't, promoting a behavior or technique that doesn't actually make a difference, developing theories or interventions or training programs based on a finding that isn't real.

What are the consequences of a Type II error?

Failing to use a treatment that would help, abandoning a line of research that would have been productive, missing an opportunity to make a difference, making a straightforward finding unnecessarily complicated.

What do the four basic steps look like in a one-sample t-test?

From your text: do babies prefer attractive faces over unattractive ones? 1. If babies have no preference (H0), they should pay equal attention to both faces. (H0: μ= 10, H1: μ≠ 10) 2. We have a sample of 9 babies, so df= 9-1 = 8. We need to use the t distribution with 8 df. Our critical value is t = 2.306. 3. 13-10= 3, Sqrt of 9/9(variance over sample size) is 1. Test statistic is 3.0. 4. 3.0 > 2.306, so we reject H0.

When do we reject the null hypothesis? When (if ever) do we prove it?

If the sample statistic we have falls in the critical region, we reject the null hypothesis.

In very broad terms, how do we estimate power, and how do we estimate the sample size we need?

If we know our α level, our sample size, and the effect size we expect, we can estimate our statistical power! Often, we estimate a range of possible effects for the sample size we need.

When would it be appropriate to use a dependent-samples t-test? What makes the samples dependent?

In other words, a dependent-samples t-test is just a one-sample test using difference scores instead of single values!

What is the conceptual definition of Cohen's d?

One common effect size index for comparing two groups Cohen's d tells us how different the "unknown population" is from the known population.

What changes if you use a one-tailed t-test instead of a two-tailed t-test? When and why would you do this?

Only if we want directionality!

How is our alpha level related to Type I error? Be as specific as you can here.

Our alpha level is the probability that we will make a Type I Error.

What is practical significance? How is it related to statistical significance (if at all)?

Practical significance = is this effect big enough to matter? No statistic for this! Depends on context and judgment.

Explain the idea of the "unknown population." What does it mean if we conclude that our sample is more likely to have come from the unknown population than the known one?

Remember that a hypothesis usually involves a comparison. And the population parameters are generally unknown. We compare a known (or assumed) population with an unknown one.

What is statistical power?

Statistical power is "the probability that the H0 will be rejected when it is false, that is, the probability of obtaining a significant result."

What is the alpha level? What is the critical region? How are these related?

The *alpha level*, or level of significance, is the decision rule we set about the level of probability we will consider "pretty unlikely." The *critical region* is the part of the distribution of sample statistics that is more extreme than (outside) the point in the distribution that corresponds to alpha.

What is the definition of the alternative hypothesis? What symbol do we use to represent it?

The alternative hypothesis states that there is a change, a difference, or a relationship for the general population. We symbolize the null hypothesis with H1.

What information do you need in order to calculate Cohen's d for a t-test?

The formula stays the same, but we again use the sample SD instead of the population SD.

What is the definition of the null hypothesis? What symbol do we use to represent the null?

The null hypothesis states that in the general population there is no change, no difference, or no relationship. We symbolize the null hypothesis with H0.

How is the t distribution different from the z distribution? How is it similar?

The z-score distribution is the set of z-scores for all possible samples of a particular size (n). In the same way, the t-score distribution is the set of t-scores for all possible samples of a particular size (n). But the shape of the t distribution varies slightly depending on the degrees of freedom (n-1).

What is a p-value? What does the p stand for?(If nothing, then what will it fall for?)

This is the probability that we would see a value as extreme or more so as our sample statistic if the null hypothesis were true. P stands for precise.

What is the difference between Type I and Type II error? How is each one defined?

We could conclude that there is an effect when there really isn't (Type I error) We could conclude that there is no effect when there really is (Type II error)

Generally speaking, how do we use the t formula to obtain a confidence interval?

We estimate t by using the t distribution. We know what % of sample ts fall in between +/-any particular value of t. Sample mean +/- the test statistic times the mean standard error. μ= M +/-(t x sM)

Do we need to report both a significance test and an effect size? Why or why not?

We need to report both the significance test and the effect size for our results to make sense.

In what situations would it be appropriate to use a t-test?

When comparing two different means from two different statistics

What do we mean when we say that a finding is statistically significant? Be precise here - this is a case where it's a good idea to memorize the exact phrase.

When we reject the null, we describe our finding as statistically significant. This means that it is unlikely we would have observed our result if the null hypothesis were true.

What is a one-tailed test? What is a two-tailed test? When would you use each one?

When we use a *one-tailed test*, our critical region is all at the same end of the distribution. When we use a *two-tailed test*, our critical region is divided between the two ends. If we're interested in values at either end of the distribution, we use a two-tailed test. If we're only interested in one end, we use a one-tailed test.

Can we quantify the probability of Type II error as we do Type I error?

Yes-but as your textbook says, it's complicated.

What is a confidence interval? What is its purpose?

a confidence interval is a range of values centered around a sample statistic. The width of the interval gives us a certain degree of confidence that the population parameter is inside that interval.

What roles do samples and populations play in hypothesis testing?

a hypothesis testis a statistical method that uses sample data to evaluate a hypothesis about a population

What's a hypothesis? How do we define it?

a specific prediction about a pattern you expect to see in your data

How does the effect size we expect to find affect the statistical power of our study?

d = 0.2 = a small effect d = 0.5 = a medium effect d = 0.8 = a large effect

Is Cohen's d affected by sample size? If so, how? If not, why not?

d is independent of the sample size!

In general terms, what are degrees of freedom?

degrees of freedom describe the number of scores in a sample that are independent and free to vary.

What is r2? How do we interpret it - what does it mean?

percent of variance in the outcome that is explained by the treatment.

What is the general conceptual formula for all three kinds of t-tests? This is another one you should commit to memory!

t = difference btwn means/estimated standard error

What is an independent-samples t-test?

you are comparing two samples with different people in each sample