Stats Exam 3

Percentage of variance accounted for by the treatment (r^2)

A measure of effect size that determines what portion of the variability in the scores can be accounted for by the treatment effect.

Null Hypothesis

(H0) states that in the general population there is no change, no difference, or no relationship. In the context of an experiment, H0 predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population.

1 Null Hypothesis and Alpha Level 2 Critical Region 3 T Statistic 4 Decision

What are the 4 steps for a hypothesis test?

Increases

What effect does increasing alpha from .01 to .05 have on power?

Estimated Standard error of M1 and M2

(sM) is used as an estimate of the real standard error σM when the value of σ is unknown. It is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean M and the population mean μ.

Independent Measures research design

A research design that uses a separate sample for each treatment condition or each population being compared.

Independent-Measures

A research design that uses a separate sample for each treatment condition or each population being compared. AKA (BETWEEN SUBJECTS)

IMD = 40 RMD = 20 MSD = 40

A researcher conduct and experiment comparing two treatment conditions and obtains data with 20 scores for each treatment condition. How many subjects would be used for an IMD, RMD, and MSD

B. M=86

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of µ = 80 and a standard deviation of σ = 12. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.50 is obtained. Based on this information, what is the mean for the treated sample?​ Select one: a. ​This cannot be answered without knowing the sample size. b. ​M = 86 c. ​M = 6 d. ​M = 82

Homogeneity of Variance

An assumption that the two populations from which the samples were obtained have equal variances.

Increases

By increasing the numerator of a Z statistic what happens to the z Score?

Type I error

Error occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation, a Type I error means the researcher concludes that a treatment does have an effect when in fact it has no effect. False Negative

A. Fail to reject H0 and make a Type II error.

Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. What outcome is likely if this happens?​ Select one: a. ​Fail to reject H0 and make a Type II error. b. ​Correctly reject H0. c. ​Correctly fail to reject H0. d. ​Reject H0 and make a Type I error.

B. If the samples are the same size and have the same mean and have the same variance.

If two samples are selected from the same population, under what circumstances are the two samples guaranteed to have exactly the same t statistic?​ Select one: a. ​If the samples are the same size and have the same mean b. ​If the samples are the same size and have the same mean and have the same variance c. ​If the samples are the same size and have the same variance d. ​If the samples have the same mean and the same variance

Independent Measures t Statistic

In a between-subjects design, a hypothesis test that evaluates the statistical significance of the mean difference between two separate groups of participants.

Type 1

Saying there is an effect, when there really is not.

Type 2

Saying there is not an effect when there really is.

Power

The ___________________ of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists.

C. 2

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 16. If there are n = 8 scores in each sample, then what is the estimated standard error for the sample mean difference?​ Select one: a. ​128 b. ​4 c. ​2 d. ​16

B. 6/2

The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points.If there are n = 8 scores in each sample, then the value for the t statistic is ____.​ Select one: a. ​6/0.25 b. ​6/2 c. ​6/4 d. ​6/0.50

Order effects

The effects of participating in one treatment that may influence the scores in the following treatment.

Alpha Level

The level of significance, is a small probability value that is used to define the concept of "very unlikely" in a hypothesis test.

Alpha

The probability of a type I error

B. ​±2.086

The results of an independent-measures research study are reported as "t(20) = 2.12, p < .05, two tails."For this study, what t values formed the boundaries for the critical region?​ Select one: a. ​±2.093 b. ​±2.086 c. ​±2.074 d. ​±2.080

One-tailed test (directional test)

The statistical hypotheses (H0 and H1) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.

Confidence interval

This is an interval, or range of values centered around a sample statistic. The logic behind a confidence interval is that a sample statistic, such as a sample mean, should be relatively near to the corresponding population parameter.

Critical Region

This is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data fall in the critical region, the null hypothesis is rejected.

Effect Size

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

t distribution

This is symmetrical and centered at zero like a normal distribution. A t distribution is flatter and more spread out than the normal distribution, but approaches a normal shape as df increases. It has greater variability and uses a sample variance rather than a population variance.

t statistic

This is used to test hypotheses about an unknown population mean, μ, when the value of σ is unknown. The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator.

Related Samples Design

Two research designs that are statistically equivalent. The scores in one set are directly related, one-to-one, with the scores in the second set.

C. The average distance between M and µ that would be expected if H0 was true.

What is measured by the denominator of the z-score test statistic?​ Select one: a. ​The position of the sample mean relative to the critical region b. ​Whether or not there is a significant difference between M and µ c. ​The average distance between M and µ that would be expected if H0 was true d. ​The actual distance between M and µ

1 Decrease 2 Increase 3 Remain Constant 4 Increase

What is the effect on the denominator, z score, Cohen's d and power when you increase N of a z statistic?

B. n = 16

A researcher reports an independent-measures t statistic with df = 30.If the two samples are the same size (n1= n2), then how many individuals are in each sample?​ Select one: a. ​n = 15 b. ​n = 16 c. ​n = 30 d. ​n = 31

Alternative Hypothesis

(H1) states that there is a change, a difference, or a relationship for the general population. In the context of an experiment, H1 predicts that the independent variable (treatment) does have an effect on the dependent variable.

estimated standard error

(sM) is used as an estimate of the real standard error σM when the value of σ is unknown. It is computed from the sample variance or sample standard deviation and ((provides an estimate of the standard distance between a sample mean M and the population mean μ.))

repeated measures design

A research design in which the different groups of scores are all obtained from the same group of participants. Also known as Within-subjects research design. Design in which the dependent variable is measured (two) or more times for each individual in a single sample. The same group of subjects is used in all of the treatment conditions.

Repeated-Measures

A research design in which the different groups of scores are all obtained from the same group of participants. Also known as repeated-measures design. AKA (WITHIN SUBJECTS)

B. b. ​σ = 5 and α = .05

A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, given the same sample size, which combination of factors is most likely to result in rejecting the null hypothesis?​ Select one: a. ​σ = 10 and α = .01 b. ​σ = 5 and α = .05 c. ​σ = 10 and α = .05 d. ​σ = 5 and α = .01

D. N = 36

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample?​ Select one: a. ​n=32 b. ​n = 34 c. ​n = 35 d. ​n = 36

Null Hypothesis Population mean 1 - Population mean 2 = 0 Alternative Hypothesis does not equal 0 Critical Value = 2.069 Significance level alpha .05 two tails Pooled Variance = 13.5 Standard error = 1.5 T Value -3.33 Decision = Reject the null hypothesis, because their is significant evidence.

A researcher conducts an independent-measures study examining how the brain chemical serotonin is related to aggression. One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin. A second sample of rats receives a drug that lowers brain levels of serotonin. Then the researcher tests the animals by recording the number of aggressive responses each of the rats display. The data are as follows. Control Low Serotonin n = 10 n = 15 M = 14 M = 19 SS = 180.5 SS = 130.0 a. Does the drug have a significant effect on aggression? Use an alpha level of .05. Show all 4 steps - You do NOT have to include formulas but must state hypotheses, critical value, pooled variance, standard error of m, t value, and decision to reject or fail to reject the null.

1. SM = 1 2. Critical Value = 2.306 = two tail, one tail = 1.860 Alpha .05 3. t Value = -3 4. Significance = Reject the Null Hypothesis becuase the data is significant. 5. The null hypothesis is Hnull = 10 6. Alternative Hypothesis H1 > 10

A researcher is testing the effect of a new cold and flu medication on mental alertness. Average mental alertness for the general population is μ = 10. A sample of n = 9 college students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's performance is measured on a video game that requires careful attention and quick decision making. The scores for the nine students produced a M = 7 and SS = 72..a. Are the data sufficient to conclude that the medication has a significant effect on mental performance? Test at the .05 level of significance. Make sure to organize your answer in the 4 steps of hypothesis testing and show the answer for each computation needed. You do not need to write formulas or draw graphs.

Significant (Statistically Significant)

A result is said to be this if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject H0.

D. r2 = 4/19

A sample of n = 16 scores produces a t statistic of t = 2.00. If the sample is used to measure effect size with r2, what value will be obtained for r2?​ Select one: a. ​r2 = 2/20 b. ​r2 = 4/20 c. ​r2 = 2/19 d. ​r2 = 4/19

C. The sample mean should be close 80 and should lead you to fail to reject the null hypothesis.

A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample. What is expected if the treatment has no effect?​ Select one: a. ​The sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis. b. ​The sample mean should be very different from 80 and should lead you to reject the null hypothesis. c. ​The sample mean should be close 80 and should lead you to fail to reject the null hypothesis. d. ​The sample mean should be close to 80 and should lead you to reject the null hypothesis.

D. 2

A sample of n = 4 scores has SS = 48. What is the estimated standard error for the sample mean?​ Select one: a. ​16 b. ​4 c. 1​ d. 2

Pooled variance

A single measure of sample variance that is obtained by averaging two sample variances. It is a weighted mean of the two variances

Cohen's d

A standard measure of effect size computed by dividing the sample mean difference by the sample standard deviation.

Test Statistic

A statistic that summarizes the sample data in a hypothesis test. The test statistic is used to determine whether or not the data are in the critical region.

Hypothesis Test

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

A. the results are significant

A study produced the following results: t(50) = 2.993, p < .05, r2 = .25. Based on the information provided, what did the researcher conclude? Select one: a. the results are significant b. there is not enough information c. the results are not significant

A. df = 23

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.What is the df value for the t statistic for this study?​ Select one: a. ​23 b. ​27 c. ​26 d. ​24

Both Increase

By decreasing alpha from .05 to .01 what is the effect on the critical region, and the likelihood of a Type I error?

Increases

By increasing sample size, what effect does it have on the likelihood if rejecting the null hypothesis

Decrease both

By increasing sample variance, what effect does it have on the effect size and the likelihood of rejecting the null hypothesis?

A. increasing the risk of a Type I error

By selecting a larger alpha level, a researcher is ____.​ Select one: a. ​increasing the risk of a Type I error b. ​attempting to make it more difficult to reject H0 c. ​decreasing the risk of a Type I error d. ​less able to detect a treatment effect

degrees of freedom

Definition:Degrees of freedom describe the number of scores in a sample that are independent and free to vary. Because the sample mean places a restriction on the value of one score in the sample, there are n − 1 degrees of freedom for a sample with n scores. Chapter 11= n+n-2.

sample standard deviation

Describes the variability of the scores in the sample. The standard distance between a score and the sample mean.

matched-subjects design

Design in which each individual in one sample is matched with an individual in the other sample. The matching is done so that the two individuals are equivalent (or nearly equivalent) with respect to a specific variable that the researcher would like to control.

Type II Error

Error occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect. False Positive

B. Reject H0 and make a Type I error.

Even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from the population mean. What outcome is likely if this happens?​ Select one: a. ​Correctly reject H0. b. ​Reject H0 and make a Type I error. c. ​Correctly fail to reject H0. d. ​Fail to reject H0 and make a Type II error.

B. 8/2

For an independent-measures research study, the data show an 8-point difference between the two treatment means and a pooled variance of 4.Given this information, what is the value of Cohen's d?​ Select one: a. ​4/8 b. ​8/2 c. ​8/1 d. ​8/4

You must use the t distribution table and df.

How to do you find a critical value for a T statistic.

D. A Type II error

If a treatment has a very small effect, then what is a likely outcome for a hypothesis test evaluating the treatment?​ Select one: a. ​A Type I error b. ​Correctly fail to reject the null hypothesis c. ​Correctly reject the null hypothesis d. ​A Type II error

D. ​It will increase the estimated standard error and decrease the likelihood of rejecting H0.

If other factors are held constant, what is the effect of increasing the sample variance?​ Select one: a. ​It will increase the estimated standard error and increase the likelihood of rejecting H0. b. ​It will decrease the estimated standard error and decrease the likelihood of rejecting H0. c. ​It will decrease the estimated standard error and increase the likelihood of rejecting H0. d. ​It will increase the estimated standard error and decrease the likelihood of rejecting H0.

B. 8

One sample has a variance of s2 = 10 and a second sample has a variance of s2 = 6.If the two samples have the same number of scores, what is the pooled variance for the two samples?​ Select one: a. ​14 b. ​8 c. ​4 d. ​16

Beta

Probability of making a type II error

A. The new naptime routine significantly reduced crying time, t(24) = -4.35, p < .05.

The mean crying time of infants during naptime at a local preschool is 12 minutes. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD) minutes. A t-test was used to test whether this new naptime routine reduced crying time at a .05 level of significance. The results produced t = -4.35, which was significant. Which is the correct interpretation of these findings? Select one: a. The new naptime routine significantly reduced crying time, t(24) = -4.35, p < .05. b. The new naptime routine significantly reduced crying time, t(24) = -4.35, p > .05. c. The new naptime routine significantly reduced crying time, t(25) = -4.35, p < .05. d. The new naptime routine did not significantly reduce crying time, t(24) = -4.35, p < .05.

Unknown Standard Deviation

Under what circumstances is a t Statistic used rather than a Z score in a hypothesis test?

1 1.96, 2.58 1 1.65, 2.33

What are the critical values for Z scores. 2 tail .05 and .01 1 tail .05 and .01

Decreases

What effect does going from 1 tail to two tails have on Power?

C. Concluding that a treatment has no effect when it really does.

What is the consequence of a Type II error?​ Select one: a. ​Concluding that a treatment has an effect when it really has no effect b. ​Concluding that a treatment has an effect when it really does c. ​Concluding that a treatment has no effect when it really does d. ​Concluding that a treatment has no effect when it really has no effect

1 Increase 2 Decrease 3 Decrease

What is the effect on the denominator, z score, and likelihood of rejecting when you increase the standard deviation of a z statistic?

A. The value for an unknown population mean

What value is estimated with a confidence interval using the t statistic?​ Select one: a. ​The value for an unknown population mean b. ​The difference between two sample means c. ​The value for an unknown sample mean d. ​The difference between two population means

B. Whenever the decision is "fail to reject H0"

When is there a risk of a Type II error?​ Select one: a. ​Whenever H1 is rejected b. ​Whenever the decision is "fail to reject H0" c. ​The risk of a Type II error is independent of the decision from a hypothesis test. d. ​Whenever H0 is rejected

Standard distance between a sample mean and a population mean.

When the null hypothesis is true what happens to the standard error?

C. Decreases the standard error and has no effect on the risk of a Type I error.

Which of the following accurately describes the effect of increasing the sample size?​ Select one: a. ​Increases the risk of a Type I error and has no effect on the standard error b. ​Decreases the risk of a Type I error and has no effect on the standard error c. ​Decreases the standard error and has no effect on the risk of a Type I error d. ​Increases the standard error and has no effect on the risk of a Type I error

D. Increase the likelihood of rejecting H0 and increase the risk of a Type I error.

Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)?​ Select one: a. ​Increase the likelihood of rejecting H0 and decrease the risk of a Type I error. b. ​Decrease the likelihood of rejecting H0 and decrease the risk of a Type I error. c. ​Decrease the likelihood of rejecting H0 and increase the risk of a Type I error. d. ​Increase the likelihood of rejecting H0 and increase the risk of a Type I error.

D. ​The probability of rejecting a false null hypothesis

Which of the following is an accurate definition for the power of a statistical test?​ Select one: a. ​The probability of supporting a false null hypothesis b. ​The probability of supporting true null hypothesis c. ​The probability of rejecting a true null hypothesis d. ​The probability of rejecting a false null hypothesis

D. The population after treatment

Which of the following is directly addressed by the null hypothesis?​ Select one: a. ​The population before treatment b. ​The sample after treatment c. ​The sample before treatment d. ​The population after treatment

D. ​μ1 - μ2 = 0

Which of the following is the correct null hypothesis for an independent-measures t test?​ Select one: a. μ1 - μ2 ≠ 0 b. M1 - M2 ≠ 0 c. ​M1 - M2 = 0 d. ​μ1 - μ2 = 0

C. n = 100 with s2 = 100

Which of the following samples will have the smallest value for the estimated standard error?​ Select one: a. ​n = 100 with s2 = 400 b. ​n = 25 with s2 = 100 c. ​n = 100 with s2 = 100 d. ​n = 25 with s2 = 400

B. ​Change the sample size from n = 25 to n = 100

Which of the following will increase the power of a statistical test?​ Select one: a. ​None of the other three options will increase the power. b. ​Change the sample size from n = 25 to n = 100 c. ​Change α from .05 to .01 d. ​Change from a one-tailed test to a two-tailed test

B. T=1.761

With α = .05, what is the critical t value for a one-tailed test with n = 15?​ Select one: a. ​t = 1.753 b. ​t = 1.761 c. ​t = 2.131 d. ​t = 2.145

D. Reject the H0

​An independent-measures research study uses two samples, each with n = 12 participants. If the data produce a t statistic of t = 2.50, then which of the following is the correct decision for a two-tailed hypothesis test with α = .05? Select one: a. b. ​It cannot be answered without additional information. c. ​Fail to reject H0 d. ​Reject the H0