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Post Hoc Comparisons
When a one-way ANOVA results in rejecting the null hypothesis, it indicates that not all population group means are equal, but it does not specify which ones differ. To pinpoint these specific differences, researchers conduct post hoc comparisons. These are follow-up statistical analyses that compare selected pairs of group means to determine exactly which groups are significantly different from each other.
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Research Methods in Psychology - 4th American Edition @ KPU
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Null and Alternative Hypotheses for One-Way ANOVA
Mean Squares Between Groups
Mean Squares Within Groups
Degrees of Freedom (One-Way ANOVA)
ANOVA Table
Sum of Squares Between Groups
Sum of Squares Within Groups
Example of a One-Way ANOVA
Post Hoc Comparisons
Repeated-Measures ANOVA
Formula for the F Statistic in ANOVA
In a psychological research study, what is the primary purpose of using a one-way analysis of variance (ANOVA)?
A researcher is planning a study using a one-way ANOVA. Match each component of the one-way ANOVA with its specific role in the research design.
A clinical psychologist is testing the effectiveness of three different dosages of a new medication (Low, Medium, and High) on reducing anxiety symptoms. Each patient is randomly assigned to receive only one of the three dosages. To evaluate whether the mean anxiety scores differ significantly across these three independent groups, the psychologist should apply a One-Way ANOVA.
A social psychologist is studying the impact of four different room temperatures (Cold, Cool, Room Temp, and Warm) on the aggressive behavior of participants. Each participant is assigned to only one temperature condition. To analyze whether the mean aggression scores differ significantly across these four groups, the researcher performs a One-Way ANOVA. Arrange the logical steps of the variance partitioning and statistical testing process in the correct order.
In the context of psychological research, which of the following scenarios best demonstrates the appropriate use of a one-way ANOVA?
A one-way ANOVA is specifically applied within a between-subjects research design where a(n) _____ independent variable is manipulated across multiple independent groups.
A senior researcher is critiquing a colleague's plan to compare the mean anxiety scores () of participants assigned to four different exercise conditions. The colleague proposes running multiple independent-samples t-tests to evaluate every possible pair. The senior researcher concludes that to prevent an increase in the familywise Type I error rate, the single most appropriate statistical analysis to perform is a(n) _____.
A clinical psychologist wants to compare the effectiveness of different therapy modalities. They randomly assign 45 anxious participants to one of three independent groups: Cognitive Behavioral Therapy (CBT), Mindfulness-Based Stress Reduction (MBSR), or a waitlist control group. After eight weeks, they compare the mean anxiety scores () of the three groups. True or False: A one-way ANOVA is the appropriate statistical test to analyze if there are significant differences among these three groups.
Match each statistical design criterion of a psychological study with the corresponding requirement or component of a one-way ANOVA.
A researcher is evaluating a draft of a research proposal to determine if a one-way ANOVA is the correct statistical test. Order the steps they should take to evaluate the research design against the requirements of a one-way ANOVA.
Learn After
Multiple Comparisons
In statistical analysis, what is the primary purpose of conducting post hoc comparisons after an initial test rejects the null hypothesis?
When comparing three or more group means, researchers must follow a logical sequence of statistical decisions. Match each statistical outcome or procedure with its specific role in this process.
A clinical psychologist is investigating the effectiveness of three different treatments for social anxiety: Cognitive Behavioral Therapy (CBT), Mindfulness-Based Stress Reduction (MBSR), and a Control group. After collecting anxiety scores from all participants, the researcher wants to identify which specific treatments are significantly more effective than the others. Arrange the following steps in the correct statistical sequence to reach this conclusion.
In a psychological experiment comparing three or more groups, a significant result from the initial overall statistical test is sufficient on its own to identify exactly which specific pairs of group means are significantly different from one another.
When a one-way ANOVA results in rejecting the null hypothesis, researchers conduct post hoc comparisons to determine exactly which pairs of group means are significantly different from each other.
A researcher compares mean anxiety scores across four therapy groups using an overall statistical test and finds a significant result. Because this overall test only indicates that not all group means are equal — without revealing which specific groups differ — the researcher must conduct _____ to identify exactly which pairs of group means are significantly different from one another.
In a psychological experiment comparing the effectiveness of three different mnemonic strategies on memory recall, a researcher obtains a significant result in a one-way ANOVA (). If the researcher concludes that 'Strategy 1 is significantly superior to Strategy 3' based solely on this result, this specific conclusion is statistically _____ because the omnibus test does not pinpoint which group means are significantly different from one another.