PSYCHOLOGY 110 FINAL
The data for a chi-square test consist of ___________.
frequencies
If other factors are held constant, which sample size and sum of squares are most likely to produce a significant value for the repeated-measures t statistic?
large sample size, small sum of squares
For the repeated-measures t statistic, df = _____.
n - 1
A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study?
n = 13 t(df)...(12+1)
A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?
n = 22
What values are specified by the null hypothesis for a chi-square test?
proportions for a population
s2p (pooled variance) = ?
ss1 + ss2 / df1 + df2
If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean, μ, what value(s) of t should be used?
t = ±1.341
What is the correct null hypothesis for an independent-measures t test?
μ1 - μ2 = 0
Which of the following Pearson correlations shows the greatest strength or consistency of relationship?
-0.90
The following data were obtained from a repeated-measures research study. What is the value of MD (population mean of difference scores) for these data? Subject 1st 2nd #1 10 15 #2 4 8 #3 7 5 #4 6 11
-3 (each participant's difference / n)
If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?
0
What is the average value expected for the independent-measures t statistic if the null hypothesis is true?
0
The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 7 participants in each treatment. Note that several values are missing in the table. What is the missing value for MSbeetween? Source SS df MS Between 20 xx xx F = xx Within xx xx 2 Total xx xx
10
A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters. The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data were used for a chi-square test for independence, what is the expected frequency for males who are registered voters?
12
An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments. What is the df value for the t statistic for this study?
12
A set of n = 10 pairs of scores has ΣX = 20, ΣY = 30, and ΣXY = 74. What is the value of SP for these data?
14
An analysis of variance produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 2, 15. For this analysis, what is the F-ratio?
15/4 = 3.75
The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 5 participants in each treatment. Note that several values are missing in the table. What is the missing value for MSwithin?
2
The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n = 11 participants in each treatment. Note that several values are missing in the table. What is the missing value for the F-ratio? Source SS df MS Between xx xx 14 F = xx Within xx xx xx Total 154 xx
2
For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase?
2 points
What is the value of the estimated standard error for the following set of D-scores? Scores: 2, 2, 10, 2
2. ( s + s + s + s /sqr root of n x n) so... (2+2+10+2 / (sqr root of n = 2 )(4)
A sample of n = 4 scores has SS = 60. What is the variance for this sample?
20
What is the pooled variance for the following two samples? Sample 1: n = 8 and SS = 168 Sample 2: n = 6 and SS = 120
24
An independent-measures study uses n = 15 participants in each group to compare two treatment conditions. What is the df value for the t statistic for this study?
28. (independent measure df = each group's n x 2, -2)
An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment. For this study, What is dfwithin treatments?
33
An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment. For this study, what is dftotal?
35
Ten years ago, only 20% of the U.S. population consisted of people more than 65 years old. A researcher plans to use a sample of n = 200 people to determine whether the population distribution has changed during the past ten years. If a chi-square test is used to evaluate the data, what is the expected frequency for the older-than-65 category?
40
A researcher would like to test the claim that 9 out of 10 doctors prefer Brand X. A sample of 60 doctors is obtained and each is asked to compare Brand X with another leading brand. The data show that 48 of the doctors picked Brand X. If these data are evaluated using a chi-square test for goodness of fit, what is the expected frequency for Brand X?
54
A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data?
6/10
For the regression equation Y = 2X - 3, if the mean for X is MX = 5, what is the mean for Y?
7
The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment. Note that several values are missing in the table. What is the missing value for SStotal? Source SS df MS Between 20 xx xx F = 5.00 Within xx xx xx Total xx xx
74
Which size mean difference and sample variance is most likely to produce a significant value for the independent-measures t statistic and a large measure of effect size?
A large mean difference and small sample variances
Which sample size and variance will produce the smallest value for the estimated standard error?
A large sample size and a small sample variance
When the data form a 2x2 matrix, the phi-coefficient is used to measure effect size for the chi-square test for independence. If other factors are held constant, how does sample size influence the values for phi and chi-square?
A larger sample increases chi-square but has no effect on phi.
If a repeated-measures study shows a significant difference between two treatments with α = .01, then what can you conclude about measures of effect size?
A significant effect does not necessarily mean that the effect size will be large.
What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?
As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.
For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (H1)?
At least one of the three population means is different from another mean.
In an analysis of variance, differences between participants contribute to which of the following variances?
Both between-treatments variance and within-treatments variance
A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×3 matrix of categories. Which test has the larger value for df?
Both tests have the same df value.
Which of the following will increase the power of a statistical test? Change α from .05 to .01, change from a one-tailed test to a two-tailed test, or change the sample size from n = 25 to n = 100?
Change the sample size from n = 25 to n = 100
What is the consequence of a Type II error?
Concluding that a treatment has no effect when it really does
For the independent-measures t statistic, what is the effect of increasing the sample variances?
Decrease the likelihood of rejecting H0 and decrease measures of effect size
The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle. For these data, what is the most likely value for the Pearson correlation?
Either positive or negative near 0
In general, a large value for chi-square indicates a good fit between the sample data and the null hypothesis.
FALSE
T/F: A researcher uses an independent-measures t test to evaluate the mean difference between two treatments. If the t statistic has df = 12, then an ANOVA evaluating the same data would produce an F-ratio with df = 1, 11.
FALSE
T/F: Effect size for analysis of variance is measured by η2, which equals SSbetween divided by SSwithin.
FALSE
T/F: For a two-tailed hypothesis test with α = .05 and a sample of n = 25 scores, the boundaries for the critical region are t = ±2.060.
FALSE
T/F: For an independent-measures study, the width of a confidence interval estimating μ1 - μ2 depends on the size of the difference between M1 and M2.
FALSE
T/F: If the null hypothesis states that μ = 70 and a researcher obtains a sample with M = 73 and s2 = 9, then Cohen's d = 0.33.
FALSE
T/F: In a test for significance of a Pearson correlation for a sample of n = 30 individuals, you determine the critical value by using df = 29.
FALSE
T/F: Nonparametric tests are used only with data from a nominal scale.
FALSE
A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile. Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices. If the researcher obtains a chi-square statistic of χ2 = 4.81, what is the appropriate statistical decision for the test?
Fail to reject the null hypothesis with either α = .05 or α = .01
Under what circumstances should the chi-square statistic not be used?
If fe = fo for any cell
For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?
If there is a treatment effect, it will add (or subtract) a constant to each score.
Which design would be used to compare the mathematics skills for 9th-grade boys versus 9th-grade girls?
Independent measures
One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can you conclude about the pooled variance for these two samples?
It will be closer to 30 than to 20.
If other factors are held constant, what is the effect of increasing the sample variance?
It will increase the estimated standard error and decrease the likelihood of rejecting H0.
A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 3, what can you conclude about the two variables?
One variable consists of 2 categories and the other consists of 4 categories
In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment. What is this problem is called?
Order effects
What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?
Points clustered close to a line that slopes up to the right
In an analysis of variance, what is determined by the size of the sample mean?
SSbetween
In analysis of variance, what is measured by the MS values?
Sample variance
Variance of a sample (s2) = ?
Sum of Squares / n-1
A chi-square test should not be used if any observed frequency is less than five.
TRUE
Although the outcome for a chi-square test for independence is influenced by sample size, measures of effect size such as the phi-coefficient or Cramér's V are not.
TRUE
For a chi-square test, the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.
TRUE
T/F: A researcher obtains SSX = 20, SSY = 5, and SP = 7 for a set of n = 25 pairs of scores. The Pearson correlation for these scores is r = 7/10 = 0.70.
TRUE
T/F: A set of n = 16 difference scores has a mean of MD = 4 and a variance of s2 = 36. Cohen's d for this sample is d = 4/6.
TRUE
T/F: Although a repeated-measures study measures two scores for each participant, the sample mean and variance are computed using only one score for each participant.
TRUE
T/F: For a regression equation with a slope of b = 3, if MX = 3 and MY = 10, then the Y-intercept for the equation is 1.
TRUE
T/F: For an independent-measures ANOVA with n = 10 participants in each treatment condition, dfwithin = 9.
TRUE
T/F: For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.
TRUE
T/F: If a set of n = 9 difference scores has a mean of MD = 3.5 and a variance of s2 = 36, then the sample will produce a repeated-measures t statistic of t = 3.5/2.
TRUE
T/F: If other factors are held constant, as the sample size increases, the estimated standard error decreases.
TRUE
T/F: If other factors are held constant, if the Pearson correlation between X and Y is r = 0.80, then the regression equation will produce more accurate predictions than would be obtained if r = 0.60.
TRUE
T/F: One or two extreme data points can have a dramatic effect on the size of a correlation.
TRUE
T/F: One sample has n = 7 scores with SS = 40, and a second sample has n = 5 scores with SS = 80. The pooled variance for these two samples is 120/10 = 12.
TRUE
T/F: Repeated-measures designs are particularly well-suited to research studies examining learning or other changes that occur over time.
TRUE
T/F: SSbetween measures the size of the mean differences from one treatment to another.
TRUE
T/F: SSwithin measures the size of the sample variances.
TRUE
T/F: The alpha level determines the risk of a Type I error.
TRUE
T/F: The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.
TRUE
T/F: The sample mean will always be exactly in the center of a confidence interval that is estimating the value of the population mean.
TRUE
T/F: When the population variance or standard deviation is not known, you must use a t statistic instead of a z-score for a hypothesis test.
TRUE
The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.
TRUE
The chi-square test for independence uses the same formula as the chi-square statistic for the goodness-of-fit test.
TRUE
What is measured by the numerator of the z-score test statistic?
The actual distance between M and μ
For the regression equation, Y = -2X + 6, what can be determined about the correlation between X and Y?
The correlation definitely will be negative.
What happens to the critical value for a chi-square test if the size of the sample is increased?
The critical value depends on the number of categories, not the sample size.
What happens to the critical value for a chi-square test if the number of categories is increased?
The critical value increases.
Why are t statistics more variable than z-scores?
The extra variability is caused by variations in the sample variance.
What is referred to by the term expected frequencies?
The frequencies computed from the null hypothesis
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen's d. How will the outcomes for the two samples compare?
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen's d.
What value is estimated with a confidence interval using the repeated-measures t statistic?
The mean for a population of difference scores
In an ANOVA, what is represented by the letter N?
The number of scores in the total research study
What must the observations be for a chi-square hypothesis test?
The observations must be independent.
For a two-tailed hypothesis test evaluating a Pearson correlation, what is stated by the null hypothesis?
The population correlation is zero
For the regression equation, Y = -2X+6 if the X value is above the mean (positive deviation), what can be determined about the predicted Y value?
The predicted Y value will be below the mean for the Y scores
A hypothesis test with a sample of n = 25 participants produces a t statistic of t = +2.53. Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision?
The researcher can reject the null hypothesis with either α = .05 or α = .01.
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?
The sample mean should be close 80 and should lead you to fail to reject the null hypothesis.
Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values?
The sample with the smaller variance will produce the larger t statistic.
What is evaluated by the chi-square test for goodness of fit?
The shape or proportions for a population distribution
What is a fundamental difference between variance use in the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) say about the treatment?
The treatment causes a change in the scores.
What is assumed by the homogeneity of variance assumption?
The two populations have equal variances.
For an ANOVA comparing three treatment conditions, what is stated by the null hypothesis (H0)?
There are no differences between any of the population means.
What is the effect on effect size and rejection of null hypothesis by increasing sample size?
There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.
What is the purpose for post tests?
To determine which treatments are significantly different
Under what conditions is Cramér's V used to measure effect size for a chi-square test for independence?
When either of the two variables consists of more than two categories
A researcher predicts that scores in treatment A will be higher than scores in treatment B. If the mean for the 10 participants in treatment A is 4 points higher than the mean for the 10 participants in treatment B and the data produce t = 2.095, what decision should be made?
With α = .05, reject H0 for a one-tailed test but fail to reject for a two-tailed test.
A linear regression equation has b = 3 and a = - 6. What is the predicted value of Y for X = 4?
Y = 6
Which of the following describes a typical distribution of F-ratios? a. Symmetrical with a mean of zero b. Positively skewed with all values greater than or equal to zero c. Negatively skewed with all values greater than or equal to zero d. Symmetrical with a mean equal to dfbetween
b. Positively skewed with all values greater than or equal to zero
A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
d = 0.50
An independent-measures study produces sample means of M1 = 20 and M2 = 17, and a pooled variance of 9. For this study, what is Cohen's d?
d = 3/3