Understanding Where You Are Key
1. Unless you know the df and/or p value associated with the obtained F, you can’t know if it exceeds chance. Unless you know the effect size (e.g., partial eta squared or d), you don’t know how big the difference in groups was. Unless you know the M, SD, and n of each cell, you don’t know if the sampling and cell variances were appropriate. Unless you know the direction of the effect and your friend’s hypothesis, you don’t know if the results match her expectations or contradict them.
2. A. Power of .80 means that you have an 80% chance of finding an effect if one exists in the population, so yes, this is a number that should satisfy you and your grant reviewers.
B. With power of .80, beta (the probability of making a Type II error) is 20%.
3. A. You would conclude that the analysis did not yield a significant finding: that is, that your obtained results did not reliably differ from those that would have been obtained if the null hypothesis (that there is no difference between groups) were true.
B. When you obtain a significant result with á set at .05, you are concluding that a finding this extreme or more so would only be obtained 5 times out of 100 if the null hypothesis were true.
4. With two groups, F = (t x t) and p for F = p for t. That is, the p values are exactly the same, and if you were to square the t value, you would have the F value.
5. A. No, the groups do not differ on religiousness.
B. Levene’s test for homogeneity of variance is not significant, which means that the null hypothesis that the variances in the two groups do not differ cannot be rejected. That is, you have no evidence that their variances are different. Thus, you should use the test that assumes equal variance.
C. Although the ns of the two groups are fairly different, they are well below the upper limit of 4:1, so a t-test is an appropriate analysis in this case.
6. A. These data would be appropriately analyzed by a multiple regression.
B. The predictor variables are all continuous, and the single outcome variable is continuous. This is the ideal set up for a multiple regression.
C. You could also analyze the data using an ANOVA (a factorial ANOVA, to be specific) if and only if you converted your predictor variables to categories. For instance, you might examine the sleep literature and determine that appropriate break points for hours of sleep would be 4 or fewer hours, 5 to 7 hours, 8 to 9 hours, and 10 or more hours. You would then recode your hours of sleep variable into these 4 categories and use that as your predictor. In this case, recoding the data might actually help your prediction, if in fact, these groups represent qualitative shifts and/or if the relation is not linear. That is, if moving from 3 to 4 hours doesn’t really gain you as much as moving from 4 to 5 hours, expressing time slept as a category would actually yield MORE power than retaining hours slept as a continuous variable.
A similar thing might be true for depressive symptoms: that is, once a threshold at which one might be seen as having a depressive disorder is reached, depressive symptoms might be better understood as a category. Both sleep and depressive symptoms probably do have critical values at which a qualitative switch occurs, and thus might well be good to categorize. On the other hand, student loan amount may not have such a critical value and thus, you might lose important information when creating categories on this variable.
7. A. The overall model is not significant, but this is not typically a question you ask in ANOVA. In contrast, typically one asks if the Main Effects of each predictor considered separately and if the Interaction Effects of the predictors considered jointly are significant.
B. Yes, there is a significant Main Effect of parental marital physical aggression, but the direction of the effect is paradoxical. That is, children of physically aggressive couples have lower levels of externalizing behavior in reaction to marital conflict. We know that there is a significant effect of marital physical aggression, because the printout lists partial eta squared = .14, F(1, 44) = 7.05, p = .01, which is interpreted as 14% of the variance in children’s externalizing is accounted for by its association with the predictor variable, and the means in the two groups are more different than we would expect by just by chance.
C. No, there is no significant interaction of marital distress and aggression (in fact, we might worry that the F is lower than we’d expect by chance!). We know this by the partial eta squared = .002, F(1, 44) = 0.10, p = .75 obtained for the interaction term.
D. Partial eta squared is the effect size calculated by SPSS. As noted above, it is interpreted as the amount of variance in the outcome variable accounted for by the effect of the IV.
8. The assumption of homogeneity of variance is that the groups have equivalent variances. It is an assumption of ANOVA, and although ANOVA is relatively robust to violations of this assumption (particularly with N > 20), it is important to assess. If significant deviations are detected (by procedures such as Levene’s test or Fmax), the researcher should take steps to correct the problem.
9. The assumption of normality is that the outcome variable is normally distributed. Again, although ANOVA is relatively robust to violations of this assumption, particularly with larger sample sizes, it is important to assess normality and to take corrective actions if significant deviations are detected.
10. The assumption of independence of observations (also referred to as uncorrelated errors) is that each observation in the data set is independent of the others: knowing something about one particular person’s score should not tell you something about another particular person’s score. Violating this assumption in a "regular" ANOVA yields positively biased results (i.e., more significant findings than are warranted). This assumption is most commonly violated when you have nested data (i.e., individual spouses within a couple, or children nested within different classrooms). Fortunately, it is possible to model the dependence within scores in ANOVA procedures (i.e., Repeated Measures ANOVA).
11. The assumption of sphericity only comes into play for Repeated Measures ANOVA, where you have more than one observation per case (either multiple observations of one person over time or observations of non independent people, as described above). The assumption of sphericity is that the difference scores of all possible pairs of observances have the same variance. That is, if I had a study with Time 1, Time 2, and Time 3, the variance of the difference score between Time 1 and Time 2 would equal the variance of the difference score between Time 1 and Time 3 which would also equal the variance of the difference score between Time 2 and Time 3. This assumption is important for Repeated Measures ANOVA because when it is violated, the results will be positively biased.
12. When we say a technique is robust with regard to a particular assumption, what we mean is that minor violations of this assumption will not render the findings invalid.
13. Predictor variable is to outcome variable as independent variable is to dependent variable.
14. In general, regression utilizes continuous predictor variables to predict continuous outcome variables whereas ANOVA uses categorical (or discrete or nominal) variables to predict continuous outcome variables.
15. The terms "within groups variance," "within subjects variance," and "error variance" are all synonymous.
16. Factorial ANOVA, by definition, has multiple predictor/IV variables. MANOVA, by definition, has multiple outcome/DV variables.
17. Sums of squares are the sum of squared deviations from some mean. In ANOVA, they are divided by the appropriate df to create Mean Square terms. The F is the ratio of the Between Groups Mean Square to the Within Groups Mean Square.
18. Power is affected by the value at which the researcher has set alpha (by convention, this is .05), the effect size in the population (that is, how different the groups being examined are), the sample size, and error in measurement.
19. As the number of predictor variables increases, the degrees of freedom for the error term decreases.
20. As the probability of making a Type I error (i.e., rejecting the null hypothesis when it is in fact true) increases, the probability of making a Type II error (i.e., failing to reject the null when it is in fact false) decreases.
2. A. Power of .80 means that you have an 80% chance of finding an effect if one exists in the population, so yes, this is a number that should satisfy you and your grant reviewers.
B. With power of .80, beta (the probability of making a Type II error) is 20%.
3. A. You would conclude that the analysis did not yield a significant finding: that is, that your obtained results did not reliably differ from those that would have been obtained if the null hypothesis (that there is no difference between groups) were true.
B. When you obtain a significant result with á set at .05, you are concluding that a finding this extreme or more so would only be obtained 5 times out of 100 if the null hypothesis were true.
4. With two groups, F = (t x t) and p for F = p for t. That is, the p values are exactly the same, and if you were to square the t value, you would have the F value.
5. A. No, the groups do not differ on religiousness.
B. Levene’s test for homogeneity of variance is not significant, which means that the null hypothesis that the variances in the two groups do not differ cannot be rejected. That is, you have no evidence that their variances are different. Thus, you should use the test that assumes equal variance.
C. Although the ns of the two groups are fairly different, they are well below the upper limit of 4:1, so a t-test is an appropriate analysis in this case.
6. A. These data would be appropriately analyzed by a multiple regression.
B. The predictor variables are all continuous, and the single outcome variable is continuous. This is the ideal set up for a multiple regression.
C. You could also analyze the data using an ANOVA (a factorial ANOVA, to be specific) if and only if you converted your predictor variables to categories. For instance, you might examine the sleep literature and determine that appropriate break points for hours of sleep would be 4 or fewer hours, 5 to 7 hours, 8 to 9 hours, and 10 or more hours. You would then recode your hours of sleep variable into these 4 categories and use that as your predictor. In this case, recoding the data might actually help your prediction, if in fact, these groups represent qualitative shifts and/or if the relation is not linear. That is, if moving from 3 to 4 hours doesn’t really gain you as much as moving from 4 to 5 hours, expressing time slept as a category would actually yield MORE power than retaining hours slept as a continuous variable.
A similar thing might be true for depressive symptoms: that is, once a threshold at which one might be seen as having a depressive disorder is reached, depressive symptoms might be better understood as a category. Both sleep and depressive symptoms probably do have critical values at which a qualitative switch occurs, and thus might well be good to categorize. On the other hand, student loan amount may not have such a critical value and thus, you might lose important information when creating categories on this variable.
7. A. The overall model is not significant, but this is not typically a question you ask in ANOVA. In contrast, typically one asks if the Main Effects of each predictor considered separately and if the Interaction Effects of the predictors considered jointly are significant.
B. Yes, there is a significant Main Effect of parental marital physical aggression, but the direction of the effect is paradoxical. That is, children of physically aggressive couples have lower levels of externalizing behavior in reaction to marital conflict. We know that there is a significant effect of marital physical aggression, because the printout lists partial eta squared = .14, F(1, 44) = 7.05, p = .01, which is interpreted as 14% of the variance in children’s externalizing is accounted for by its association with the predictor variable, and the means in the two groups are more different than we would expect by just by chance.
C. No, there is no significant interaction of marital distress and aggression (in fact, we might worry that the F is lower than we’d expect by chance!). We know this by the partial eta squared = .002, F(1, 44) = 0.10, p = .75 obtained for the interaction term.
D. Partial eta squared is the effect size calculated by SPSS. As noted above, it is interpreted as the amount of variance in the outcome variable accounted for by the effect of the IV.
8. The assumption of homogeneity of variance is that the groups have equivalent variances. It is an assumption of ANOVA, and although ANOVA is relatively robust to violations of this assumption (particularly with N > 20), it is important to assess. If significant deviations are detected (by procedures such as Levene’s test or Fmax), the researcher should take steps to correct the problem.
9. The assumption of normality is that the outcome variable is normally distributed. Again, although ANOVA is relatively robust to violations of this assumption, particularly with larger sample sizes, it is important to assess normality and to take corrective actions if significant deviations are detected.
10. The assumption of independence of observations (also referred to as uncorrelated errors) is that each observation in the data set is independent of the others: knowing something about one particular person’s score should not tell you something about another particular person’s score. Violating this assumption in a "regular" ANOVA yields positively biased results (i.e., more significant findings than are warranted). This assumption is most commonly violated when you have nested data (i.e., individual spouses within a couple, or children nested within different classrooms). Fortunately, it is possible to model the dependence within scores in ANOVA procedures (i.e., Repeated Measures ANOVA).
11. The assumption of sphericity only comes into play for Repeated Measures ANOVA, where you have more than one observation per case (either multiple observations of one person over time or observations of non independent people, as described above). The assumption of sphericity is that the difference scores of all possible pairs of observances have the same variance. That is, if I had a study with Time 1, Time 2, and Time 3, the variance of the difference score between Time 1 and Time 2 would equal the variance of the difference score between Time 1 and Time 3 which would also equal the variance of the difference score between Time 2 and Time 3. This assumption is important for Repeated Measures ANOVA because when it is violated, the results will be positively biased.
12. When we say a technique is robust with regard to a particular assumption, what we mean is that minor violations of this assumption will not render the findings invalid.
13. Predictor variable is to outcome variable as independent variable is to dependent variable.
14. In general, regression utilizes continuous predictor variables to predict continuous outcome variables whereas ANOVA uses categorical (or discrete or nominal) variables to predict continuous outcome variables.
15. The terms "within groups variance," "within subjects variance," and "error variance" are all synonymous.
16. Factorial ANOVA, by definition, has multiple predictor/IV variables. MANOVA, by definition, has multiple outcome/DV variables.
17. Sums of squares are the sum of squared deviations from some mean. In ANOVA, they are divided by the appropriate df to create Mean Square terms. The F is the ratio of the Between Groups Mean Square to the Within Groups Mean Square.
18. Power is affected by the value at which the researcher has set alpha (by convention, this is .05), the effect size in the population (that is, how different the groups being examined are), the sample size, and error in measurement.
19. As the number of predictor variables increases, the degrees of freedom for the error term decreases.
20. As the probability of making a Type I error (i.e., rejecting the null hypothesis when it is in fact true) increases, the probability of making a Type II error (i.e., failing to reject the null when it is in fact false) decreases.
posted by Mari @ 7:56 PM
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