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Chapter 10: Problem 43

Step 5 of the five-step process for hypothesis testing is communication of results. What is involved in completing this step?

Short Answer

Expert verified
To effectively communicate the results of a hypothesis test, follow these steps: 1. Review the hypothesis test results, including null and alternative hypotheses, test statistic, p-value, and conclusion. 2. Choose an appropriate communication method based on your target audience. 3. Present the background information, introducing the research question/problem and defining the null and alternative hypotheses. 4. Explain the test methodology, including the type of hypothesis test, sample data, choice of test, and any assumptions or conditions. 5. Share the test results, with test statistic value, p-value, significance level, decision rule, and conclusion. 6. Discuss the implications and limitations of the test results, relating them to the research question/problem, previous findings, theories, and potential biases or factors affecting the results.

Step by step solution

01

Review the Hypothesis Test Results

In order to communicate the results of the hypothesis test effectively, it is important to first review the results thoroughly. This involves understanding the null and alternative hypotheses, the test statistic, the p-value, and the conclusion drawn based on these values. Make sure you have a clear understanding of the test results and how they were derived.
02

Choose an Appropriate Communication Method

Depending on the target audience, choose the most appropriate method to convey the results. This could include presenting the results in a formal report, presenting them in a PowerPoint presentation, or discussing them in a meeting. Consider the level of understanding of statistical concepts within your audience, as this will influence how you present the information.
03

Present the Background Information

Begin by presenting the background information that led to the hypothesis test, such as the research question or the problem that was being investigated. Clearly define the null and alternative hypotheses, ensuring that the audience understands the context of the test.
04

Explain the Test Methodology

Provide a brief overview of the test methodology, including the type of hypothesis test used (e.g., t-test, ANOVA, chi-squared, etc.) and the sample data that were analyzed. Explain the choice of the test and why it was appropriate for the given situation. Additionally, discuss any assumptions made or the conditions that were met in order to perform the hypothesis test.
05

Share the Test Results

Clearly present the test results, including the test statistic value and the p-value. Explain the significance level used (commonly 0.05) and the decision rule for rejecting or failing to reject the null hypothesis. Then, share the conclusion of the test based on these results, whether it was to reject or fail to reject the null hypothesis.
06

Discuss the Implications and Limitations

Finally, discuss the implications of the test results in relation to the research question or problem being investigated. Explain how the results support or contradict any previous findings, theories, or hypotheses. Additionally, discuss any limitations of the test, such as potential biases, sample size, or other factors that may have impacted the results. By following these steps, the communication of the results of the hypothesis test will be both clear and effective, allowing the audience to fully understand and engage with the findings.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Test Statistic
The test statistic is a crucial part of hypothesis testing. It provides a quantitative measure to decide whether to reject the null hypothesis.
When you perform a hypothesis test, you calculate this number using your data and the specific test method you choose (e.g., t-test, chi-square test). Its main job is to compare actual observations from the sample with the expected results if the null hypothesis is true.

Here's how it works:
  • If the test statistic is too extreme (either too high or too low), it suggests that the observed results are unlikely under the null hypothesis.
  • Different tests have different formulas for the test statistic. For example, a t-test will use a different calculation than a chi-square test.

Once calculated, the test statistic is used to find the P-value by comparing it to a standard distribution.
Null Hypothesis
The null hypothesis, often denoted as \( H_0 \), is a statement in hypothesis testing that assumes no effect or no difference in the parameters being studied.
It's the default assumption that there is no change, no effect, or no difference, and it serves as a starting point for testing.

The goal of hypothesis testing is to determine whether available evidence supports rejecting the null hypothesis. Here are some key points to understand:
  • The null hypothesis typically represents the "status quo" or a position of no change.
  • We never prove that the null hypothesis is true; we either reject or fail to reject it.
  • Failing to reject the null hypothesis does not mean it is true, only that there wasn't enough evidence to prove it false.

Deciding to reject or fail to reject \( H_0 \) is a critical component of the hypothesis testing process.
P-value
The P-value is a probability that helps you understand the strength of the evidence against the null hypothesis. It's a key concept in determining whether to reject \( H_0 \) in your hypothesis test.

The P-value tells you how likely it is to observe your data, or something more extreme, assuming that the null hypothesis is true.
  • A small P-value (typically 鈮� 0.05) indicates strong evidence against the null hypothesis, so you reject \( H_0 \).
  • A large P-value (> 0.05) suggests weak evidence against the null hypothesis, so you fail to reject \( H_0 \).
  • P-values are calculated using the test statistic and the chosen statistical test's probability distribution.

Understanding P-values helps you make informed decisions in hypothesis testing, balancing between type I and type II errors.
Research Question
Formulating a research question is often the first step in the hypothesis testing process. It guides the entire research study and dictates the formulation of your hypotheses.

A well-defined research question should be clear, focused, and researchable. Here are some important considerations:
  • Your research question should help you decide how to collect data and choose the right test method.
  • The clarity of the research question influences the hypothesis setting (both null and alternative).
  • A good research question considers the scope of the research, targeted outcomes, and possible limitations.

The effectiveness of the hypothesis test and the relevance of its results depend largely on how well the research question is constructed and addressed.

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Most popular questions from this chapter

A study of treatment of hospitalized patients who develop pneumonia reported that 1 in \(5(20 \%)\) are readmitted to the hospital within 30 days after discharge ("Comparison of Therapist-Directed and Physician-Directed Respiratory Care in COPD Subjects with Acute Pneumonia," Respiratory Care \([2015]: 151-154)\) The study reported that 15 out of \(n=162\) hospital patients who had been treated for pneumonia using a respiratory therapist protocol were readmitted to the hospital within 30 days after discharge. You would like to use this sample data to decide if the proportion readmitted is less than 0.20 . a. What hypotheses should be tested? b. Discuss whether the conditions necessary for a largesample hypothesis test for one proportion are satisfied. c. The exact binomial test can be used even in cases when the sample size condition for the large-sample test is met.

According to a survey of a random sample of 2278 adult Americans conducted by the Harris Poll ("Do Americans Prefer Name Brands or Store Brands? Well, That Depends" (theharrispoll.com, February 11, 2015, retrieved November 29,2016 ), 1162 of those surveyed said that they prefer name brands to store brands when purchasing frozen vegetables. Suppose that you want to use this information to determine if there is convincing evidence that a majority of adult Americans prefer name-brand frozen vegetables over store brand frozen vegetables. a. What hypotheses should be tested in order to answer this question? b. The \(P\) -value for this test is 0.173 . What conclusion would you reach if \(\alpha=0.05 ?\)

Describe the two types of errors that might be made when a hypothesis test is carried out.

Past experience is that when individuals are approached with a request to fill out and return a particular questionnaire in a provided stamped and addressed envelope, the response rate is \(40 \%\). An investigator believes that if the person distributing the questionnaire were stigmatized in some obvious way, potential respondents would feel sorry for the distributor and thus tend to respond at a rate higher than \(40 \%\). To test this theory, a distributor wore an eye patch. Of the 200 questionnaires distributed by this individual, 109 were returned. Does this provide evidence that the response rate in this situation is greater than the previous rate of \(40 \%\) ? State and test the appropriate hypotheses using a significance plevel of 0.05 .

How accurate are DNA paternity tests? By comparing the DNA of the baby and the DNA of a man that is being tested, one maker of DNA paternity tests claims that their test is \(100 \%\) accurate if the man is not the father and \(99.99 \%\) accurate if the man is the father (IDENTIGENE, www.dnatesting .com/paternity-test-questions/paternity-test-accuracy/, retrieved November 16,2016 ). a. Consider using the result of this DNA paternity test to decide between the following two hypotheses: \(H_{0}:\) a particular man is not the father \(H:\) a particular man is the father In the context of this problem, describe Type I and Type II errors. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) b. Based on the information given, what are the values of \(\alpha\), the probability of a Type I error, and \(\beta\), the probability of a Type II error?
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