PSYC FPX 4700 Assessment 3 Hypothesis, Effect Size, Power,

Hypothesis, Effect Size, and Power

Problem Set 3.1: Sampling Distribution of the Mean Exercise

Criterion: Interpret population mean and variance.

Instructions: Read the information below and answer the questions.

Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20 36 . Based on the parameters given in this example, answer the following questions:

1. What is the population mean (μ)? The population mean (μ) is 20.
2. What is the population variance ?  The population variance is 36.
3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and label the mean plus and minus three standard deviations.

The population distribution is a normal curve with a mean (μ) of 20, labeled with values 2, 8, 14, 26, 32, and 38 for ±3 standard deviations (σ = 6).

Problem Set 3.2: Effect Size and Power

Criterion: Explain effect size and power.

Instructions: Read each of the following three scenarios and answer the questions.

Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher A determines that the effect size in the population of males is d = 0.36; Researcher B determines that the effect size in the population of females is d = 0.20. All other things being equal, which researcher has more power to detect an effect? Explain.

Researcher A has more power to detect an effect because the effect size is larger in the population of males than in the population of females (d = 0.36 vs d = 0.20). Generally, effect sizes that are larger result in greater statistical power.

Two researchers make a test concerning the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (n = 22); Researcher B collects a sample of 40 married couples (n = 40). All other things being equal, which researcher has more power to detect an effect? Explain.

Researcher B has greater power to detect an effect since a larger sample size (n = 40) magnifies the precision of the estimate and increases the power to detect an effect compared with a smaller sample size (n = 22).

Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 (); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 (). All other things being equal, which researcher has more power to detect an effect? Explain.

Researcher B has greater sensitivity to detect the effect because σ of test scores in the south community is relatively small at 60, but it is enormous at 110 in the northern community, smaller variability in the data increases sensitivity and makes it less noisy, enabling an effect easier to detect.

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.

Directional versus nondirectional hypothesis testing. Cho and Abe (2013) provided a commentary on the appropriate use of one-tailed and two-tailed tests in behavioral research. In their discussion, they outlined the following hypothetical null and alternative hypotheses to test a research hypothesis that males self-disclose more than females:

• H0: µmales − µfemales ≤ 0
• H1: µmales − µfemales > 0

1. What type of test is set up with these hypotheses, a directional test or a nondirectional test?

It is a directional test as set up by these hypotheses.

This is because the alternative hypothesis H1 indicates direction specifying the fact that males self-disclose more than females-that µmales − µfemales > 0-indicates that the test is one tailed and focused on the detection of the difference in one specific direction.

2. Do these hypotheses encompass all possibilities for the population mean? Explain.

No, these hypotheses don’t encompass all possibilities of the population mean. The null hypothesis is: H0, where males have lower self-disclosure than females. The alternative hypothesis is: H1, males have a greater self-disclosure than females. This is a one-tailed test as it only checks the difference in one direction and not both, therefore, cannot tell if the case is such that females might be having greater self-disclosures than males. This would require a two-tailed test to allow for all the possibilities, such as females having a higher mean.

Problem Set 3.4: Hypothesis, Direction, and Population Mean

Criterion: Explain decisions for p values.

Instructions: Read the following and respond to the prompt.

The value of a p value. In a critical commentary on the use of significance testing, Lambdin (2012) explained, “If a p < .05 result is ‘significant,’ then a p = .067 result is not ‘marginally significant’” (p. 76).

Explain what the author is referring to in terms of the two decisions that a researcher can make.

Two possible decisions a researcher can make while hypothesis testing include rejecting or failing to reject the null hypothesis. If the p-value is smaller than or equal to the chosen significance level (usually 0.05), the null hypothesis is rejected, and a statistically significant result is indicated. If the p-value is larger than the significance level, then the null hypothesis cannot be rejected; this means there is not enough evidence to support the alternative hypothesis. These decisions determine whether the data are supportive of an effect or relationship in the population.

t Tests

Problem Set 3.5: One-Sample t test in JASP

Criterion: Calculate a one-sample t test in JASP.

Data: Use the dataset minutesreading.jasp. The dataset minutesreading.jasp is a sample of the reading times of Riverbend City online news readers (in minutes).  Riverbend City online news advertises that it is read longer than the national news. The mean for national news is 8 minutes per week.

Instructions: Complete the steps below.

1. Download minutesreading.jasp. Double-click the icon to open the dataset in JASP.
2. In the Toolbar, click T-tests. In the menu that appears, under Classical, select One-sample t-test. 
3. Select Time and then click Arrow to send it over to the Variables box.
4. Make sure the box is checked for Student. In the box labeled Test value, enter 8. Hit enter.
5. Copy and paste the output into the Word document.
6. State the nondirectional hypothesis.
7. State the critical t for a = .05 (two tails).
8. Answer the following: Is the length of viewing for Riverbend City online news significantly different than the population mean? Explain.

Independent Samples T-Test