Exam 1: 468
Cons of Bonferroni Correction
-greatly reduces the power of each test! makes it more difficult to detect a real-world effect because the bar needed to detect the effect is higher, the threshold is more stringent.
Describe the limitation of conducting multiple t-tests
-inflates probability of making a type 1 error (detecting an effect when the difference observed was by chance alone)
In a 3 x 4 factorial design, how many IVs are there and how many conditions are there?
2 IV's with 3 conditions in IV #1 and 4 conditions in IV #2
In a 2 x 2 x 3 factorial design, how many IVs are being tested and how many conditions are there
3 IV's being testes; 2 conditions in IV #1, 2 conditions in IV #2, and 3 conditions in IV #3
How is within-groups variance partitioned in one-way repeated ANOVA
Between-SUBJECTS and residual error rate
How can you reduce experiment-wise type 1 error rate?
Bonferroni Correction -reduces test-wise error rate by dividing alpha level by number of tests (e.g. a = .05, .05/3 = .017), this new alpha level is now the new threshold your statistics must cross in order to be considered statistically significant
This is a measure of effect size calculated in t-tests that tells the standardized distance between a sample mean and the population mean. An effect size of .50 tells us that M is .50 SD units away from the population mean
Cohen's d
Describes the levels within each factor (IV)
Conditions
Differences between dependent samples t-test and one-way repeated ANOVA
Dependent samples t-test: used when you want to compare two samples of data from the SAME sample of participantsOne-Way Repeated ANOVA: used when you want to compare MORE than two samples of data from the same sample of participants- or when one group is compared more than two times (e.g. before treatment, during treatment, and after treatment)
This is a measure of effect size calculated in ANOVA analyses, describing the proportion of variance in scores that is caused by the IV (fr pup membership). An effect size of .50 reflects that 50% of the variance in scores can be explained by group membership
Eta-squared (n^2)
Total risk of a type 1 error across all tests. Increases as the number of t-tests increases. Calculated by multiplying the probability of those events (e.g. 3 t-tests at a = .05, there is a .95 chance of NO type 1 error; .95 x .95 x .95 = 85.70%)
Experiment-wise error rate
What is the ratio of variances in ANOVA
F = between-groups variance/within-groups variance
What does the F value represent in ANOVA
F = whether the observed variability between-groups is more than what we would expect from sampling error (chance) alone
Hypothesis for a one-way repeated ANOVA
H0: treatment has no effectμ1 = μ2 = μ3H1: treatment does have an effectat least one mean will be different from at least one other mean
Analytical hypothesis for one-way ANOVA
H0: wall color (IV) will not effect productivity (DV)H0: μred = μblue = μgreenH1: wall color (IV) will effect productivity (DV)H1: at least one mean will be different from at least one other mean
What does the variance between-groups tell us?
How spread out, or clustered together, the group means are from the overall mean. Tells us about treatment effect
What type of statistical test must be calculated to answer a research question in which there are: - one IV with two conditions - Compares data from two separate samples of participants to determine if they came from the same population - Between-subjects design, each participant experiences only one level of the IV
Independent samples t-test
What does between-subjects variance account for?
Individual differences
This describes when the effect of one IV on the DV differs across levels of (dependent on) the other IV
Interaction
this describes the influence IV #1 has on the DV which is dependent on the level of another IV
Interaction
Describe the Bonferroni Correction
It is a procesure in which we divide the experiment-wise alpha level by the number of tests run, thereby reducing the test-wise error rate oft each test. It' purpose is to reduce the inflation of the experiment-wise error rate that occurs when you run multiole tests. The problem is that decreasing the alpha level (e.g. from .05 to .02) reduces our power to detect an effect because this new alpha level is now the new threshold your statistics must cross in order to be considered statistically significant
This describes when an IV produces a significant difference in the DV, while ignoring (independent of) the other IV.
Main effect
How to write up APA 2-way ANOVA results
Main effects:"there was a significant main effect for factor A, such that A1 level (M = x.xx) scored higher than A2 level (M = x.xx), F(DFa, DFwithin) = x.xx, p = .xx, η2 = .xx."OR "there was no main effect for factor A, F(DFa, DFwithin) = x.xx, p = .xx, η2 = .xx."Interactions:There was an interaction between A and B, F(DFaxb,DFwithin) = x.xx, p =.xx, η2 = .xx. As can be seen in figure below, A1xB1 were more popular than A1xB2, but A2xB2 were more popular than A2xB1.OR "there was no interaction between A and B, F(DFaxb,DFwithin) = x.xx, p =.xx, η2 = .xx
When predicting an interaction by simply looking at a line graph, what do the lines look like when there IS a possible interaction?
Non-parallel, intersecting at some point
What type of statistical test must be calculated to answer a research question in which there are: -one IV with > 2 levels -between-subjects design, different participants in each condition -evaluates whether the observed variability between groups is more than what would be expected by sampling error alone
One-way ANOVA
When predicting an interaction by simply looking at a line graph, what do the lines look like when there IS NOT a possible interaction?
Parallel, never intersecting
only conducted when we reject the null hypothesis (H0) used to determine which group significantly differs from one another
Post-hoc tests
What type of statistical test must be calculated to answer a research question in which there are: - one IV with > 2 levels - within-subjects design, participants experience all levels of the IV, same participants - eliminates individual differences as an explanation for why a difference was observed in the DV
Repeated-measures ANOVA
What does dividing SSbetween into SSwithin produce in an ANOVA analysis?
SSbetween is divided into SSwithin to give a ratio of how much more variability there is between group means than would be expected by chance alone
ANOVA analyses require that between-groups variance be divided by within-groups variance. Explain how SSbetween relate to these sources of variance
SSbetween represents how far group means are from the overall mean, reflecting our treatment effect.
ANOVA analyses require that between-groups variance be divided by within-groups variance. Explain how SSwithin relate to these sources of variance
SSwithin represents how much variability there is between individual scores within each group, reflecting the degree of sampling error.
Describe the steps to conducting hypotheses tests using a one-way ANOVA
Step 1: State analytical hypotheses Step 2: Determine the criteria for decision (Fcrit) using DFbetween and DFwithin Step 3: Calculate sample statistics, N, G, sum of x squared, SStotal, SSbtw, SSwithin, MS total, MSbetween, MSwithin, F, n^2, Step 4: Make a decision, compare Fcrit to Fobt and reject or retain the null, post-hoc if necessary Step 5: Report your results in APA style
What are the steps to hypothesis testing using a Two-way ANOVA
Step 1: State analytical hypotheses, M.E. for both levels of IV and interaction effect between both IVs Step 2: Determine the criteria for a decision (find Fcrit for A, B, and AxB using DFbtw and DFwithin) Step 3: Calculate sample statistics; Marginal Means (M & T), G, sum of X sqaured, N, SStotal, SSbetween, SSwithin, SSa, SSb, SSaxb, F, partial eta-squared n2, build ANOVA source table, Step 4: Make a decision, compare Fcrit to Fobt for A, B, and AxB. Fcrit > Fobt, retain H0, if <, reject H0, post-hoc if necessary Step 5: Report your results in APA style, include descriptive and inferential statistics for main effects and interactions
Describe the steps to conducting hypotheses tests using a repeated-measures ANOVA
Step 1: State the analytical hypotheses Step 2: Determine the criteria for a decision (Fcrit) using DFbetween and DFwithin) Step 3: Calculate sample statistics, P, M, n, N, G, sum of x squared, SStotal, SSbetween, SSwithin, SSbn-sub, SSerror, F, n^2, Step 4: Make a decision, compare Fcrit to Fobt, post-hoc if necessary Step 5: Report results in APA style
the risk of a type one error for each individual test, determined by the alpha level (e.g. a = .05 there is a 5% chance for making a type 1 error). This rate increases as the number of tests run increases.
Test-wise error rate
find q using k (# of treatment conditions) and DFerror/within the minimum difference between group means that is required to say that they came from different populations compare difference scores from all possible group means to q to determine significance
Tukey's HSD (Honestly Significant Difference)
What type of statistical test must be calculated to answer a research question in which there are two independent variables?
Two-way ANOVA
Why do interactions take precedence over main effects?
because if an interaction occurs, we cannot just say one IV produced this change in the DV. This is because we know the effect one IV has on the DV is dependent on IV #2. We must take both IVs into account - which is what an interaction does.
What gives a one-way repeated ANOVA its power?
by dividing within-subjects (denominator) into two - you are dividing by a smaller #, you are lily to obtain a larger f-value, therefore leading to the ability to detect an effect.this is why a within-subjects experiment design gives you a better ability to detect effect.
a measure of effect size in a one way ANOVA that measures the total amount of variance that can be explained by group membership
eta-squared
What kind of design is used in an experiment with two or more IV's (factors)
factorial design
number of IVs in a study
factors
Describe the numerator and denominator in the ANOVA ratio
if the numerator (between-groups) variance is larger than the denominator (within-subjects), you would likely obtain a F-value that is large. Therefore likely to be statistically significant (reject Ho!)if the numerator (between-groups) is smaller than the denominator (within-groups), you would likely obtain an F-value that is small - therefore likely to not be statistically significant (retain Ho!)
this describes one IV that produces a significant difference in the DV, while ignoring the other IV, computed by comparing differences in DV across levels of a single IV by calculating marginal means
main effects
Hypothesis for two-way ANOVA
must write null and alternative hypothesis for every main effect and interactione.g.Null A:μa1 = μa2Alterative A:μa1 ≠ μa2Null Bμb1 = μb2Alterative B:μb1 ≠ μb2Interaction Null:there will be no interaction between factor A and B.Interaction Alternative:there will be an interaction between A and B.
a measure of effect size in a two-way and repeated-measures ANOVA in which the effects of other IVs and interactions are partitioned out individually to measure the total amount of variance that is due to group membership
partial eta-squared
unexplained source of variance after taking into account both treatment effect and individual differences left over variance - most likely a result of sampling error describes what?
residual error
APA write-up of One-Way Repeated Measures ANOVA
state whether or not your null was rejected or retained, provide F-stat(DFbn, DFerror), p-value, η2. Write up results of Tukey's HSD - is one treatment more effective than the other
What does the within-groups variance tell us?
the spread of individual data points from each other within the group reflects sampling error
A repeated measures ANOVA has more statistical power than a between-groups ANOVA because:
we can remove variability between subjects from the within-groups term.