Quiz 11 - Chapter 11: Analysis of Variance (ANOVA) Flashcards
A researcher is interested in studying the effect of different learning strategies on students’ school performance. College students were randomly assigned to one of the three conditions: control group who studied without spacing, short spacing group who spaced their learning into 10 short slots, and long spacing group who spaced their learning into 3 long slots. The outcome variable was students’ performance on a subsequent quiz. Suppose the researcher found that the F statistics for the ANOVA was significant. What does that mean?
A: We cannot reject the conclusion that the three groups have identical mean quiz scores
B: At least one pair of group mean quiz scores is different
C: The three groups have identical mean quiz scores
D: All three pairs of groups have different mean quiz scores
B: At least one pair of group mean quiz scores is different
Following the previous question, if the researcher had found that the F statistic was not significant, what would that mean?
A: We cannot reject the conclusion that the three groups have identical mean quiz scores
B: At least one pair of group mean quiz scores is different
C: All three pairs of groups have different mean quiz scores
D: The three groups have identical mean quiz scores
A: We cannot reject the conclusion that the three groups have identical mean quiz scores
A clinical trial was created to test whether two drugs increased the mood of people with depression. A researcher randomly assigned 18 people to one of 3 conditions: Drug A, Drug B, and Placebo. They then measured whether people’s mood increased. Look at the ANOVA table for the researcher’s data below. What is the F value? Round your final answer to one decimal place.
It’s helpful if you look at the image to solve this but…
Drug:
Sum of squares = 3.45
df = ?
Mean square = ?
Residuals:
Sum of squares = ?
df = ?
Mean sqaure = 0.09
ANSWER = 19.2
HERE’S THE INFO WE HAVE:
N = 18
G# = 3
Drug (MSbg):
Sum of squares = 3.45
df = ?
Mean square = ?
Residuals (MSresidual):
Sum of squares = ?
df = ?
Mean sqaure = 0.09
HERE’S HOW I SOLVED F = MSbg ÷ MSresidual 👇🏽
FIRST FIND THE DEGREES OF FREEDOM:
MSbg df = (G# -1) So…. 3-1 = 2
MSresidual df = (N - G#) So…. 18-3 = 15
NOW HERE’S THE INFO I HAVE:
HERE’S THE INFO WE HAVE:
Drug (MSbg):
Sum of squares = 3.45
df = 2
Mean square = ?
Residuals (MSresidual):
Sum of squares = ?
df = 15
Mean sqaure = 0.09
NOW FIND THE MEAN SQUARE FOR MSbg
Sum of squares ÷ df = mean square
3.45 ÷ 2 = 1.725
NOW FIND THE F-STATISTIC:
F = MSbg ÷ MSresidual
1.725 ÷ 0.09 = 19.2
A psychologist is interested in exploring the treatment effect differences between an old treatment group, a new treatment group, and a placebo treatment group on depression levels. The probability value (p-value) is .08. Which of the following conclusions is true regarding the treatment?
A: If the treatment effects from the old treatment, new treatment, and placebo treatment are truly different in the entire population, the probability of observing mean differences as large as those in the sample is .08
B: The probability that the three groups differ in the entire population is .08
C: The probability that the null hypothesis is true is .08
D: If the treatment effects from the old treatment, new treatment, and placebo treatment are truly the same in the entire population, the probability of observing mean differences as large as those in the sample or more extreme differences is .08
D: If the treatment effects from the old treatment, new treatment, and placebo treatment are truly the same in the entire population, the probability of observing mean differences as large as those in the sample or more extreme differences is .08
A psychologist is interested in exploring the treatment effect differences from an old treatment group, a new treatment group, and a placebo treatment group on depression levels. The F statistic is 7.5. Which of the following conclusions is true regarding the treatment?
A: On a standardized metric, score variation due to the group effects is 7.5 times as large as that due to the total variation
B: On a raw score metric, score variation due to the group effects is 7.5 times as large as that due to naturally-occurring differences
C: On a standardized metric, score variation due to the group effects is 7.5 times as large as that due to naturally-occurring differences
D: On a raw score metric, score variation due to the group effects is 7.5 times as large as that due to the total variation
C: On a standardized metric, score variation due to the group effects is 7.5 times as large as that due to naturally-occurring differences
The sum of squares of the between-group effect is 20 and total sum of squares is 100. What is the sum of squares of the residual?
A: 120
B: 5
C: 80
C: 80
100 = 20 + x
Solve for x
A researcher found that the independent variable explains 10% of the total variation in the outcome. What does this imply about the magnitude of the between-group variability based on η2
A: The effect size is small
B: The effect size is large
C: The effect size is moderate
D: The effect size is negligible
C: The effect size is moderate
A researcher found that the independent variable explains 25% of the total variation in the outcome. How is this calculated?
A: Sum of squares of the between-group effect / Total sum of squares
B: Sum of squares of the between-group effect / Sum of squares of the residual
C: Sum of squares of the residual / Total sum of squares
D: Sum of squares of the residual / Sum of squares of the between-group effect
A: Sum of squares of the between-group effect / Total sum of squares
If the η2 effect size for an ANOVA is equal to .60, which of the following is true:
A: The between group variation is 0.6 times as large as the residual variation.
B: The group effect explained 60% of the residual variation of the dependent variable.
C: The group effect explained 60% of the total variation of the dependent variable.
C: The group effect explained 60% of the total variation of the dependent variable.
A researcher has an observed F-statistic of 11.17 and p-value <.001. Based on these results what can you conclude?
A: The results are not statistically significant based on the p-value.
B: The results are statistically significant based on the p-value and we cannot do any further analyses to examine which group means were significantly different.
C: The results are statistically significant based on the p-value and we can conduct post-hoc tests to determine which group means were significantly different.
C: The results are statistically significant based on the p-value and we can conduct post-hoc tests to determine which group means were significantly different.
A researcher records anxiety levels among first-, second-, third-, and fourth-year undergraduate students at a local university. The researcher analyzes their data using ANOVA and finds an η2 effect size of 0.22. What does this value tell us? Check all that apply.
A: The mean anxiety levels of students in different school years are .22 standard deviation units apart.
B: School year explains 22% of the total variation in students’ anxiety levels.
C: The variance in anxiety explained by school year is 22% larger than the variance explained by other unknown factors.
D: 22% of the variance in student anxiety is due to what school year a student is in.
B: School year explains 22% of the total variation in students’ anxiety levels.
D: 22% of the variance in student anxiety is due to what school year a student is in.
An educational psychologist wants to determine whether the type of cheat sheet (typed or written) affects students’ self-reported understanding level. The psychologist runs an ANOVA on these two groups instead of an independent-samples t-test. Which of the following statements are true? Check all that apply.
A: The effect sizes in both tests will be the same
B: The F-statistic will be the same as the t-statistic
C: The p-values in both tests will be the same
D: The ANOVA will give the same conclusion as the t-test
C: The p-values in both tests will be the same
D: The ANOVA will give the same conclusion as the t-test
A researcher wants to conduct an ANOVA on four sample means. What would be the appropriate null hypothesis?
A: All of the sample means are equal
B: The first two sample means are equal to the last two
C: None of the sample means are equal
D: All of the population means are equal
D: All of the population means are equal
When there are three treatment groups, what is the degrees of freedom in the numerator of the F-statistic calculation?
2
The numerator is MSbg and you find the degrees of freedom by (#G -1)
So… 3-1 = 2
When there are three treatment groups and 300 participants, what is the degrees of freedom in the denominator of the F-statistic calculation?
297
The denominator is Msresidual and you find the degrees of freedom by (N - #G)
So…. 300 - 3 = 297
