**PUB-550 Topic 3: Hypothesis Testing DQs**

### Topic 3: Hypothesis Testing

- Evaluate the importance of hypothesis testing in statistics and public health research.

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## Hypothesis Testing |

**Data Resource Document**

**CDC WONDER**

Explore the CDC WONDER website.

**Gapminder**

Explore the Gapminder website.

**Behavioral Risk Factor Surveillance System**

Explore the Behavioral Risk Factor Surveillance System, located on the CDC website.

https://www.cdc.gov/brfss/index.html

**PovcalNet**

Explore the PovcalNet: An Online Analysis Tool for Global Poverty Monitoring page of The World Bank website.

http://iresearch.worldbank.org/PovcalNet/home.aspx

**Demographic and Health Survey Data**

Explore the Demographic and Health Survey (DHS) data website.

**Alcohol-Related Disease Impact Application**

Explore the Alcohol-Related Disease Impact Application (ARDI) page of the CDC website.

https://nccd.cdc.gov/DPH_ARDI/default/default.aspx

**Public Health Partners**

Explore the Health Data Tools and Statistics page of the Public Health Partners website. This site provides many public health data sources.

https://phpartners.org/health_stats.html

**National Health Interview Survey**

Explore the National Health Interview Survey page of the CDC website. Review the documents.

https://www.cdc.gov/nchs/nhis/index.htm

**Global School-Based Student Health Survey**

Explore the purpose and methodology of the international Global School-Based Student Health Survey, located on the World Health Organization (WHO) website.

http://www.who.int/chp/gshs/en/

**Youth Risk Behavior Surveillance System**

Explore the methods, data, and documentation of the Youth Risk Surveillance System, located on the CDC website.

https://www.cdc.gov/healthyyouth/data/yrbs/

## Topic 3 DQ 1 |

Discuss the four potential outcomes of hypothesis testing and describe what is meant by type 1 and type 2 errors. Provide an example of when these errors might occur. PUB-550 Topic 3: Hypothesis Testing DQs

**Topic 3 DQ 1**

Hypothesis testing is used to evaluate a hypothesis about an entire population (Corty, 2016). Hypothesis testing is extremely statistic based with makes it objective not subjective. Statisticians use hypothesis testing to make sure that decisions remain data-based and not emotional based. The data from hypothesis testing is from the sample used to evaluate a population. There are six steps in hypothesis testing (Corty, 2016):

- Pick the right statistical test (TEST)
- Check the assumptions to ensure it is okay to do the test (ASSUMPTION)
- List all null and alternative hypothesis options (HYPOTHESIS)
- Find the value of the static that determines when to reject or accept the null hypothesis (DECISION)
- Calculate the value of the test statistics (CALCULATION)
- State what the results are (INTERPRETATION)
- PUB-550 Topic 3: Hypothesis Testing DQs

In every hypothesis test, the outcomes are dependent on a correct interpretation of the data (Illowsky, n.d.). Incorrect calculations or misunderstood summary statistics can lead to errors that affect the results. A Type I error occurs when a true null hypothesis is rejected (Illowsky, n.d.). A Type II error occurs when a false null hypothesis is not rejected (Illowsky, n.d.).

The probabilities of these errors are denoted by the Greek letters α and β, for a Type I and a Type II error respectively (Illowsky, n.d.). The power of the test, 1 – β, quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted (Illowsky, n.d.). A high power is desirable.

Formula Review (Illowsky, n.d.).

α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true. PUB-550 Topic 3: Hypothesis Testing DQs

β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

- The decision is not to reject H0 when H0 is true (correct decision).
- The decision is to reject H0 when H0 is true (incorrect decision known as a Type I error).
- The decision is not to reject H0 when, in fact, H0 is false (incorrect decision known as a Type II error).
- The decision is to reject H0 when H0 is false (correct decision whose probability is called the Power of the Test).

Example (Illowsky, n.d.):

It’s a Boy Genetic Labs claim to be able to increase the likelihood that a pregnancy will result in a boy being born. Statisticians want to test the claim. Suppose that the null hypothesis, *H0*, is: It’s a Boy Genetic Labs has no effect on gender outcome.

**Type I error:**This result when a true null hypothesis is rejected. In the context of this scenario, we would state that we believe that It’s a Boy Genetic Labs influences the gender outcome, when in fact it has no effect. The probability of this error occurring is denoted by the Greek letter alpha,*α*.**Type II error:**This result when we fail to reject a false null hypothesis. In context, we would state that It’s a Boy Genetic Labs does not influence the gender outcome of a pregnancy when, in fact, it does. The probability of this error occurring is denoted by the Greek letter beta,*β*. PUB-550 Topic 3: Hypothesis Testing DQs

References

Corty, E. (2016). Using and interpreting statistics. A practical text for the behavioral, social, and health sciences 3^{rd} Edition. Retrieved from https://viewer.gcu.edu/GGdEcj

Illowsky, B. (n.d.). Introduction to Statistics. Retrieved from https://courses.lumenlearning.com/introstats1/chapter/outcomes-and-the-type-i-and-type-ii-errors/

**opic 3 DQ 1**

Banerjee et al., (2009) study found the following: Hypothesis testing is an important activity of empirical research and evidence-based medicine. A well worked up hypothesis is half the answer to the research question. For this, both knowledge of the subject derived from extensive review of the literature and working knowledge of basic statistical concepts are desirable. The present paper discusses the methods of working up a good hypothesis and statistical concepts of hypothesis testing (p.127)

Banerjee et al., (2009) study found the following: Just like a judge’s conclusion, an investigator’s conclusion may be wrong. Sometimes, by chance alone, a sample is not representative of the population. Thus, the results in the sample do not reflect reality in the population, and the random error leads to an erroneous inference. A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population. Although type I and type II errors can never be avoided entirely, the investigator can reduce their likelihood by increasing the sample size (the larger the sample, the lesser is the likelihood that it will differ substantially from the population) (p.127). PUB-550 Topic 3: Hypothesis Testing DQs

Banerjee et al., (2009) study found the following: False-positive and false-negative results can also occur because of bias (observer, instrument, recall, etc.). (Errors due to bias, however, are not referred to as type I and type II errors.) Such errors are troublesome, since they may be difficult to detect and cannot usually be quantified (p.127).

Reference

Banerjee, A., Chitnis, U. B., Jadhav, S. L., Bhawalkar, J. S., & Chaudhury, S. (2009). Hypothesis testing, type I and type II errors. *Industrial psychiatry journal*, *18*(2), 127–131. doi:10.4103/0972-6748.62274

## Topic 3 DQ 2 |

Review the Healthy People 2020 website. Identify one of the health issues and propose a scenario that would use a z-test as the first step in the six steps of hypothesis testing. Discuss the remaining five steps based on your scenario, including clearly articulating the null and alternative hypotheses for your scenario.

**Topic 3 DQ 2**

Topic Three, Discussion Question Two.This assignment requires visiting the Healthy People 2020 website and identify one health issue and propose a scenario that would use a z-test as the first step in the six steps of hypothesis testing. Last, discuss the remaining five steps based on your scenario, including clearly articulating the null and alternative hypotheses for the scenario. PUB-550 Topic 3: Hypothesis Testing DQsHypothesis testing is used to evaluate a hypothesis about an entire population (Corty, 2016). Hypothesis testing is extremely statistic based with makes it objective not subjective. Statisticians use hypothesis testing to make sure that decisions remain data-based and not emotional based. The data from hypothesis testing is from the sample used to evaluate a population. There are six steps in hypothesis testing (Corty, 2016):

- Pick the right statistical test (TEST)
- Check the assumptions to ensure it is okay to do the test (ASSUMPTION)
- List all null and alternative hypothesis options (HYPOTHESIS)
- Find the value of the static that determines when to reject or accept the null hypothesis (DECISION)
- Calculate the value of the test statistics (CALCULATION)
- State what the results are (INTERPRETATION)

Now that we have defined hypothesis testing let’s understand what a z-test is. It is a type of hypothesis test that is used when (Statistics How To, 2018): PUB-550 Topic 3: Hypothesis Testing DQs

- The sample size is greater than 30
- Data points are independent from each other (one data point isn’t related or doesn’t affect another data point)
- The data should be normally distributed
- The data should be randomly selected from a population, where each item has an equal chance of being selected.
- The sample size should be equal if at all possible.

When running a z-test with the data – there are five steps that are required (Statistics How To, 2018):

- State a null and alternate hypothesis
- Choose an alpha level
- Find the critical value of “z” in the z table
- Calculate the z test statistic
- Compare the test statistic to the critical z value and decide if you shoul support or reject the null hypothesis

After reviewing the Healthy People 2020 website, the health issue I have decided to pin-point is childhood obesity. One scenario that would use a z-test as the first hypothesis step in a scenario that would use a z-test as the first step in the six steps of hypothesis testing is kids eating fast food multiple times a week impact childhood obesity.

To do this scenario we would have two different proportion ztests that will allow us to compare the two proportions to see if they are the same or different. As stated above:

- The null hypothesis (H
_{0}) for the test is that the proportions are the same. – Yes, survey results and data (weight measurements combined) show that children that eat out three times a week with fast food gain weight faster than those who do not eat out. PUB-550 Topic 3: Hypothesis Testing DQs - The alternate hypothesis (H
_{1}) is that the proportions are**not**the same. The survey results and the data do not show that eating out three times a week with fast food support weight gain in children.

Now that we have the right statistical test (z-test) we need to make sure the rest of the hypothesis testing is ready to go.

- Check the assumptions to ensure it is okay to do the test (ASSUMPTION)
- List all null and alternative hypothesis options (HYPOTHESIS) – listed above.
- Find the value of the static that determines when to reject or accept the null hypothesis (DECISION)
- Calculate the value of the test statistics (CALCULATION)
- State what the results are (INTERPRETATION)

References

Corty, E. (2016). Using and interpreting statistics. A practical text for the behavioral, social, and health sciences 3^{rd} Edition. Retrieved from https://viewer.gcu.edu/GGdEcj

Statistics How To. (2018). Z Test: Definition & Two Proportion Z-Test. Retrieved from https://www.statisticshowto.datasciencecentral.com/z-test/ PUB-550 Topic 3: Hypothesis Testing DQs