BST 611 Study Set Exam With Correct Solution
A trial evaluated the fever-reducing effects of three substances. Study subjects were
adults seen in an emergency room with diagnoses of flu with body temperatures
between 100.0 and 100.9ᵒ F. The three treatments (aspirin, ibuprofen, and
acetaminmophen) were assigned randomly to study subjects. Body temperatures were
reevaluated 2 hours after administration of treatment. Assume a normal distribution.
What would be the most appropriate statistic you would use to analyze the data? -
ANSWER ANOVA
The ANOVA is used because we are looking for the difference between three
treatments. We have to check the assumptions to make sure that we would still use the
ANOVA. First, we need to have an interval-ratio or continuous dependent variable. Yes,
body temperature is interval-ratio. Next we need a normal distribution. Yes, the text
states that we can "assume a normal distribution". Because of this statement, I do not
need to worry about sample size. The final assumption is that we have equal variances
across all three groups. We cannot test that at this point, so we would first start off with
the ANOVA. If we found unequal variances, we would then move to the Welch's ANOVA
A researcher is interested in whether a special reading program will improve students'
reading scores on a standardized test (scores range from 0 to 100). To determine how
much improvement will occur, the researcher obtains a sample of n = 35 students and
measures each individual's reading performance before and after the special program.
What would be the most appropriate statistic you would use to analyze the data? -
ANSWER Paired t-Test
Whenever you see the words before and after some kind of treatment such as "special
program", we are looking at a repeated measures design. When we have a repeated
measures design, we use the paired t-test to analyze this design. Let's see if the
assumptions for the paired t-test are met. First, we need to have an interval-ratio or
continuous dependent variable. Yes, standardized test scores are interval-ratio. Next,
we need a normal distribution. We are not told that we can assume a normal distribution
so we need to see if we can invoke the central limit theorem (CLT). With the paired t-test,
the statistical test is conducted on the difference distribution, so I only need 30
students. I am told that I have 35 students. Yes, the normality assumption is met by using
the CLT. Thus, I stay with my preliminary response, a paired t-test. You could have used
the flowsheet, noting the scaling of the dependent variable and invoking the CLT. With
this approach, you would then identify that you have two samples (i.e., the before
sample and the after sample). You would then select that the samples are related
because we have the same students from the before sample also in the after sample.
A nonexperimental study looked at whether people who angered easily were more likely
to develop coronary heart disease than those who angered less easily. Spielberger
anger scale scores were classified into low, moderate, and high categories. Coronary
,heart disease at 53 months was classified as yes and no. They collected data on 15
individuals What would be the most appropriate statistic you would use to analyze the
data? - ANSWER Chi-Square
This would be the chi-square. The research questions is looking at the difference among
three levels of anger on coronary heart disease. Anger (low/moderate/high) is the IV and
Coronary Heart Disease (yes/no) is the dependent variable. Since the dependent
variable is not interval-ratio, we default down to non-parametric which in our case is
chi-square. The independent variable is ordinal which is categorical so, yes, chi-square
would be appropriate. The only assumption is that the expected frequency of any cell
must be at least 5 or greater. With a sample size of 15, we would really want to check
this assumption because it may be violated.
In a study on mental health service utilization, data from 36 counties were obtained. The
researchers were interested in whether the distance in miles from the nearest mental
health care center predicted the percent of patients cared for in the home. What would
be the most appropriate statistic you would use to analyze the data? - ANSWER Simple
OLS Regression
This is a simple OLS regression. Because the research question is distance (miles)
predicts patient care (%), only one statistical test handles prediction and, that is, OLS
regression. We only have one independent variable so this is a simple OLS regression.
Lithium carbonate is a drug used to treat bipolar mental disorders. The average dose in
well-maintained patients is 1.3 mEq/L with standard deviation of 0.3 mEq/L. A random
sample of 25 patients on lithium demonstrates a mean level of 1.4 mEq/L. Researchers
are interested in whether this mean is significantly higher than that of a well-maintained
patient population. Assume a normal distribution. What would be the most appropriate
statistic you would use to analyze the data? - ANSWER Z-Score
This is the Z-score. The research question is one of difference: Is our sample mean
different from the population mean? The variable of interest is lithium carbonate (mEq/L)
which is interval-ratio and we can assume a normal distribution. We have one sample,
and we know the population standard deviation (0.3 mEq/L). Thus, we would use the
Z-score.
A cross-sectional survey of bicycle safety assessed the relationship between the
neighborhood socioeconomic status (percent below poverty) and the percent of bicycle
riders wearing a helmet. What would be the most appropriate statistic you would use to
analyze the data? - ANSWER Pearson Correlation
This is the Pearson correlation. The research question is bicycle safety (%) related to
socioeconomic status (% below poverty. This is a question of association—notice the
independent variable is interval-ratio scaled. If the independent variable was measured
as yes/no, then it would have been the difference between those respondents who wore
helmets versus those who did not. Because the question looks at relationship—not
predict, we would use correlation. Both variables are interval-ratio or continuous so we
, would use Pearson correlation.
Researchers were interested in the cultural differences in parenting practices. They
sampled Taipei (N=215) and Iowa (N=727) parents of 12-13 year old boys. Parenting
practices were assessed with a self-reported questionnaire on the boys' perceived
parental involvement. Parental involvement was the questionnaire's total score. What
would be the most appropriate statistic you would use to analyze the data? - ANSWER
Independent t-Test
This is a research question of difference in parenting practices between Taipei and Iowa
parents on perceived parental involvement (total score on a questionnaire). My
dependent variable is interval-ratio scale (total score), and I can invoke the central limit
theorem because I need at least 30 Taipei parents and 30 Iowa parents. Recall, that the
normal distribution assumption applies to each sample or group. I have two samples
(Taipei and Iowa), and these two samples are independent in that if a parent is in the
Taipei group, he/she is not in the Iowa group. Thus, it would be the independent t-test.
A geriatric researcher was interested in whether cognitive functioning (normal or
abnormal) is predicted by age (years), education level (years of schooling) and sex
(male and female) in centurians (N=20). What would be the most appropriate statistic
you would use to analyze the data? - ANSWER Multiple Logistic Regression
This is the multiple logistic regression. The research question is whether age, education
level, and sex predicts cognitive functioning (normal or abnormal). The word predicts
indicates that we are using regression; however, the dependent variable is nominal in
scale with two categories (normal/abnormal). This means that we would use logistic
regression. We have three independent variables, so this is multiple logistic regression.
Recall that we should have 10 subjects per independent variable. With this problem, we
only have 20 subjects; thus, we can only include 2 independent variables in the
regression equation; however, we have identified 3 potential independent variables.
One would need to be left out of the regression equation.
A researcher is interested in gender differences (males/females) in assault
victimizations (# of assaults in last 6 months). The researcher selected 80 subjects and
made sure that each subject in one group (40 males) had the same social economic
status as another subject in the other group (40 females). What would be the most
appropriate statistic you would use to analyze the data? - ANSWER Paired t-Test
The research question is whether gender (male/female) affects assault victimization (#
of assaults). This is a question of difference. My dependent variable is interval-ratio in
scale (# of assaults), and I can invoke the central limit theorem as I have more than 30
males and more than 30 females. I have two groups that are independent of each other
(male/female); however, the two groups were "made sure that each subject in one group
had the same social economic status as another subject in the other group"—this is
matching! So, we have artificially reduced the variation in the groups (i.e., the groups
are no longer independent) so instead of an independent t-test, we would need to use
the paired t-test instead.
A trial evaluated the fever-reducing effects of three substances. Study subjects were
adults seen in an emergency room with diagnoses of flu with body temperatures
between 100.0 and 100.9ᵒ F. The three treatments (aspirin, ibuprofen, and
acetaminmophen) were assigned randomly to study subjects. Body temperatures were
reevaluated 2 hours after administration of treatment. Assume a normal distribution.
What would be the most appropriate statistic you would use to analyze the data? -
ANSWER ANOVA
The ANOVA is used because we are looking for the difference between three
treatments. We have to check the assumptions to make sure that we would still use the
ANOVA. First, we need to have an interval-ratio or continuous dependent variable. Yes,
body temperature is interval-ratio. Next we need a normal distribution. Yes, the text
states that we can "assume a normal distribution". Because of this statement, I do not
need to worry about sample size. The final assumption is that we have equal variances
across all three groups. We cannot test that at this point, so we would first start off with
the ANOVA. If we found unequal variances, we would then move to the Welch's ANOVA
A researcher is interested in whether a special reading program will improve students'
reading scores on a standardized test (scores range from 0 to 100). To determine how
much improvement will occur, the researcher obtains a sample of n = 35 students and
measures each individual's reading performance before and after the special program.
What would be the most appropriate statistic you would use to analyze the data? -
ANSWER Paired t-Test
Whenever you see the words before and after some kind of treatment such as "special
program", we are looking at a repeated measures design. When we have a repeated
measures design, we use the paired t-test to analyze this design. Let's see if the
assumptions for the paired t-test are met. First, we need to have an interval-ratio or
continuous dependent variable. Yes, standardized test scores are interval-ratio. Next,
we need a normal distribution. We are not told that we can assume a normal distribution
so we need to see if we can invoke the central limit theorem (CLT). With the paired t-test,
the statistical test is conducted on the difference distribution, so I only need 30
students. I am told that I have 35 students. Yes, the normality assumption is met by using
the CLT. Thus, I stay with my preliminary response, a paired t-test. You could have used
the flowsheet, noting the scaling of the dependent variable and invoking the CLT. With
this approach, you would then identify that you have two samples (i.e., the before
sample and the after sample). You would then select that the samples are related
because we have the same students from the before sample also in the after sample.
A nonexperimental study looked at whether people who angered easily were more likely
to develop coronary heart disease than those who angered less easily. Spielberger
anger scale scores were classified into low, moderate, and high categories. Coronary
,heart disease at 53 months was classified as yes and no. They collected data on 15
individuals What would be the most appropriate statistic you would use to analyze the
data? - ANSWER Chi-Square
This would be the chi-square. The research questions is looking at the difference among
three levels of anger on coronary heart disease. Anger (low/moderate/high) is the IV and
Coronary Heart Disease (yes/no) is the dependent variable. Since the dependent
variable is not interval-ratio, we default down to non-parametric which in our case is
chi-square. The independent variable is ordinal which is categorical so, yes, chi-square
would be appropriate. The only assumption is that the expected frequency of any cell
must be at least 5 or greater. With a sample size of 15, we would really want to check
this assumption because it may be violated.
In a study on mental health service utilization, data from 36 counties were obtained. The
researchers were interested in whether the distance in miles from the nearest mental
health care center predicted the percent of patients cared for in the home. What would
be the most appropriate statistic you would use to analyze the data? - ANSWER Simple
OLS Regression
This is a simple OLS regression. Because the research question is distance (miles)
predicts patient care (%), only one statistical test handles prediction and, that is, OLS
regression. We only have one independent variable so this is a simple OLS regression.
Lithium carbonate is a drug used to treat bipolar mental disorders. The average dose in
well-maintained patients is 1.3 mEq/L with standard deviation of 0.3 mEq/L. A random
sample of 25 patients on lithium demonstrates a mean level of 1.4 mEq/L. Researchers
are interested in whether this mean is significantly higher than that of a well-maintained
patient population. Assume a normal distribution. What would be the most appropriate
statistic you would use to analyze the data? - ANSWER Z-Score
This is the Z-score. The research question is one of difference: Is our sample mean
different from the population mean? The variable of interest is lithium carbonate (mEq/L)
which is interval-ratio and we can assume a normal distribution. We have one sample,
and we know the population standard deviation (0.3 mEq/L). Thus, we would use the
Z-score.
A cross-sectional survey of bicycle safety assessed the relationship between the
neighborhood socioeconomic status (percent below poverty) and the percent of bicycle
riders wearing a helmet. What would be the most appropriate statistic you would use to
analyze the data? - ANSWER Pearson Correlation
This is the Pearson correlation. The research question is bicycle safety (%) related to
socioeconomic status (% below poverty. This is a question of association—notice the
independent variable is interval-ratio scaled. If the independent variable was measured
as yes/no, then it would have been the difference between those respondents who wore
helmets versus those who did not. Because the question looks at relationship—not
predict, we would use correlation. Both variables are interval-ratio or continuous so we
, would use Pearson correlation.
Researchers were interested in the cultural differences in parenting practices. They
sampled Taipei (N=215) and Iowa (N=727) parents of 12-13 year old boys. Parenting
practices were assessed with a self-reported questionnaire on the boys' perceived
parental involvement. Parental involvement was the questionnaire's total score. What
would be the most appropriate statistic you would use to analyze the data? - ANSWER
Independent t-Test
This is a research question of difference in parenting practices between Taipei and Iowa
parents on perceived parental involvement (total score on a questionnaire). My
dependent variable is interval-ratio scale (total score), and I can invoke the central limit
theorem because I need at least 30 Taipei parents and 30 Iowa parents. Recall, that the
normal distribution assumption applies to each sample or group. I have two samples
(Taipei and Iowa), and these two samples are independent in that if a parent is in the
Taipei group, he/she is not in the Iowa group. Thus, it would be the independent t-test.
A geriatric researcher was interested in whether cognitive functioning (normal or
abnormal) is predicted by age (years), education level (years of schooling) and sex
(male and female) in centurians (N=20). What would be the most appropriate statistic
you would use to analyze the data? - ANSWER Multiple Logistic Regression
This is the multiple logistic regression. The research question is whether age, education
level, and sex predicts cognitive functioning (normal or abnormal). The word predicts
indicates that we are using regression; however, the dependent variable is nominal in
scale with two categories (normal/abnormal). This means that we would use logistic
regression. We have three independent variables, so this is multiple logistic regression.
Recall that we should have 10 subjects per independent variable. With this problem, we
only have 20 subjects; thus, we can only include 2 independent variables in the
regression equation; however, we have identified 3 potential independent variables.
One would need to be left out of the regression equation.
A researcher is interested in gender differences (males/females) in assault
victimizations (# of assaults in last 6 months). The researcher selected 80 subjects and
made sure that each subject in one group (40 males) had the same social economic
status as another subject in the other group (40 females). What would be the most
appropriate statistic you would use to analyze the data? - ANSWER Paired t-Test
The research question is whether gender (male/female) affects assault victimization (#
of assaults). This is a question of difference. My dependent variable is interval-ratio in
scale (# of assaults), and I can invoke the central limit theorem as I have more than 30
males and more than 30 females. I have two groups that are independent of each other
(male/female); however, the two groups were "made sure that each subject in one group
had the same social economic status as another subject in the other group"—this is
matching! So, we have artificially reduced the variation in the groups (i.e., the groups
are no longer independent) so instead of an independent t-test, we would need to use
the paired t-test instead.
