Exam 4 Data Analysis
Which type of error is used to compute the confidence interval for one sample selected from a population with an unknown variance?
estimated standard error
In a sample of 18 participants, a researcher estimates the 80% CI for a sample with a mean of M1 - M2 = 8.8 and an estimated standard error for the difference (SM1 - M2) of 1.8. What is the upper confidence limit for this interval?
11.2
What is the minimum number of groups that can be observed using the one-way between-subjects ANOVA design?
2
In a sample of 20 participants, a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error (SM) of 1.6. What is the lower confidence limit for this interval?
2.1
A researcher computes the following analysis of regression table. Based on the data given, what is the value of the standard error of estimate? (Note: Complete the table first.) Source of Variation SS df MS F --------------------------------------------------- Regression 28 1 5.60 Residual --------------------------------------------------- Total 118 19
2.24
The following is a summary of a one-way between-subjects ANOVA: F(2, 37) = 3.42, p < .05, n^2 = .12. How many pairwise comparisons need to be made for this ANOVA result?
3
Which of the following statements is the appropriate way to read the degrees of freedom for an ANOVA with 10 participants in each of four groups?
3 and 36 degrees of freedom
A researcher assigned participants (n = 8 per group) to read vignettes describing a person engaging in either a helpful, hurtful, or neutral act. Different participants were assigned to each group and asked to rate how positively they viewed the person described in the vignette. What is the critical value for the one-way between-subjects ANOVA at a .05 level of significance?
3.47
A researcher reports with 90% confidence that 31% to 37% of Americans believe in ghosts. What is the point estimate for this interval?
34%
A researcher reduces her level of confidence from 99% to 90%. What will happen to the precision of her estimate?
The estimate will be more precise
In a sample of 22 participants, suppose we conduct an analysis of regression with one predictor variable. If = 4.07, then what is the decision for this test at a .05 level of significance?
X does not significantly predict Y
The more that the variability in ____ is associated with regression variation, the more likely it is that Xpredicts Y
Y
A researcher has the same 18 participants rate 6 pictures (k = 6), each depicting a person with a different body type. The one-way between-subjects ANOVA is an appropriate test statistic to test for mean differences in the ratings of each type of picture
false
Which of the following is the assumption that there is an equal variance of data points dispersed along the regression line?
homoscedasticity
We convert r to a t statistic for which of the following correlation tests?
point-biserial
For the same data, increasing the certainty of an estimate will result in a less precise estimate.
true
There is no difference between a point estimate and an interval estimate
false
A researcher computes the following one-way between-subjects ANOVA table. State the decision at a .05 level of significance. (Hint: Complete the table first.) Source of Variation SS df MS F -------------------------------------------------- Between groups 32 4 Within groups 45 (error) -------------------------------------------------- Total 122
Reject the null hypothesis
The equation for a straight line is Y = bX + a
true
To summarize the results of a one-way between-subjects ANOVA test, we report the test statistic, the degrees of freedom, and the p value
true
The confidence interval for one sample selected from a population with a known variance is computed using a critical value for which type of test?
z test
Which measure of proportion of variance tends to overestimate the size of an effect in a population?
η2
A researcher assigns 21 adolescents to rate the likability of a person described in a vignette as having one of three personality traits. An equal number of participants are assigned to each group. If Fobt= 4.08 for this study, then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?
Reject the null hypothesis
A correlation coefficient can ______ demonstrate cause
never
Correlation does not show causation
true
If SSxy = -16.32 and SSx = 40.00 for a set of data points, then what is the value of the slope for the best-fitting linear equation?
-0.41
A researcher estimates the 95% CI for a sample with a mean of M = 3.26 and a standard error of 0.91. What is the lower confidence limit for this interval?
1.48
A point estimate is typically reported with an interval estimate. Why?
The interval estimate gives researchers a higher level of confidence, the interval estimate adds certainty to the estimate of the population mean, using only a point estimate is associated with low certainty (all of these)
Which of the following is a characteristic of confidence intervals?
The less certain an estimate, the more precise the estimate, and the more certain an estimate, the less precise the estimate
Linear regression is used to measure the extent to which a criterion variable causes changes in a predictor variable
false
The estimated standard error is used in the formula to estimate the population mean for the one-sample z
false
The same participants are observed in each group using the between-subjects design
false
When the null hypothesis is outside a confidence interval, this indicates that it would likely be retained with hypothesis testing
false
If the value stated by a null hypothesis is ______ the confidence interval, then the decision would likely be to reject the null hypothesis
outside
A researcher computes the following one-way between-subjects ANOVA table for a study where k = 3 and n = 12. State the decision at a .05 level of significance. (Hint: Complete the table first.) Source of Variation SS df MS F -------------------------------------------------- Between groups 120 Within groups (error) -------------------------------------------------- Total 780
retain the null hypothesis
Homogeneity of variance is an assumption for the one-way between-subjects ANOVA. What does this assumption mean?
that the variance is equal in each population from which samples are selected
For an analysis of variance, the term "one-way" refers to
the number of factors in the design
A researcher conducts a study in which k = 4 and n = 22 in each group. What are the degrees of freedom for the one-way between-subjects ANOVA?
(3, 84)
The correlation coefficient ranges between ____ and ____
-1;+1
A researcher measures the following correlation between number of years of education and life satisfaction: r = +.08. What is the value of the coefficient of determination?
.01
Suppose a correlation is computed in each of two samples. If the value SSXY of is the same in each sample, and (square root of SSxSSy) is larger in Sample 1, then in which sample will the value of the correlation coefficient be larger?
Sample 2
A researcher measures the extent to which years of marriage predict perceptions of forgiveness. Which factor is the criterion variable in this example?
perceptions of forgiveness
How does omega-squared for the one-way between-subjects ANOVA correct for the fact that eta-squared tends to be a biased estimate of effect size?
It includes the degrees of freedom between groups (dfBG) in the formula, it accounts for the number of groups that were observed, it corrects for the size of error by including MSE in the formula (all of the above)
The normality assumption states that the population of X and Y scores form a bivariate ("two variable") normal distribution, such that
for each X score, the distribution of Y scores is normally distributed, the population of X and Y scores are normally distributed, for each Y score, the distribution of X scores is normally distributed (all of the above)
For the same data, increasing the certainty of an estimate will result in a less precise estimate
true
Homoscedasticity is the assumption that there is an equal variance of data points dispersed along the regression line
true
In a study with three groups and 13 participants in each group, the sum of squares for the within-groups source of variation is 18. What is the value for the mean square within-groups in this study?
0.5
A researcher measures the relationship between two variables, X and Y. If = 340 and = 320,000, then what is the value of the correlation coefficient?
0.60
A researcher assigns 21 adolescents to rate the likability of a person described in a vignette as having one of three personality traits. An equal number of participants are assigned to each group. If Fobt = 4.08 for this study, then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?
reject the null hypothesis
Using an analysis of regression, the variability in Ythat is associated with error is measured by the
residual variation
Without changing the value of error variance, the ________ the between-groups variability, the more likely we are to retain the null hypothesis
smaller
Which type of error is used to compute the confidence interval for one sample selected from a population with a known variance?
standard error
A researcher conducts two studies using the one-way between-subjects ANOVA. The sum of squares between groups is smaller in Study 1 than in Study 2; the sum of squares total is the same in both studies. Using η2, in which study will the effect size be larger?
study 2
The coefficient of determination is mathematically equivalent to eta-squared.
true
A researcher measures the correlation in rankings for a sample of restaurants and consumers' rankings of their favorite restaurants. If = 96 and n = 12, then what is the value of the correlation coefficient?
0.66
If r = 0.65 and n = 36, then what is the value of X^2?
15.21
A researcher computes the following phi correlation coefficient: r= 0.42. If the sample size was 20, then what is the decision for this correlation test?
Retain the null hypothesis
A researcher randomly assigned 32 children to observe a short clip depicting either their favorite superhero, a parent, a teacher, or no person at all (n = 8 per group). If = 30 and = 104, then what was the decision at a .05 level of significance for a one-way between-subjects ANOVA?
Retain the null hypothesis
The Spearman correlation coefficient is used to measure the correlation between two nominal variables
false
The Spearman correlation coefficient is used to measure the correlation between two nominal variables.
false
The correlation coefficient varies between 0 and 1 and can never be negative
false
The denominator of the Pearson correlation coefficient measures the extent to which two factors vary together
false
The numerator of the test statistic for a one-way between-subjects ANOVA is the mean variability associated with error
false
The test statistic for a one-way between-subjects ANOVA is the sum of squares between groups divided by the sum of squares error
false
Unlike omega-squared, the formula for eta-squared corrects for the number of groups and the size of error in its estimate of effect size
false
While it is common to report the result of an ANOVA, researchers rarely report the results of a post hoc test
false
The appropriate correlation coefficient for measuring the direction and strength of the linear relationship between one continuous and one dichotomous variable is
the point-biserial correlation coefficient
The predictor variable is a known value that is used to predict the value of another variable.
true
There are two sources of variation in a one-way between-subjects ANOVA: one attributed to differences between groups and one attributed to error
true
A researcher conducts a study in which k = 6 and n = 6 per group. What are the critical values for the one-way between-subjects ANOVA at a .05 level of significance?
2.53
If b = -0.57, MY = 2.75, and MX = 5.25 for a set of data points, then what is the value of the y-intercept for the best-fitting linear equation?
5.74
Which of the following is a limitation for interpreting a correlation?
Conclusions should not be drawn beyond the range of scores measured, outliers can change the direction and/or strength of the correlation, correlations do not demonstrate cause-and-effect (all of the above)
Following a significant one-way between-subjects ANOVA in which k > 2, what is the next appropriate step?
Conduct post hoc tests
The appropriate correlation coefficient for measuring for the direction and strength of the linear relationship between two dichotomous variables is
the phi correlation coefficient
Post hoc tests control for the total alpha level for a series of tests conducted on the same data
true
The "left-over" or remaining variation attributed to error in an analysis of regression is called residual variation.
true
The closer that data points fall to the regression line, the more closely two factors are related
true
The estimation formula for the one-sample t is M ±t(sM)
true
The formula for the point-biserial correlation coefficient was derived from the formula for the Pearson correlation coefficient
true
The slope (b) is a measure of the change in Y relative to the change in X.
true
The smaller the level of confidence, the more precise the estimate
true
The value of the sum of products can be positive or negative.
true
To standardize the coefficients, we first convert the original data to standardized z scores
true
