Psych 250 Unit 2 Test

Briefly describe 3 assumptions of the independent-samples t-test.

1. Data is sampled from normally distributed populations 2. Homogeneity of the variances of the populations 3. Independent observations

Is it possible to generate a 100% CI? Explain.

A 100% confidence level could happen if the population is bounded and every member of the population is tested

For a sample of n=100, what will produce a broader confidence interval: a 90% confidence level or a 95% confidence level?

A 95% confidence level will produce a broader confidence interval because the higher the confidence level, the more values are being used

What kind of error has occurred if you falsely rejected the null hypothesis?

A Type I error

What kind of error has occurred if you overlooked a real difference between two means?

A Type II error has occurred because by overlooking a real difference, the null hypothesis was claimed true when in reality it's false

In general, what will produce narrower confidence intervals, sample sizes of n=10 or n=20?

A larger sample size would result in a narrower confidence level because the population would be better represented so there would be a smaller margin of error, therefore a narrower confidence interval

In the context of hypothesis testing, what is alpha?

Alpha is the probability of rejecting the null hypothesis when it is true

If p = .525 and a researcher rejects the null hypothesis, what was alpha?

Alpha was greater than .525

Describe how CIs change if you increase the sample size.

As a sample size increases, the margin of error decreases, so the CI becomes narrower

What is the relationship between sample size and power?

As sample size increases, power increases

In everyday language, define Type I error in the context of a two tailed, independent-samples t-test.

Claiming that the mean of the two samples are different when they really aren't

In everyday language, define Type I error in the context of a two-tailed, dependent samples t-test.

Claiming that the mean of the two samples are different when they really aren't

In everyday language, define Type II error in the context of a two tailed, independent-samples t-test.

Claiming that the mean of the two samples are the same but they are really different

In everyday language, define Type I error in the context of a two-tailed, single sample t-test.

Claiming the sample is different fromt the expected value when it really isn't

In everyday language, what are confidence intervals?

Confidence intervals represent the range of values that contain the population mean, some number of times out of 100

What is the difference between "power" and "effect size"?

Effect size shows how different the means of the samples are taken into consideration the size of the sample and its variability.

You run a null hypothesis statistical test (NHST). What is the appropriate conclusion if p < alpha? What is the probability that you have made a Type I error?

If p < alpha, then the null hypothesis should be rejected. The probability of a Type I error is p.

You run a null hypothesis statistical test (NHST). What is the appropriate conclusion if p > alpha? What is the probability that you have made a Type I error?

If p > alpha, then the null hypothesis should be retained, so the probability of a Type 1 error is 0.

If you do not reject the null hypothesis, what is the probability that you made a Type I error? Explain.

If you do not reject the null hypothesis, then the probability that you made a Type I error is 0 because a Type I error can only happen if you reject the null hypothesis when in reality it's actually true.

If you reject the null hypothesis, what is the probability that you made a Type II error? Explain.

If you reject the null hypothesis, then the probability that you made a Type II error is 0 because a Type II error can only happen when the null hypothesis is retained when in reality it is false.

In general, what is the effect of increasing sample size on the likelihood of statistically significant differences between group means?

Increasing sample size will increase the likelihood of statistically significant differences between group means

In general, what is the effect of increasing the difference between sample means on the p value of an independent-samples t-test?

Increasing the difference between sample means of an independent t test will increase p.

When is it most important to use a dependent-samples t-test instead of an independent-samples t-test?

It's more important to use a dependent samples t test instead of an independent samples t test when you study a subjects behavior twice, meaning they have related samples

If you calculate a 95% CI, do 95% of the values lie within the CI? Explain.

No, a 95% CI is a range of values with a 95% certainty that the range contains the true mean of the population.

Does a large p value prove that the null hypothesis is true? Explain.

No, a large p value does not prove that the null hypothesis is true. The larger the p value, the more likely it is to be retained, but it does not prove that it's true.

In statistical work, is a "statistically significant effect" one that would be expected by chance? Explain.

No, a statistically significant effect would not be expected by chance, it would be influenced by some nonrandom cause. A statistically significant effect is the rejection of the null hypothesis. The null hypothesis assumes that the effect is due to chance, so the rejection of the null hypothesis rejects the idea that the relationship is affected by chance.

Can p values be negative? Explain.

No, p values cannot be negative because a p value is a probability and probabilities cannot be negative.

In the context of hypothesis testing, what is p?

P is the probability that the null hypothesis is true.

In general, what is the effect of reducing within-group variance on the p value of an independent-samples t-test?

P will increase if within group variance decreases in an independent sample t test

Why is random sampling important for statistical inference? (Hint: Think in terms of Type I and II errors and the problem of having a biased sample.)

Random sampling is important for statistical inference because if a sample is biased, then the p value could be artificially small, leading to you incorrectly rejecting the null hypothesis, resulting in a Type I error. Or, the p value could be artificially large, leading to incorrectly retaining the null hypothesis, resulting in a Type II error.

What does the phrase "statistical significance" mean?

Statistical significance means that the relationship found in the data did not occur by random chance, the probability of the event happening within the sample is less than the defined criteria

What value of alpha guarantees that you will not reject the null hypothesis?

The alpha level 0 should be used to guarantee that the null hypothesis will be retained

What value of alpha should you use to (almost) guarantee that you will reject the null hypothesis?

The alpha level 1 should be used to guarantee that the null hypothesis will be rejected

What is an alternative or research hypothesis?

The alternative hypothesis is the hypothesis that sample observations are influenced by some non-random cause. The difference between sample observations and the pattern of data is anticipated by the researchers.

In everyday language, under what condition should we reject the null hypothesis that a sample came from or represents a particular population?

The condition when we should reject the null hypothesis is when the probability of the event happening within the sample is less than the defined criteria.

If you use alpha = .05 instead of alpha = .10, then does the difference between group means need to be larger, smaller, or the same to obtain statistical significance?

The difference between group means needs to be larger to obtain statistical significance

What is the mean of all t distributions?

The mean of all t distributions is 0.

What is a null hypothesis?

The null hypothesis is a hypothesis with information about some aspect of the state of the world that researchers work to reject. The sample observations are influenced by some random cause.

Is the p value the probability that the null hypothesis is true? If not, what is it?

The p value is the probability of a particular outcome or a more extreme one. When null is rejected, it's the probability of a Type I error.

If p = .0002 and alpha is .50, what is the probability that you will make a Type I error?

The probability is .0002

Describe the assumption "homogeneity of variance."

The variance within each population are equal to each other

When do you use a dependent-samples t-test?

Use a dependent-sample t test when there are two related samples, meaning that there is a common membership in both samples.

When do you use a single-sample t-test?

Use a single-sample t test when there is only one sample to test and an expected value.

When do you use an independent-samples t-test?

Use an independent-sample t test when there are two independent samples, meaning the membership in both samples are different.

What does it mean for a test to be robust to violations of one or more of its assumptions?

When a test is robust to violations of one or more assumptions, it means that even though an assumption is violated, it still yields an accurate p value.

When do you use a one-tailed test?

You use a one-tailed test when you are testing an effect in only one direction. For example, if you are testing if a machine is overfilling bags, you would use a one-tailed test because you are only testing if the bags are being filled with more chips than the average number of chips, you don't have to test if the bags are being filled with less chips than the average.

When do you use a two-tailed test?

You use a two-tailed test when you are testing an effect in both directions. For example, if you are testing if a chip filling machine is broken, you would use a two-tailed test to find whether the bags are being underfilled or overfilled compared to the average number of chips.