StatisticsLocate a recent newspaper or magazine article that describes the results of a statistical study. Include a full citation for the source so your instructor can verify it. Respond to the following questions.
Identify the sample and the population, the variables of interest, and the sampling method that was used. Describe the advantages and disadvantages of having used this particular sampling method. (5 points)
What is inferred from the results, i.e., what is the conclusion? What alternative explanations could there be for the results? (5 points)
Use outside resources (online, library, etc.) to locate a data set with at least 20 scores (or you can make one up). Note: You may not use data from the textbook in this exercise. Show all calculations so your instructor can review your work and provide feedback.
Summarize those scores in both a frequency distribution table with appropriate classes and frequencies shown. (3 points)
Calculate the mean, median, variance, and standard deviation of the data. (3 points)
Calculate the 25th percentile. (2 points)
What is the z-score of the second highest score (second score counting down)? Would this be considered an unusual event? (2 points)
Show all calculations so your instructor can check your work and provide feedback on any errors.
In Lesson 3, you’ve learned the basics of probability theory and how to calculate probabilities of outcomes in various circumstances.
Make up an original “real life” example (e.g., not card decks or dice) of how to use the multiplication rule to determine the probability of an outcome. Explain why the events in your example are either dependent or independent. (5 points)
Make up an original “real life” example (e.g., not card decks or dice) of how to use the addition rule to determine the probability of an outcome. Explain why the events in your example are either mutually exclusive or not mutually exclusive. (5 points)
Create a scenario where the binomial probability formula could be used to determine the probability of some number of successes, x, in some given number of trials, n. Base your scenario on a situation that you might be familiar with, for example, at work or at school. Start with a paragraph of text describing your scenario and the variable involved, and then complete the following:
Describe the possible outcomes of a set of trials involving this variable, and explain why it can be described as a binomial experiment. (5 points)
Assign values for p and q, suggest possible values for x and n in a hypothetical set of experimental trials, and calculate the probability of x successes in n trials given those values. Show all work. (5 points)
Lesson 5 Roundup Exercise
Psychological tests are often standardized. This means the administration is consistent, and test administrators can use published norms to score the results (i.e., an individual’s results can be compared to the normative data, which represents the population as a whole, and that individual’s scores can be summarized and reported in terms of how they compare to the population from which the normative data was collected).
An example often used in psychology textbooks is the Wechsler Adult Intelligence Scale (WAIS), often referred to as an IQ test. The WAIS has a normative mean of 100 and a standard deviation of 15 points. Any person’s score on the WAIS can be summarized in various ways, for example, as the distance from the mean, or in terms of quartiles or percentiles.
Use the Assessment Psychology Online website, or conduct an Internet search to identify another behaviorally oriented standardized test (i.e., not the WAIS), and respond to the following:
Start with a general description of the instrument, including who developed it, its intended purpose, and how it is administered. (3 points)
Describe the normative data (i.e., the mean, standard deviation, and any other relevant parameters). (3 points)
What would be the probability of a person chosen at random from the population scoring more than 1.0 standard deviation above or below the mean? (2 points)
Describe, in behavioral terms, what a z-score of 1.0 represents. (2 points)
Lesson 6 Roundup Exercise
In Chapter 6, you’ve learned how to construct confidence intervals for population parameters and proportions, based on data from samples.
Respond to the following to describe a “real world” scenario where a researcher might want to construct a confidence interval to support a conclusion about a population parameter.
Provide an overview of the scenario and the variable involved. Include an explanation of why and how constructing the confidence interval adds value. I.e., why might this information be important to know? (4 points)
Identify any assumptions that must be met. (3 points)
Describe an overview of the process of constructing the confidence interval along with the steps involved. (3 points)
Lesson 7 Roundup Exercise
Scenario:
Behavioral researchers often use statistical techniques to support conclusions about behavioral differences between particular groups of people and the general population of people. This approach has been useful, for example, in identifying memory decrements that result from head injuries. One such study observed participants with lesions in the frontal lobe of the brain, which is thought to be involved in memory functions, and compared their performance on a simple recall task to established norms on the task to see if memory performance was reduced. The normative (general population) data for the task was normally distributed. The researcher measured the performance of 24 people in the sample being studied and compared their scores to the normative data, using an alpha value of .05.
Answer the following regarding the scenario:
State the null and alternative hypotheses, both in words and in symbols. (3 points)
Under the conditions described in the scenario, what statistical test would be appropriate? Explain the rationale for your answer. (3 points)
Would it be most appropriate to use a two-tailed test, a left-tailed test, or a right-tailed test? Why? (2 points)
In one paragraph, describe the conclusion you would reach about the participants’ performance if the P-value of the hypothesis test was determined to be .035. Include the rationale for your conclusion. (2 points)
Lesson 8 Roundup Exercise
Scenario:
One well-known psychological experiment measures reaction time (RT) to a stimulus in microseconds (msec). In one version, intended to simulate the effects of texting while driving, participants in an experimental group (EG) are directed to attend to a visual display of words and quickly press a button when a loud noise is heard. A control group (CG) is directed to ignore the visual display and quickly press the button when the noise is heard. Assume the researcher is using an alpha value of .05 in analyzing the results of the experiment, and that she is interested in whether the RT of the experimental group is greater than the RT of the control group. Also assume that RT scores generally tend to be normally distributed, and that the researcher has a sample of at least 30 participants in each group to compare, but that the population parameters are not known.
Answer the following regarding the scenario:
State the null and alternative hypotheses, both in words and in symbols. (3 points)
Under the conditions described in the scenario, what statistical test would be appropriate? Explain the rationale for your answer. (3 points)
Would it be most appropriate to use a two-tailed test, a left-tailed test, or a right-tailed test? Why? (2 points)
In one paragraph, describe the conclusion you would reach about the participants’ performance if the P-value of the hypothesis test was determined to be .065. Include the rationale for your conclusion. (2 points)
Lesson 9 Roundup Exercise
The text tells us that a Pearson correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. A scatter plot provides a visual representation of the relationship. Answer the questions below, but use your own examples and do not take examples from the text.
Make up an example of two variables that might be related in such a way that the Pearson correlation coefficient could not be used to measure the relationship strength but the Spearman coefficient could be used instead. Explain the rationale for your answer. (4 points)
Use an example to describe a situation where a scatter plot of the data would result in all of the data points falling exactly on a straight line. What would be the calculated value of r? (3 points)
Use an example to describe a situation where a researcher might be misled into thinking there is a causal relationship between two variables when in fact there is none. Give three possible alternative explanations for the relationship. (3 points)
Lesson 9 Roundup Exercise
The text tells us that a Pearson correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. A scatter plot provides a visual representation of the relationship. Answer the questions below, but use your own examples and do not take examples from the text.
Make up an example of two variables that might be related in such a way that the Pearson correlation coefficient could not be used to measure the relationship strength but the Spearman coefficient could be used instead. Explain the rationale for your answer. (4 points)
Use an example to describe a situation where a scatter plot of the data would result in all of the data points falling exactly on a straight line. What would be the calculated value of r? (3 points)
Use an example to describe a situation where a researcher might be misled into thinking there is a causal relationship between two variables when in fact there is none. Give three possible alternative explanations for the relationship. (3 points)
Lesson 10 Roundup Exercise
Respond to the following to describe a scenario where a researcher might use a Goodness of Fit Test, a Test for Independence, or an Analysis of Variance to investigate a research question.
Example Scenarios
Provide an overview of the scenario and an explanation of why the selected statistical test is appropriate. (2 points)
Provide brief descriptions of the variables that you think might be related such that the technique represents an appropriate test. (2 points)
Identify any assumptions that must be met. (2 points)
Describe an overview of the process of conducting the test along with the steps involved. (2 points)
Provide an example of outcomes that might be reported, expressed in appropriate statistical notation. (2 points)
