module 3 practice problems
Dr. Holley is running a clinical trial for a new stress medication. The study has three treatment groups (50 mg, 100 mg, 150 mg) and a control group. Additionally, the participants are separated based on socioeconomic status (low-class, middle-class, high-class).You will measure their cortisol levels every 3 days for one month. What is the most appropriate statistical test to run on this data?
Analysis of Covariance
Which one of these tests can be used to test whether the regression lines are different from each other in either slope or intercept?
Analysis of covariance (ANCOVA)
Dr. Torres, an orthopedic surgeon, is interested in seeing how torso length changes with age. She randomly selects 100 subjects, records their age, and measures their torso length. As expected, the torso length increases as age increases. However, Dr. Torres noted that after 65 years of age, torso length began to decrease as age increased - perhaps as a result of bone degeneration. What statistical test would be best to analyze this data?
Curvilinear Regression
Which of the following can NOT be answered from a regression equation?
Estimate whether the association is linear or non-linear
TCOM conducted a study compare the average MCAT score of their first-year students to their average undergraduate GPA. Linear regression was used to estimate this relationship, and the equation was y = 506 + 1.5x. In this equation, what does 1.5 indicate?
It is the slope of the best fit line, and it indicates a positive relationship between the variables.
You are conducting an experiment to see if people with more flexible hips tend to have more flexible shoulders. You randomly select 30 subjects and measure the range of motion in their hips and shoulders. What is the appropriate statistical test to determine the strength of association?
Linear Correlation
Dr. Taylor Swift is testing a new anti-anxiety medication. She splits participants into three conditions - 0mg, 50mg, 100mg. She then asks them to rate their anxiety level on a scale of 1 to 10. What statistical test should be used to analyze this data?
Linear Regression
You measure air temperature and running speeds in lizards, and you hypothesize that warmer lizards run faster than cooler lizards. You decide to measure the running speeds at 5C, 10C, 15C, and 20C. After statistical analysis using an alpha value of .05, you obtain P-value = .09. What statistical test was likely used, and how would you interpret the P-value?
Linear Regression: there is not an association between the two variables.
In regression analysis, if the independent variable is measured in kilograms, the dependent variable
can be any units
If the coefficient of determination is equal to 1, then the correlation coefficient
can be either -1 or +1
If the coefficient of determination is 0.81, the correlation coefficient
could be either + 0.9 or - 0.9
If the coefficient of determination is a positive value, then the regression equation
could have either a positive or a negative slope
A dummy variable:
is one nominal category versus all of the other nominal categories of a variable.
The coefficient of correlation
is the square root of the coefficient of determination
Larger values of r2 (R2) imply that the observations are more closely grouped about the
least squares line
With the growth of internet service providers, a researcher decides to examine whether there is an association between cost of internet service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10, with a 1 being not at all satisfied and a 10 being extremely satisfied). What is the appropriate statistical test?
linear correlation
If there is a very strong correlation between two variables then the correlation coefficient must be
much smaller than 0, if the correlation is negative
If the correlation coefficient is a positive value, then the slope of the regression line
must also be positive
What variables are used in simple logistic regression?
one measurement (X) variable and one nominal (Y) variable with two values
Regression modeling is a statistical framework for developing a mathematical equation that describes how
one response and one or more explanatory variables are related
In regression analysis, the variable that is being predicted is the
response, or dependent, variable
UNTHSC is conducting a study to compare student's GPAs in the Master's of Medical Science program and if they received medical school interviews. The students completed a survey which asked: "what was your final GPA? Did you receive a medical school interview?" What is the best statistical test to use for this experiment?
simple logistic regression
You want to know whether the abundance of dandelions is associated with the amount of phosphate in the soil. You separate one field of sunflowers into nine quadrants. You then count the amount of dandelions and measure the phosphate concentration in each quadrant. What statistical test should be used to analyze this data?
spatial autocorrelation
In the case of an algebraic model for a straight line, if a value for the x variable is specified, then
the exact value of the response variable can be computed
In regression, the equation that describes how the response variable (y) is related to the explanatory variable (x) is
the regression model
Correlation and regression are concerned with
the relationship between two quantitative variables.
Two variables have a positive association when
the values of one variable tend to increase as the values of the other variable increase.
In regression analysis, the variable that is used to explain the change in the outcome of an experiment, or some natural process, is called
the x-variable the independent variable the predictor variable the explanatory variable
If two variables, x and y, have a very strong linear relationship, then
there might not be any causal relationship between x and y
What variables are used in spearman's rank correlation (rho)?
two ordinal variables
Backwards elimination in multiple regression is:
when a variable is allowed to leave a regression because its removal makes little difference to the prediction.
The correlation coefficient is used to determine:
The strength of the relationship between the x and y variables
It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizzes, etc.) would also perform well on a standardized achievement test. A teacher decides to examine this hypothesis. At the end of the academic year, she computes a correlation between the students' achievement test and the overall GPA for each student computed over the entire year. She obtains an r2 of .27. How would you interpret this?
27% of the achievement test performance is related to the GPA, and vice versa. 73% of the variability is left unexplained.
Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individual's degree of religiosity (high score = greater religiosity). After running statistical analysis, the researchers conclude that r2 = .92. What statistical test is appropriate for this data, and how would you interpret r2?
Linear correlation; there is a strong association between death anxiety and degree of religiosity.
Which of the following methods is used to best fit the data in Logistic Regression?
Maximum Likelihood
Dr. Yang, an entomologist, wants to reintroduce a nearly-extinct species of monkey into a jungle, in order to try to conserve the species. To guide her conservation efforts, she wants to examine various resources in jungles where the monkey already lives. She visits a number of jungles and measures the amount of monkeys, sun exposure, tree height, density of prey organisms, and nutrient concentration. What is the appropriate statistical test to run on this data?
Multiple Linear Regression
A marine biologist uses correlation to examine the relationship between the weight of dolphins and the abundance of their main prey fish in the environment. The marine biologist samples the fish in the waters near Surfside Beach and then captures and weighs 20 dolphins from that area. Which of the following might be an issue with this experiment?
Non-independence due to spatial autocorrelation.
You are interested in seeing if certain allele frequencies in sand crabs are associated with the latitude that they live in. You record the latitude of 25 different beaches and then record the presence or absence of allele X in 100 different sand crabs. What statistical test is most appropriate for this experiment?
Simple Logistic Regression
You are looking at the strength of association between prices of convenience store items and distance from the Contemporary Art Museum. You hypothesize that the prices will decrease as the distance from the key area of gentrification surrounding the Contemporary Art Museum increases. Due to different factors - type of retail outlet, amount of tourist traffic, and the store's location to main roads - the data appears to be non-linear and non-normal. What is the appropriate statistical test to use?
Spearman's Rank Correlation
Dr. Wilson, a professor in the School of Public Health, wanted to see if there was a correlation between the numbers of hours studying and the test scores that those students received. She calculated r = -.8 and r2 = .93. What conclusions can be drawn from this study?
The Pearson's r-value shows a negative correlation between the 2 variables. The r2 value shows that the best of fit line created for the data plot displays little variance from the actual data.
The correlation between two variables is given by r = 0.0. What does this mean?
The best straight line through the data is horizontal.
In least squares regression, which of the following is not a required assumption about the error term ε?
The expected value of the error term is one.