Questions and Answers of Fundamentals Of Statistics

The t value that you obtain in Exercise 14.1 will be somewhat smaller than the t value from Exercise 13.1. Why should we have anticipated this?Exercise 14.1In Exercise 13.1 we had paired data because
Why isn’t the difference between the results of Exercises 13.1 and 14.1 greater than it is?Exercise 13.1Hout, Duncan, and Sobel (1987) reported on the relative sexual satisfaction of married
In the example in this chapter about the treatment of anorexia, what basic assumption would we have to make if we compared the final weights of the two groups (rather than comparing the amount of
What is the role of random sampling in the anorexia study?
In Exercise 14.8 a significant difference might lead someone to suggest that poor parent–child relationships are the cause of schizophrenia. Why might this be a troublesome conclusion?Exercise
Calculate the 95% confidence limits on μ1 – μ2 for the data in Exercise 14.11.Exercise 14.11Much has been made of the concept of experimenter bias, which refers to the fact that for even the most
Calculate a measure of effect size for the data in Exercise 14.11.Exercise 14.11Much has been made of the concept of experimenter bias, which refers to the fact that for even the most conscientious
What would be the confidence limits on the results in Exercise 14.13?Exercise 14.13Calculate a measure of effect size for the data in Exercise 14.11.Exercise 14.11Much has been made of the concept of
Using the data in the file Add.dat on the Web, compare grade point averages for those having ADDSC scores of 65 or less with those having ADDSC scores of 66 or more.
Calculate Cohen’s for the data in Exercise 14.15.Exercise 14.15Using the data in the file Add.dat on the Web, compare grade point averages for those having ADDSC scores of 65 or less with those
What do the answers to Exercises 14.15 and 14.16 tell you about the predictive utility of the ADDSC score?Exercise 14.16Calculate Cohen’s d^ for the data in Exercise 14.15.Exercise 14.15Using the
Brescoll and Uhlman(2008), in the study described in Exercise 14.18, found the reverse effect for females. They thought that perhaps this latter result was related to the way anger is judged in
With respect to the previous exercise, what would happen if regardless of ni? 2 s=s 2
Use R or other software to repeat the results for Exercise 14.8.Exercise 14.8The Thematic Apperception Test (TAT) presents participants with ambiguous pictures and asks them to tell a story about
Use R or other software to repeat the results for Exercise 14.11.Exercise 14.11Much has been made of the concept of experimenter bias, which refers to the fact that for even the most conscientious
What do we mean by power?
List three things that affect the power of a test.
Why does power depend upon sample size?
As a rough estimate, a medium effect size would have d = _____.
What do we mean when we write “d (delta) 5 d[f(n)]”?
Why do we have a special formula for calculating power in a two-group experiment with quite unequal sample sizes?
What name do we give to our adjusted sample size with unequal ns?
Calculate the correlations among all numeric variables in Exercise 9.1 using SPSS, or R.(In R read in the data as a data.frame (e.g., theData) and then use (cor(theData). You don’t need to attach
Using one of the online calculators, how large a correlation would you need for the relationships shown in Exercise 9.2 to be significant? (This will involve a bit of trial and error.)Calculate the
What are the strongest single predictors of infant mortality in Exercise 9.2?Exercise 9.2Calculate the correlations among all numeric variables in Exercise 9.1 using SPSS, or R.(In R read in the data
In Exercise 9.1 the percentage of mothers over 40 does not appear to be important, and yet it is a risk factor in other societies. Why do you think that this might be?Exercise 9.1In Sub-Saharan
Use the code given earlier for R to make this plot. The command would be plot(percentage)
Why would you not feel comfortable computing a Pearson correlation on the data in Exercise 9.10?Exercise 9.10Down syndrome is another problem that psychologists deal with. It has been proposed that
One way to get around the problem you see in Exercise 9.12 would be to convert the incidence of Down syndrome to ranked data. Replot the data using ranked incidence and calculate the correlation. Is
Do Exercise 9.13 using R. You can rank the data with ranked. data 5 rank(percent).Exercise 9.13One way to get around the problem you see in Exercise 9.12 would be to convert the incidence of Down
The data relevant to Exercise 9.15 are the test scores and SAT-V scores for the 28 people in the group that did not read the passage. These data areExercise 9.15In the study by Katz, et al., referred
The data relevant to Exercise 9.15 are the test scores and SAT-V scores for the 28 people in the group that did not read the passage. These data areExercise 9.15In the study by Katz, et al., referred
The correlation in the Katz et al. study between Score and SAT-V for the 17 subjects in the group that did read the passage was .68. This correlation is not significantly different from the
Expand on Exercise 9.19 to interpret the conclusion that the correlations were not significantly different.Exercise 9.19The correlation in the Katz et al. study between Score and SAT-V for the 17
Do the results of the Katz et al. study fit with your expectations, and why?
Plot and calculate the correlation for the relationship between ADDSC and GPA for the data in Appendix D. Is this relationship significant? You can use both R and SPSS to do this.
One of the examples in this chapter dealt with the relationship between vitamin D and cancer.Do a simple Internet search to find additional data on that question.
Use one of the sources given in the text (R or http://vassarstats.net/rho.html) to calculate a confidence interval on the correlation between Expenditures for education and SATcombined from Figure
Modify the code in the chapter’s Web page by making y
Regression refers to
A linear regression is one in which _____.
In linear regression the symbol b is used to refer to the intercept. (T or F)
Express “error of prediction” algebraically.
We often use the phrase “least squares regression” because _____
We always need to compute a value for the intercept because that anchors our line, butdo we always need to pay attention to it?
If we standardized our data and computed a slope (here called beta), what would beta tell us?
The measure of error that we use with regression is called _____.
Two important measures of the size of an effect in regression are _____ and _____.
The following data are from 10 health-planning districts in Vermont. Y is the percentage of live births ≤ 2500 grams. X1 is the fertility rate for women ≤ 17 or ≥ 35 years of age (X1 is known
Calculate the standard error of estimate for the regression equation in Exercise 10.1.Exercise 10.1The following data are from 10 health-planning districts in Vermont. Y is the percentage of live
If, as a result of ongoing changes in the role of women in society, we saw a change in the age of childbearing such that the high-risk fertility rate jumped to 70 in Exercise 10.1, what would we
Why should you feel uncomfortable making a prediction in Exercise 10.3 for a rate of 70?Exercise 10.3If, as a result of ongoing changes in the role of women in society, we saw a change in the age of
In Exercise 9.1 in Chapter 9 we saw data on infant mortality and risk factors. Why might you feel more comfortable making a prediction based on Income for Senegal than for Ethiopia or
Again referring to Exercise 9.1 in Chapter 9, how does what you know about regression contribute to your understanding of infant health in developing countries?Exercise 9.1In Sub-Saharan Africa, more
Suppose that we know that the correlation between two variables named X and Y is .56. What would you expect would happen to the correlation if we subtracted 10 points from every X score?
With regard to Exercise 10.9, suppose that the mean of X was 15.6 and the mean of Y was 23.8.What would happen to the slope and intercept if we subtracted 10 points from every Y?
Draw a diagram (or diagrams) to illustrate Exercise 10.10.Exercise 10.10With regard to Exercise 10.9, suppose that the mean of X was 15.6 and the mean of Y was 23.8.What would happen to the slope and
Take the data that you just created in Exercise 10.12 and add 2.5 to each Y value. Plot the original data and the new data. On the same graph, superimpose the regression lines.a) What has happened to
Using the data in Appendix D, compute the regression equation for predicting GPA from ADDSC. These data can be found at https://www.uvm.edu/~dhowell/fundamtnals9/DataFiles/Add.dat.Appendix D ADDSC
Using the data on self-enhancement given in Exercise 10.16, add two scores to each year, keeping the year mean unchanged. (For example, if the 1982 mean SelfEn score was 0.40, you could make two
Using your own height and the appropriate regression equation from Exercise 10.19 or 10.20, predict your own weight. (If you are uncomfortable reporting your own weight, predict mine—I am 5980 and
Use your scatterplot of the data for students of your own gender and observe the size of the residuals. (Hint: You can see the residuals in the vertical distance of points from the line.)What is the
The slope (b) used to predict the weights of males from their heights is greater than the slope for females. What does this tell us about male weights relative to female weights?
Wainer (1997) presented data on the relationship between hours of TV watching and mean scores on the 1990 National Assessment of Educational Progress (NAEP) for eighth-grade mathematics assessment.
In simple regression the intercept is denoted as “a.” How is it denoted in multiple regression?
Assume that the multiple correlation between a criterion measure and several predictors is .48. How would you interpret that?
How would you interpret a regression coefficient of 1.3?
What do we mean by “multicollinearity?”
In standard computer printout, to what does the word “constant” refer?
List two different ways to think of multiple regression.
What is a residual?
What do we mean by “stepwise regression” and why should you be wary of it?
What do we mean by a “mediated” relationship?
Why do we care about large residuals?
A psychologist studying perceived “quality of life” in a large number of cities (N = 150) came up with the following equation using mean temperature (Temp), median income in $1000(Income), per
In Exercise 11.2, which variables make a significant contribution to the prediction of Optimism as judged by the test on their slopes?Exercise 11.2Sethi and Seligman (1993) examined the relationship
In Exercise 11.2 the column headed “Tolerance” (which you have not seen before) gives you 1 minus the squared multiple correlation of that predictor with all other predictors. What can you now
On the basis of your answer to Exercise 11.4, speculate on one of the reasons why Religious Influence might be an important predictor of Optimism, while Religious Involvement is not.Exercise 11.4In
Calculate the adjusted R2 for the 15 cases in Exercise 11.6. Twice in this chapter I said that we were going to ignore the adjusted R2, even though it is a perfectly legitimate statistic. Can you
Using the output from Exercise 11.8, interpret the results as if they were significant. (What is one of the reasons that this current analysis is not likely to be significant, even if those
The data set Harass.dat, included on this book’s website, contains data on 343 cases created to replicate the results of a study of sexual harassment by Brooks and Perot (1991). The variables are,
In the text I have recommended against the use of stepwise procedures for multiple regression, whereby we systematically hunt among the variables to predict some sort of optimal equation.a) Explain
Now restrict the data set in Exercise 11.15 to eight, then six, then five cases, and record the changing values of R. Remember that these are only random data.Exercise 11.15Use the table of random
Compute a weighted average of the slopes of Weight predicted from Height for each gender in Exercise 11.18. Reasonable weighting coefficients would be the two sample sizes. (A weighted average is
A great source of data and an explanation to go with them is an Internet site called the Data and Story Library (DASL) maintained by Carnegie Mellon University. Go to that site and examine the
Since you have the DASL data on brain size, note that it also includes the variables of height and weight. Predict weight from height and sex and compare with the answer for Exercise 11.17.Exercise
In Exercise 9.1 we saw data on infant mortality and a number of other variables. There you predicted infant mortality from income. There is reason to believe that infants of young mothers are at
List three things that the central limit theorem tells us.
Why do we care about the standard error of a statistic?
How does the formula for t differ from the standard formula for z?
Why is the sampling distribution of the variance relevant to the use of t tests?
When we are dealing with one set of scores, the degrees of freedom for t will be _____.
Name three things that affect the size of the t we calculate.
What do we mean when we speak of an “effect size measure?”
What do we mean by a confidence interval?
In general, what do we mean by Cohen’s effect size measure d?
What is the sampling distribution of t?
I drew 50 samples of five scores each from the same population that the data in Exercise 12.1 came from, and calculated the mean of each sample. The means are shown below. Plot the distribution of
Compare the means and the standard deviations for the distribution of digits in Exercise 12.1 and the sampling distribution of the mean in Exercise 12.2.a) What would the Central Limit Theorem lead
Use R to repeat Exercises 12.1 and 12.2. (The code for this exercise can be found on the chapter’s Web page along with other pieces of code. This code will generate its own set of 100 random

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