Statistics Final

Explain the differences between one way ANOVA and factorial (2 way) ANOVA, include information about main effects and interaction effects.

One-way or two-way refers to the number of independent variables (IVs) in your Analysis of Variance test. One-way has one independent variable (with 2 levels) and two-way has two independent variables (can have multiple levels). For example, a one-way Analysis of Variance could have one IV (brand of cereal) and a two-way Analysis of Variance has two IVs (brand of cereal, calories). Interaction effects indicate that a third variable influences the relationship between an independent and dependent variable. Example Let's say you are studying if Alcoholics Anonymous and individual counseling combined is the most effective treatment for lowering alcohol consumption. You might split the study participants into three groups or levels: medication only, medication and counseling, and counseling only. Your dependent variable would be the number of alcoholic beverages consumed per day.

Evaluating a difference is a three-step process. What is the first step? A. Determining if it is statistically significant. B. Considering the practical implications of an insignificant difference. C. Considering the practical implications ofa statistically significant difference.

A. Determining if it is statistically significant.

Which type of hypothesis predicts that one particular group's mean will be higher than another group's mean? A. Directional hypothesis. B. Nondirectional hypothesis. C. Null hypothesis.

A. Directional hypothesis.

Which of the following is a symbol for the null hypothesis? A. He,. B. H1

A. He,.

Suppose a researcher randomly selected 10 classrooms (as clusters). Each classroom had 20 students. The researcher should report the sample size as A. I 0. B. 20. C. 200.

A. I 0.

Suppose you read that as the result of a chi-square test, p < .05. By conventional standards, what decision should be made about statistical significance? A. It is significant B. It is not significant.

A. It is significant

Suppose you read that as the result of a chi-square test, p < .00 I. By conventional standards, what decision should be made about the null hypothesis? A. Reject it B. Do not reject it

A. Reject it

What does it mean when d= 1.00? A. The average participant in the experimental group is one standard deviation higher than the average participant in the control group. B. The average participant in the control group is one standard deviation higher than the average participant in the experimental group.

A. The average participant in the experimental group is one standard deviation higher than the average participant in the control group.

If a researcher rejects the null hypothesis, what else is true? A. The difference is statistically significant B. The difference is not statistically significant

A. The difference is statistically significant

Rejecting the null hypothesis when In reality it is true is known as a A. Type l Error. B. Type ll Error.

A. Type l Error

At what point is it conventional to reject the null hypothesis? A. When the probability is less than .O5. B. When the probability is greater than .05.

A. When the probability is less than .O5.

Can a very small difference between two means be statistically significant? A. Yes. B. No.

A. Yes.

Is the size of the sample one of the factors that contribute to determining statistical significance? A. Yes. B. No.

A. Yes.

For the scores on Test D and Test E shown below, there is A. a direct relationship. B. an inverse relationship. C. no relationship. student . TestX . TestY B . 303 20 T . 343 53 K 479 70 Z 599 88

A. a direct relationship.

When low scores on one variable are associated with low scores on the other variable, this suggests that the relationship is A. direct. B. inverse.

A. direct.

The null hypothesis states that the true difference between the means A. equals zero. B. is greater than zero. C. is less than zero.

A. equals zero.

Increasing sample size A. increases precision. B. decreases bias. C. increases precision and decreases bias.

A. increases precision.

The larger the variability in a population, the A. larger the standard error of the mean. B. smaller the standard error of the mean.

A. larger the standard error of the mean.

"If a t-test yields p < .05, the null hypothesis normally would be rejected." This statement is A. true B. false

A. true

"A t test yields a probability." This statement is A. true. B. false.

A. true.

"Dependent data may have less sampling error than independent data." This statement is A. true. B. false.

A. true.

"Equating a significant difference with a large difference is a mistake." This statement is A. true. B. false.

A. true.

"For the data in the following table, a two-way chi-square would be an appropriate test of significance." This statement is A. true. B. false. Happy. Unhappy Boys. n=30. n=40 Girls. n=40. n=30

A. true.

"The purpose of effect size is to standardize the difference between two means." This statement is A. true. B. false.

A. true.

A direcJ relationship is sometimes called a positive relationship." This statement is A. true. B. false

A. true.

An r of-.95 represents a stronger relationship than an r of .88." This statement lS A. true. B. false.

A. true.

For an r of .80, the ability to predict is 64% better than zero." This statement is A. true. B. false.

A. true.

For most practical purposes, values of d rarely exceed 3.0." This statement is A. true. B. false.

A. true.

For nominal data, researchers normally report frequencies and percentages instead of means and standard deviations." This statement is A. true. B. false.

A. true.

For samples with very limited variability, even small samples can yield precise results." This statement is A. true. B. false.

A. true.

In an inverse relationship, those who arc high on one variable tend to be low on the other." This statement is A. true. B. false.

A. true.

In the table below, there appears to be an interaction." This statement is A. true. B. false. X. Y. D. M=40.00. M=30.00. E. M=30.00. M=40.00

A. true.

It is possible for a relationship to be both inverse and strong." This statement is A. true. B. false.

A. true.

It is usually better to use a small, unbiased sample than a large, biased one." This statement is A. true. B. false.

A. true.

The acronym ANOVA stands for analysis of variance." This statement is A. true. B. false.

A. true.

The smaller the anticipated difference between groups, the larger the sample size should be." This statement is A. true. B. false.

A. true.

The symbol for the coefficient of detennination is?." This statement is A. true. B. false.

A. true.

When r = .40, the percentage of variance accounted for is 16%." This statement is A. true. B. false.

A. true.

Suppose a researcher is examining the validity of a combination of scores on a spatial relations test and previous math grades as a predictor of geometry grades. Which correlational statistic should the researcher compute for this research problem? A.R. B.r.

A.R.

When low scores on one variable are associated with low scores on the other variable, this suggests that the relationship is A.direct. B. inverse.

A.direct.

f If= .75, what percentage of the variance is accounted for? A. 25%. B. 75%.

B. 75%.

Which of the following yields a probability? A. A descriptive statistic. B. A significance test

B. A significance test

To compute Cohen's d, first subtract the control group's mean from the experimental group's mean, and then do what? A. Multiply the difference between the means by the control group's standard deviation. B. Divide the difference between the means by the control group's standard deviation. C. Determine the significance between the means at p<.05.

B. Divide the difference between the means by the control group's standard deviation.

Suppose you read the following: F • 0.641, df• 3, 29, p > .OS. What conclusion would you normally draw about the null hypothesis? A. Reject it. B. Do not reject it.

B. Do not reject it.

Which of the following will produce a greater reduction in sampling errors? A. Increasing the size of a sample from 800 to 900 (an increase of 100). B. Increasing the size of a sample from 200 to 300 (an increase of 100).

B. Increasing the size of a sample from 200 to 300 (an increase of 100).

If you increase the sample size, what effect does this have on the size of the standard error of the mean? A. It increases it. B. It decreases it.

B. It decreases it.

Suppose you read the following: F-= 3 .50, <!f• 2, 20,p < .05. What conclusion would you normally draw about statistical significance? A. lt is statistically significant. B. It is not statistically significant

B. It is not statistically significant

Which of the following usually creates less sampling error? A. Simple random sampling. B. Stratified random sampling.

B. Stratified random sampling.

If you read that t = 0.452, df .. 100,p > .05, what should you conclude? A. The difference is statistically significant B. The difference is not statistically significant

B. The difference is not statistically significant

For the typical consumer of research, which one of the following values in an ANOV A table is of greatest interest? A. Mean squares. B. The value of p. C. The value of F.

B. The value of p.

Which of the following is a correct statement of the null hypothesis? A. There is a true difference between the means. B. There is no true difference between the means.

B. There is no true difference between the means.

Under which of the following circumstances is the null hypothesis more likely to be rejected? A. When there is a small observed difference between means. B. When there is a large observed difference between means.

B. When there is a large observed difference between means.

For the scores on Test X and Test Y shown below, there is A. a direct relationship. B. an inverse relationship. C. no relationship student . TestX . TestY J . 25 9 B 30 7 R 35 4 W 40 1

B. an inverse relationship.

If participants are matched (i.e., paired) across experimental and control groups, the resulting data are A. independent. B. dependent.

B. dependent.

According to the central limit theorem, the sampling distribution of means is skewed." This statement is A. true. B. false.

B. false

Collelation is the best way to examine cause-and-effect" This statement is A. true. B. false

B. false

Reporting a t test makes it unnecessary to report the values of the means and standard deviations." This statement is A. true B. false

B. false

Using random sampling guarantees freedom from sampling errors." This statement is A. true. B. false

B. false

"For a given study, the research hypothesis and the null hypothesis usually say the same thing." This statement is A. true. B. false.

B. false.

"In the table below, there appear to be two main effects." This statement is A. true. B. false. I J G. M=40.00. M=50.00. H. M=30.00. M=20.00.

B. false.

"It is safe to assume that if a difference is statistically significant, it is of practical significance." This statement is A. true. B. false.

B. false.

"The smaller the sample, the more likely that the null hypothesis will be rejected." This statement is A. true B. false.

B. false.

4. "An r of .60 is equivalent to 60%." This statement is A. true. B. false.

B. false.

ANOVA can be used to test for the difference(s) between only two means." This statement is A. true. B. false.

B. false.

For the difference between two means, the null hypothesis says that the difference is large." This statement is A. true. B. false.

B. false.

In the table below, there appears to be an interaction." This statement is A. true. B. false. S. T U. M=300.00. M=200.00. V. M=350.00. M=250.00

B. false.

Using stratified random sampling eliminates all sampling errors." This statement is A true. B. false.

B. false.

In order to examine an interaction, you A. temporarily ignore one way that the participants were classified while examining the results of the other way they were classified. B. look at both ways participants were classified at the same time in order to see how the two classification variables affect each other.

B. look at both ways participants were classified at the same time in order to see how the two classification variables affect each other.

If the Pearson r equals .30, the coefficient of A.If= 1.00. detennination is calculated by A. taking the square root of .30. B. multiplying .30 by .30.

B. multiplying .30 by .30.

By conventional standards, if p < .01, researchers declare the difference statistically A. insignificant. B. significant

B. significant

Putting the names of girls in one hat and those of boys in another hat and drawing 20% of the girls' names and 20% of the boys' names from each hat constitutes A. cluster sampling. B. stratified random sampling. C. simple random sampling.

B. stratified random sampling.

Suppose participants were classified according to their religion and their country of origin in order that means for both religious groups and national origin groups to be compared. This would call for a A. one-way ANOVA. B. two-way ANOVA

B. two-way ANOVA

Which of the following values ofr represents the strongest relationship? A .. 64. B. -.79. C. 0.00

B.-.79.

For determining the correlation between one variable as a predictor of a second variable, which of the following should be computed? A.R. B.r.

B.r.

When there is a perfect, inverse relationship, what is the value of ,1 A. 1.00. B. 0.00. C. -1.00. D. Some other value.

C. -1.00.

4. If m = 40.00 and SEu - 3.00, what are the limits of the 68% confidence interval for the mean? A. 37.00 and 40.00. B. 40.00 and 43.00. C. 37.00 and 43.00. D. Some other values.

C. 37.00 and 43.00.

Which of the following values of R represents the weakest relationship? A.If R2= 1.00 B. If R2= .96 C. If R2= .22

C. If R2= .22

3. The null hypothesis can be rejected with the greatest confidence when which one of the following is true? A. p < .O5. B. p< .01. C. p < .001.

C. p < .001.

The symbol for chi-square is A. p B. r2 (squared) C. x2 (squared) D. p2 (squared)

C. x2 (squared)

Suppose there are 500 people in a population and you want to draw a sample using a table of random numbers. Which of the following would be an appropriate number name for the first person to whom you assign a number before using the table? A. 00. B. 01. C. 05. D. 001.

D. 001.

4. When a coefficient of determination equals 20, what percentage of the variance on one variable is not predicted by the other variable? A. 4% B. 20% C. 96% D. Some other percentage.

D. Some other percentage.

Select two effect size examples to discuss in detail, when to use them, and some of their advantages (Cohen's D, r^2, R^2, etc)

Effect size is a statistical concept that measures the strength of the relationship between two variables on a numeric scale. Cohen's d is an appropriate effect size for the comparison between two means. It can be used, for example, to accompany the reporting of t-test and ANOVA results. It is also widely used in meta-analysis. Pearson's r a measure of the linear correlation between two variables