PBSI 301 Exam III Review

In analysis of variance (ANOVA), the F-ratio compares:

• Total variance to sample variance

• Between-groups variance to within-groups variance

• Sample means to variances

• Sample variances to population means

Answer explanation

The F-ratio in ANOVA measures the ration of systematic variance (differences between group means) to unsystematic variance (differences within groups, due to chance). A large F-ratio suggests the between-group differences are greater than the within-group differences, indicating potential significance.

In ANOVA, the variability between groups is due to

• Individual differences

• Treatment effects

• Sampling error

• All of the above

What value would the F-ratio likely have if the null hypothesis is false?

• 0

• 1

• Greater than 1

• Less than 1

Answer explanation

If the null hypothesis is false, we expect the between-groups variance to be larger than the within-groups variance, making the F-ratio greater than 1. An F-ratio close to 1 suggests no significant differences among group means.

In a one-way ANOVA, the number of levels refers to:

• The sample size

• The number of treatment conditions

• The number of groups within the sample

• The degrees of freedom

Answer explanation

Ex: Im an experiment testing 3 types of diets, the variable "diet" has 3 levels

Which of the following is a potential drawback of a between-subjects study?

• Practice effects may influence results

• Results could be influenced by individual differences

• Participants may perform differently across conditions

• All of the above

Answer explanation

In between-subjects designs, participants are only tested in one condition. This can lead to variability in results due to differences between participants, such as baseline abilities, which can potentially influence outcomes.

Which situation would be ideal for a within-subjects research design?

• Comparing test scores for boys and girls in high school

• Comparing reactions to a task under two different lighting conditions (i.e., working under low light, working under bright lights, etc.)

• Comparing employee productivity across different departments

• Comparing anxiety levels of two distinct age groups

Answer explanation

A within-subjects design is suitable when the same participants can be tested in multiple conditions (as with lighting changes) since it controls for individual differences and minimizes variability due to participant characteristics.

For the independent-measures t-test, what is the effect of reducing the sample variance?

• Increases the likelihood of rejecting the null hypothesis

• Decreases the likelihood of rejecting the null hypothesis

• Increases the calculated t-value and reduces effect size

• Has no effect on hypothesis testing

Answer explanation

Lower variance reduces the denominator of the t-statistic, increasing its value and the likelihood of rejecting the null hypothesis if there is a real effect. Reduced variance leads to more precision in detecting differences between groups.

If a research study reports t(30) = 2.04, p < .05, what are the boundaries for the critical region? (Use your table!)

• ±2.042

• ±2.000

• ±1.697

• ±2.050

Answer explanation

Critical values for a two-tailed test at df = 30 and a = .05 are approximately ±2.042. This value represents the threshold for rejecting the null hypothesis in both tails of the distribution.

In an independent-samples t-test, if t = 0, then:

• The two population variances must be equal

• The sample variances must be equal

• The sample means are identical

• None of the above

Answer explanation

A t-value of 0 occurs when the difference between sample means is 0, suggesting no difference between groups. This means the sample means are exactly the same, although variances may differ.

Increasing sample size in a t-test will:

• Increase the likelihood of rejecting the null hypothesis and increase effect size

• Increase the likelihood of the null hypothesis with little or no effect on effect size

• Decrease the likelihood of rejecting the null hypothesis with no effect on effect size

• Increase effect size without impacting the null hypothesis

Answer explanation

A larger sample size decreases the standard error, which can lead to a larger t-statistic and a higher chance of rejecting the null hypothesis. However, effect size remains independent of sample size.