Question 1

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced resulting in a _____ F statistic, making it _____ to reject the null hypothesis.

Accepted Answer

In a one-way within-groups ANOVA, the variability due to individual differences is part of the error term, which is reduced, leading to a larger F statistic. This increase in the F statistic makes it easier to reject the null hypothesis, as it indicates a greater likelihood that the observed differences between groups are not due to chance.

Question 2

A researcher examines the effectiveness of different body lotions by having 12 participants apply four different lotions to the same, unique body locations daily for two weeks.For example, lotion #1 is always applied to the right thigh, while lotion #2 is applied to the upper right arm.The participants were randomly selected at a drugstore in a busy area.What is the research hypothesis for this study?

Accepted Answer

The research hypothesis is that there are differences between the average effectiveness assessments of each lotion, as the study aims to compare the effectiveness of different lotions. Options B, C, and D are all incorrect as they do not accurately reflect the goal of the study.

Question 3

A researcher examines the effectiveness of different body lotions by having 12 participants apply four different lotions to the same, unique body locations daily for two weeks.For example, lotion #1 is always applied to the right thigh, while lotion #2 is applied to the right upper arm.The participants were randomly selected at a drugstore in a busy area.Which assumption for the ANOVA is met?

Accepted Answer

The participants were randomly selected at a drugstore, which meets the assumption of random selection for ANOVA. The other assumptions (B: normal population distributions, C: homoscedasticity, D: order effects) cannot be confirmed based on the information provided.

Question 4

For the data in the ANOVA source table, calculate the value of the statistic of interest to researchers. $$\begin{array} { l | l l | l l } 
\hline \text { Source } & \mathbb { S S } & d f & M S & F \
\hline \text { Between-groups } & 13.72 & 3 & 4.573 \
\hline \text { Subjects } & 6.01 & 5 & 1.202 \
\hline \text { Within-groups } & 4.76 & 15 & 0.317 \
\hline \text { Total } & 24.49 & 23 & \
\hline
\end{array}$$

Accepted Answer

The answer of For the data in the ANOVA source...

Question 5

The one-way within-groups ANOVA has an additional assumption compared to the between-groups ANOVA.Which assumption is unique to the within-groups ANOVA?

Accepted Answer

The unique assumption to within-groups ANOVA (also known as repeated measures ANOVA) is that order effects are considered and controlled. This is because the same participants are used across all conditions, and thus, the order in which they experience conditions could affect their responses.

Question 6

Which statistical analysis can handle multiple measures or repeated measures based on the same individuals?

Accepted Answer

One-way within-groups ANOVA is designed to handle repeated measures or multiple measures from the same individuals, allowing for the analysis of data where the same subjects are measured multiple times.

Question 7

A researcher conducts a within-groups ANOVA, fails to find a significant F statistic for the independent variable, and finds an R² value of 0.02.What does the effect size statistic tell the researcher about the research?

Accepted Answer

An R² value of 0.02 indicates a small effect size, which can help to explain the nonsignificant F statistic in a within-groups ANOVA. The conventions for R² suggest that effect sizes of 0.01, 0.06, and 0.14 are small, medium, and large, respectively. Therefore, a value of 0.02 would correspond to a small effect size.

Question 8

The subjects sum of squares calculated in the one-way within-groups ANOVA assesses:

Accepted Answer

The subjects sum of squares calculated in the one-way within-groups ANOVA assesses the variability due to participant differences. It represents the variability in the data that cannot be accounted for by the effects of the independent variable or treatment.

Question 9

A researcher examines the effectiveness of different body lotions by having 12 participants apply four different lotions to the same, unique body locations daily for two weeks.For example, lotion #1 is always applied to the right thigh, while lotion #2 is applied to the upper right arm.The participants were randomly selected at a drugstore in a busy area.What is the null hypothesis for this study?

Accepted Answer

The null hypothesis should always state that there is no difference between groups or conditions being compared in the study. In this case, the null hypothesis should be that the effectiveness of the four different lotions is the same, on average. Option A suggests that there are differences between the lotions, which is not the null hypothesis. Option B makes a causal claim, which is not appropriate for a null hypothesis. Option D is incorrect because the researcher is specifically testing whether the lotions differ in effectiveness.

Question 10

The National Collegiate Athletic Association (NCAA) cares about success for athletes both in their sports and in their education.A researcher hired by the NCAA wants to know how athletes' academic performance is affected by the stage of their competitive season.She examines performance in the preseason, throughout the active competitive season, and postseason, having 150 athletes, from across several different sports, assessed during each period.What statistical analysis would be appropriate for this research?

Accepted Answer

A one-way within-groups ANOVA would be appropriate for this research because the researcher is examining differences in academic performance within the same group of athletes across three different time periods (preseason, active competitive season, and postseason). It is a within-groups analysis because the same group of athletes is being measured at each time point. A one-way between-groups ANOVA would be inappropriate because the researcher is not comparing separate groups of athletes, but rather the same group at different time points. Paired-samples t tests and independent-samples t tests would also be inappropriate because they are not designed for analyzing multiple time points within the same group.

Question 11

Following a one-way within-groups analysis of variance that results in a significant F statistic, the researcher should:

Accepted Answer

Post hoc tests are used to determine where the significant differences between levels of the independent variable exist after obtaining a significant F statistic in the within-groups ANOVA. Replicating the research with matched groups or conducting planned comparisons may be appropriate in some situations, but post hoc tests are the most appropriate next step in this scenario. Conducting a power analysis is only useful before data collection to determine the necessary sample size.

Question 12

Within-groups variability is reduced in the one-way within-groups ANOVA because:

Accepted Answer

By using the same participants across all conditions, individual differences that could contribute to variability are controlled for, thus reducing within-groups variability. This is because the same participants are exposed to all levels of the independent variable, minimizing the impact of their individual differences on the outcome.

Question 13

The one-way within-groups ANOVA has a new source of variability, known as the subjects sum of squares.To calculate this sum of squares, subtract:

Accepted Answer

The subjects sum of squares is calculated by subtracting the grand mean from each participant's mean for all of his or her scores. This measures the variability among individuals in the same group or condition.

Question 14

When it is not possible to have participants experience all levels of the independent variable, an alternative approach to a within-groups design can be used.This approach offers the same advantage in statistical power as the within-groups design by:

Accepted Answer

The alternative approach referred to in the question is a between-groups design. The best choice is option D, which suggests using matching participants across conditions to control for variables of interest. This helps to ensure that any differences in the dependent variable are due to the independent variable manipulation and not due to differences between participants in different conditions. This approach can result in a reduction in variability in the data, increasing statistical power.

Question 15

An advantage of the one-way within-groups ANOVA is that researchers can:

Accepted Answer

By having the same participants in each group, researchers can control for individual differences and reduce within-groups variability, leading to more precise results. A, C, and D are not true advantages of the one-way within-groups ANOVA.

Question 16

The one-way within-groups ANOVA is used when there are:

Accepted Answer

The one-way within-groups ANOVA is used when there is one nominal or ordinal independent variable with more than two levels, a scale-dependent variable, and every participant is in every group. This is because the within-groups ANOVA compares the means of the dependent variable for each level of the independent variable within the same group of participants, allowing for the control of individual differences. Therefore, Option D best fits this description.

Question 17

When using a one-way within-groups ANOVA, the variability due to individual differences is _____, resulting in a _____ F statistic.

Accepted Answer

In a one-way within-groups ANOVA, the variability due to individual differences is reduced because the same participants are used across all conditions. This reduction in variability (or noise) makes it easier to detect true effects, resulting in a larger F statistic.

Question 18

Although the hypothesis test can provide the probability that the levels of the independent variable lead to differences in the dependent variable, it is important to calculate effect size to:

Accepted Answer

Effect size allows researchers to determine if the differences between conditions are clinically or practically significant, as opposed to just statistically significant. It helps to determine if the differences between conditions are large enough to matter, which can inform decisions in the field being studied.

Question 19

A researcher interested in the impact of "dress-down Fridays" on work performance decides to study the impact of attire at work.She randomly selects 35 people at a large company to participate.Across the course of three weeks, she has all 35 participants experience working under three different levels of work attire: casual, dress-casual, and formal attire.How many post hoc tests will be needed to determine where significant differences occurred?

Accepted Answer

Since the researcher is comparing three different levels of work attire, three post hoc tests will be needed to determine where significant differences occurred.

Question 20

For the data in the ANOVA source table, what is the effect size? $$\begin{array} { l l | l | l | l | } 
\hline \text { Source } & \text { SS } & d f & M S & F \
\hline \text { Between-groups } & 13.72 & 2 & 6.86 & 7.831 \
\hline \text { Subjects } & 9.01 & 5 & 1.802 & 2.057 \
\hline \text { Within-groups } & 8.76 & 10 & 0.876 & \
\hline \text { Total } & 24.49 & 17 & & \
\hline
\end{array}$$

Accepted Answer

The answer of For the data in the ANOVA source...

Quiz 13: One-Way Within-Groups Anova

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced resulting in a _ F statistic, making it _ to reject the null hypothesis.

The one-way within-groups ANOVA has an additional assumption compared to the between-groups ANOVA.Which assumption is unique to the within-groups ANOVA?

Which statistical analysis can handle multiple measures or repeated measures based on the same individuals?

A researcher conducts a within-groups ANOVA, fails to find a significant F statistic for the independent variable, and finds an R² value of 0.02.What does the effect size statistic tell the researcher about the research?

The subjects sum of squares calculated in the one-way within-groups ANOVA assesses:

Following a one-way within-groups analysis of variance that results in a significant F statistic, the researcher should:

Within-groups variability is reduced in the one-way within-groups ANOVA because:

The one-way within-groups ANOVA has a new source of variability, known as the subjects sum of squares.To calculate this sum of squares, subtract:

When it is not possible to have participants experience all levels of the independent variable, an alternative approach to a within-groups design can be used.This approach offers the same advantage in statistical power as the within-groups design by:

An advantage of the one-way within-groups ANOVA is that researchers can:

The one-way within-groups ANOVA is used when there are:

When using a one-way within-groups ANOVA, the variability due to individual differences is _, resulting in a _ F statistic.

Although the hypothesis test can provide the probability that the levels of the independent variable lead to differences in the dependent variable, it is important to calculate effect size to:

Quiz 13: One-Way Within-Groups Anova

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced resulting in a _____ F statistic, making it _____ to reject the null hypothesis.

The one-way within-groups ANOVA has an additional assumption compared to the between-groups ANOVA.Which assumption is unique to the within-groups ANOVA?

Which statistical analysis can handle multiple measures or repeated measures based on the same individuals?

A researcher conducts a within-groups ANOVA, fails to find a significant F statistic for the independent variable, and finds an R2 value of 0.02.What does the effect size statistic tell the researcher about the research?

The subjects sum of squares calculated in the one-way within-groups ANOVA assesses:

Following a one-way within-groups analysis of variance that results in a significant F statistic, the researcher should:

Within-groups variability is reduced in the one-way within-groups ANOVA because:

The one-way within-groups ANOVA has a new source of variability, known as the subjects sum of squares.To calculate this sum of squares, subtract:

When it is not possible to have participants experience all levels of the independent variable, an alternative approach to a within-groups design can be used.This approach offers the same advantage in statistical power as the within-groups design by:

An advantage of the one-way within-groups ANOVA is that researchers can:

The one-way within-groups ANOVA is used when there are:

When using a one-way within-groups ANOVA, the variability due to individual differences is _____, resulting in a _____ F statistic.

Although the hypothesis test can provide the probability that the levels of the independent variable lead to differences in the dependent variable, it is important to calculate effect size to:

When using a one-way within-groups ANOVA, the variability due to individual differences is reduced resulting in a _ F statistic, making it _ to reject the null hypothesis.

A researcher conducts a within-groups ANOVA, fails to find a significant F statistic for the independent variable, and finds an R² value of 0.02.What does the effect size statistic tell the researcher about the research?

When using a one-way within-groups ANOVA, the variability due to individual differences is _, resulting in a _ F statistic.