QUIZZES after midterm2 Flashcards
Q1. A researcher is conducting post-hoc tests for a one-way between-groups ANOVA. They have three different conditions with six people in each condition. Which of the following differences between means would be considered statistically different at alpha = .05?
4.17
3.69
2.85
both a) and b)
d)both
We will need to find our critical q value for this study in Table B-5.
The columns use the number of treatments or conditions (in this case 3 - don’t use conditions - 1 here - the table just says number of treatments.
The row uses the degrees of freedom within, in this case we take N - 1 for each group and add them up: 5 + 5 + 5 = 15.
Alpha of .05 is the non-bolded row.
Here we see the critical value is 3.67.
Now we need to make our comparisons. Both 4.17 AND 3.69 are more extreme than 3.67. 2.85 is not. Consequently, the answer is both a) and b).
LO9: Complete Tukey HSD post-hoc tests for a one-way between-groups ANOVA, and recognize how Bonferroni post-hoc tests are completed
Q2. A researcher is interested in how different instructions affect reading comprehension. She asks college students to read a text on physics and randomly assigns them to one of three groups: (1) finish the reading as quickly as possible, (2) read at a normal pace, or (3) read at a normal pace, but pause after each paragraph for reflection. Within each group, students differ in how much they remember from the text. These differences reflect:
a) the within-group variance
b) the between-group variance
c) individual differences in reading ability
d) individual differences in following instructions
A)
The within-group variance looks at the differences between the performance within each group, due to reading speed, reading ability, attention, comprehension skills. It’s a measure of how much ‘random error’ there is simply because people differ and will fluctuate in performance day to day, etc.
LO3: Identify and describe what the F statistic measures and how the F distributions are related to the t distributions
Q3. You would like to explore the effect of temperature on memory. You will have three different conditions: moderate temperature (20 degrees Celsius), low temperature (10 degrees Celsius) and high temperature (30 degrees Celsius). You are particularly concerned that individual differences in memory and temperature performance will affect the results. What statistical test should you use to test your hypothesis?
a) within-groups ANOVA
b) paired-samples t test
c) independent-samples t test
d) between-groups ANOVA
A)
In this case, since you are worried about participant differences, and there are more than 2 conditions, you should do a within-groups ANOVA. (Note that you would have to counterbalance the conditions across participants.)
LO1: Recognize situations in which a one-way between-groups ANOVA and one-way within-groups ANOVA is used to analyze data
LO10: Recognize how a one-way within-groups ANOVA allows us to remove error variability from our data
Q4.
a) 0.59
b) 0.69
c) 0.41
d) 1.46
see below
Q5. Consider this fictional scenario: A researcher uses data collected from the Canadian census to determine whether IQ score is affected by level of education (measured as high school, college/university, and post-graduate degree). They find the following data:
high school: M = 97 (s = 3)
college/university: M = 101 (s = 2)
post-graduate degree: M = 106 (s = 20)
Which of the following assumptions are not met?
A) The underlying population distribution is normal
B) Homoscedasticity (homogeneity of variances)
C) None of the assumptions is met
D) The participants are randomly selected from the population
B) HOMOSCEDASTICITY
- The Canadian census uses a random sample of Canadians, so assumption 1 is met.
- IQ is normally distributed in the population, so assumption 2 is met.
- The problem here is the variability in each group. The post-graduate degree group has a much, much higher standard deviation. Consequently, the variances are very different (and so homoscedasticity is not met).
Homoscedasticity means that the variances of the dependent variable (IQ scores in this case) are approximately equal across all levels of the independent variable (level of education - high school, college/university, and post-graduate degree) – and they aren’t.
LO5: Accurately use the language of ANOVAs and identify the three assumptions of the ANOVA
Q6. A researcher reports the following statistics in their paper:
F(2,15) = 4.32, p<0.05, w^2= 0.36
If this finding is in error the researcher has made what type of error?
A) Type II error
B) sampling bias
C) statistical error
D) Type I error
D) TYPE 1 error
In the given scenario, the p-value (p < 0.05) indicates that the result is statistically significant at the 0.05 level (it is less than 0.05)
However, the effect size w^2 is 0.36, which represents a relatively large effect size. An effect size of 0.36 suggests that there is a substantial difference between groups.
Type 1 error (False Positive): This occurs when the researcher incorrectly rejects a true null hypothesis. In other words, the researcher concludes that there is a significant effect (i.e., rejects the null hypothesis which states there is no difference) when, in reality, there is no effect in the population.
LO7: Conduct all 6 steps of a one-way between-groups ANOVA and interpret the results.
Q7.
ANSWER
Q8. A researcher conducts three statistical tests using an alpha rate of 0.05. By completing multiple tests without any correction, he is:
A) HARKing
B) increasing his F ratio
C) increases his Type I error rate
D) increasing his Type II error rate
Conducting multiple tests means you will be more likely to find something just by chance (a Type I error). Remember, we accept that 1 out of every 20 findings will be a Type I error. Consequently, the more tests we run, the more likely we are to hit that 1 in 20. That’s why we need to make statistical corrections when we have more than two groups.
This is known as the problem of multiple comparisons or multiple testing. As more tests are performed, the likelihood of obtaining a significant result purely by chance (Type I error) increases. To control the overall Type I error rate, researchers can use various correction methods to adjust the significance threshold for each individual test, thus maintaining the desired level of alpha across all the tests. Failure to correct for multiple tests can lead to an inflated Type I error rate and an increased risk of false positives.
LO2: Recognize and explain why we cannot perform multiple t tests when comparing three or more groups
Q9. A researcher conducts a study on WEIRD participants. She makes a note in her paper stating, “I expect my results to generalize to any sample of undergraduate students in Canada.” This is known as a(n) _______________ statement.
A) sampling methodology
B) constraint on generality
C) population of interest
D) WEIRD bias
B) CONSTRAINT ON GENERALITY
The researcher is acknowledging that the sample used in the study consists of WEIRD participants (Western, Educated, Industrialized, Rich, and Democratic), which is not representative of the broader population. By making this note, the researcher is recognizing that the findings may not apply to individuals outside the WEIRD population and that the generalizability of the results is limited to Canadian undergraduate students,
A constraint on generality (COG) statement is used to help researchers explain who they believe their research can be generalized to. This can help us from over-generalizing our results.
LO11: Recognize critiques of ‘WEIRD’ samples in psychology and actions researchers are taking to improve how our research is generalized
Q 10. A researcher is conducting a one-way between-groups ANOVA. He has four experimental conditions with 18 participants in each of the conditions. What is the critical value for alpha = .01?
A) 2.74
B) 2.75
C) 3.62
D) 4.10
D) 4.10
To find our critical value, we go to Table B-3. We have:
dfbetween = 3
dfwithin = 17 + 17 + 17 +17 = 68
We look at the table with 3 for our columns and round down to 65 for the row. With alpha of .01, we find the value of 4.10 (the bolded one).
LO4: Use the F table to determine a critical value
LO7: Conduct all 6 steps of a one-way between-groups ANOVA and interpret the results
QUIZ:
Q1. If a person had two independent variables with three levels each, and different participants were in each group, what type of ANOVA would they need to conduct?
a) One-Way Within-Groups ANOVA
b) Two-Way Within-Groups ANOVA
c) Two-Way Between-Groups ANOVA
d) One-Way Between-Groups ANOVA
C) 2-WAY Between-Groups ANOVA
- Since we have two levels of the independent variable, we need to call our study a Two-Way. Since different participants are in different groups, we call it Between-Group.
- The “Between-Groups” aspect refers to the fact that the participants are assigned to specific groups based on the levels of the independent variables. The “Two-Way” aspect indicates that there are two independent variables being considered simultaneously.
See also The Language and Assumptions of ANOVA in Chapter 12
Q2. To find the effect size for an ANOVA, we calculate:
a) Cohen’s d
b) R2
c) the p value
d) Tukey’ SD
B) R^2
- R^2 is a common measure of effect size for ANOVA.
- R2 represents the proportion of variance in the dependent variable that is accounted for by the independent variables in the ANOVA model. It measures the strength of the relationship between the independent variables and the dependent variable.
- R2 ranges from 0 to 1, with higher values indicating a larger effect size and a stronger relationship between the independent variables and the dependent variable.
*WHY NOT A),C), D)? Cohen’s d is a measure of effect size commonly used in the context of comparing means between two groups, not ANOVA. The p-value represents the statistical significance of the results, indicating the probability of obtaining the observed effect or a more extreme effect under the null hypothesis. Tukey’s HSD (honestly significant difference) is a post-hoc test used to determine which specific group means are significantly different from each other after conducting an ANOVA
Testing for the One-Way Between-Groups ANOVA in Chapter 12.
Q3. It is advantageous to use a within-groups ANOVA compared to a between-groups ANOVA because a within-groups ANOVA:
a) has greater variance of scores
b) is more likely to include more research participants in the study
c) is more likely to discover a research result that has cause-effect implications
d) reduces error since the same participants contribute to each condition
d) reduces error since the same participants contribute to each condition
By using the same participants in each group, we can reduce some of the error variability in our study (that based on our participants’ natural tendencies).
See also Chapter 13: The Benefits of Within-Groups ANOVA
Q4. In a one-way between-group analysis of variance, how does the magnitude of the mean differences from one condition to another contribute to the F-ratio?
a) The mean differences contribute to the denominator of the F-ratio
b) The mean differences contribute to both the numerator and denominator of the F-ratio
c) The mean differences contribute to the numerator of the F-ratio
d) The sample mean differences do not influence the F-ratio
c) The mean differences contribute to the numerator of the F-ratio
- The F-ratio explores whether the differences between groups is higher than the differences within the groups.
- If the ratio is 1, the differences between groups is no larger than those within.
- However, if it is larger than 1, the differences between groups is larger than those within. Thus, the differences between the groups is in the numerator.
Q6. When comparing three or more groups, we use ANOVA because conducting multiple t tests would result in an increased likelihood of a:
a) Type III error
b) All of these are correct.
c) Type I error
d) Type II error
C) TYPE 1 ERROR
- If we do multiple tests, we increase the chance of finding a significant difference by random chance. Thus, we increase the probability of a Type I error. See also Type I
- Errors When Making Three or More Comparisons in Chapter 12.
Q8 . The graphs below provides 3 different distributions. Based on a visual inspection of these distributions, which would give you the best outcome for an ANOVA?
C)
- In this case, c is the most likely to show a significant ANOVA. Each group’s distribution is thin, showing little within-group variability. However, the differences between groups is large, showing a lot of between-group variability. This should give us a large F statistic.
- See also the section on The logic and Calculations of the F Statistic in Chapter 12.
Q6.
A) SMALL
B) LARGE
C) IMPOSSIBLE TO DETERMINE
D) MEDIUM
LARGE
- The closer the values are to a straight line, the closer they are to a perfect correlation. These dots all cluster close to a line drawn down the middle, indicating that this is a large negative correlation).
