PSYC FPX 4700 Assessment 3 Hypothesis Effect Size Power and Tests PSYC FPX 4700 Statistics for the Behavioral Sciences
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Hypothesis Effect Size Power and Tests
Work through the problems listed below in this Word document. Do not submit any additional files. Provide examples of your work for problem sets requiring calculations. Make sure your solution to each problem is easy to see. To differentiate your response, you might want to highlight it or use a different typeface color.
Criterion: Interpret population mean and variance.
Instructions: Answer the questions after reading the information below.
Assume a scientist needs to conduct a more in-depth study of the mean focusing ability of individuals in a hypothetical population. The following characteristics are cited by the researcher as evidence of a normal distribution of attention span—the amount of time spent on a given task in minutes—in this population: 20 and 36. Provide responses to the following questions based on the parameters presented in this example:
What is the mean population size (μ)? 20 minutes: What is the variance in the population? Draw a map of this population’s distribution in 36 minutes. Label the mean plus and minus three standard deviations and draw the distribution’s shape.
Standard deviation of the population = σ = 36 = 6
μ – 3σ = 20 – (3 × 6) = 2
μ – 2σ = 20 – (2 × 6) = 8
μ – σ = 20 – 6 = 14
μ + σ = 20 + 6 = 26
μ + 2σ = 20 + (2 × 6) = 32
μ + 3σ = 20 + (3 × 6) = 38
PSYC FPX 4700 Assessment 3 Hypothesis, Effect Size, Power, and t Tests
Problem Set 3.2: Effect Size and Power
Criterion: Explain effect size and power.
Instructions: Read each of the three scenarios below and respond to the questions.
A test designed by two researchers measures the efficacy of drug treatment. According to Researcher A, the effect size for the male population is d = 0.36; Scientist B confirms that the effect size for the female population is d = 0.20. If all other factors are equal, which researcher has a greater ability to identify an effect? Explain.
Researcher A is likely to have a higher ability to identify the effect due to the larger disparity between the null and alternative means. This is because the test is more powerful with a larger effect size.
Two researchers conduct a study on the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (n = 22), while Researcher B gathers a sample of 40 married couples (n = 40). All other factors being equal, which researcher has a greater ability to detect an effect? Explain.
Researcher B has a greater ability to detect an effect due to the larger sample size, as power is positively correlated with sample size.
Two researchers conduct a study on standardized test performance among high school students in two nearby communities. Researcher A tests performance in the northern community, where the standard deviation of scores is 110 (σ); Researcher B tests performance in the southern community, where the standard deviation of scores is 60 (σ). If all other factors are equal, which researcher has a greater ability to identify an effect? Explain.
Researcher B has a greater ability to detect an effect due to the smaller standard deviation, which typically indicates less variability in scores and thus a clearer signal of any potential effect.
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion: Explain the relationship between hypothesis, tests, and population mean.
Instructions: Read the following and answer the questions.
Testing hypotheses in a directional or nondirectional manner. A commentary on the appropriate use of one-tailed and two-tailed tests in behavioral research was provided by Cho and Abe (2013). To test a research hypothesis that males self-disclose more than females, they discussed the following hypothetical null and alternative hypotheses:
H0: Males = Females
H1: Males > Females
Which type of test is used to test these hypotheses? A directional or nondirectional test?
Since the alternative hypothesis (H1) is stated in a way that specifies a single direction of effect—indicating that males engage in greater self-disclosure than females—the hypothesis is formulated as a directional test.
Do these hypotheses encompass all population mean possibilities? Explain.
The provided hypotheses account for all potential outcomes regarding the population mean. Si