# statistic discussions

Please read the lecture and respond to the questions.

**How to Use Statistics to Make Decisions**

**Introduction**

To make decisions, statistical inference will be used.Statistical inference is making statements about population parameters based on information from a sample statistics. These statements offer insight into making data-based decisions. A good example of this can be seen in the pharmaceutical industry. Hypothesis testing is used to determine if a new drug is a better treatment than one that currently exists. This lecture will look at two basic hypothesis tests, a one-sample test and a two-sample test.

Hypothesis Testing

In order to study hypothesis testing, the basic elements of the test need to be discussed. A hypothesis test can be broken down into 7 steps.

1.State the null hypothesis.

2.State the alternative hypothesis.

3.State the test statistic.

4.State the level of significance.

5.Compute the test statistic and the p-value.

6.Determine the statistical conclusion.

7.State the experimental conclusion.

Steps 1 and 2 state the null and alternative hypothesis, respectively. In order to understand the null and alternative hypothesis, a basic understanding of a hypothesis statement should first be considered.A hypothesis is a statement about the value of a population parameter or a population model. This statement is one that is to be proven or disproven. The hypothesis statement is broken up into two hypothesis statements. The null hypothesis is the statement of no effect, meaning the treatment did nothing different. The alternative hypothesis is the statement that is to be tested. It is what is expected to happen. Step 3 determines which test statistic is needed to perform the test. A test statistic is used to measure how far (or close) the sample statistic, estimating the parameter, is from the value of the parameter specified by the null hypothesis. The formula will change, depending on the test that is being conducted. Step 4 states the level of significance. Step 5 occurs when all the calculations are performed. The test statistic, as well as the p-value, is calculated in this step. P-value is the probability of observing a value of the test statistic as extreme, or more extreme, than the actual value computed from the data. The p-value is then compared to the level of significance, found in Step 6, to determine whether to reject or fail the null hypothesis. The rule is: If the p-value is less than the level of significance, then reject the null hypothesis. Once the decision has been made, step 7, the experimental conclusion, can be written. The experimental conclusion is applying the statistical conclusion to the problem statement.

One-Sample Test

A one-sample hypothesis test compares an existing value (from an existing treatment) to the data collected under the new treatment. Specifically, a one-sample test about the population mean (t-test) is to be studied. In order to perform this test, the data must come from a simple random sample, and the data must either follow a normal distribution or have a sample size greater than 30. The sample size of greater than 30 allows the assumption of normality. The test statistic that will be needed is as follows (Triola, 2010):

An example of a one-sample hypothesis test is available in the Visual Learner: Statistics.

Two-Sample Test

A two-sample hypothesis test compares two samples. This test allows two treatments to be compared directly, or a treatment to be compared to a control. The control is most commonly referred to as a placebo. Remember, in statistics a treatment can refer to anything that needs to be tested. For example, if the heart rate of males and females needs to be compared, then the treatment is actually gender.

In order to perform the two-sample test about populations means (two-sample t-tests), there must be two independent samples that are obtained through simple random sampling. Also both samples must either come from normal distributions or have sample sizes of 30 or larger. The test statistics for a two-sample test about means is as follows (Triola, 2010):

An example of a one-sample hypothesis test is available in the Visual Learner media piece.

Multiple Comparisons

What if there are more than two treatments that need to be compared? This is a common question in statistics classes. Two possible answers will be explored, one here and one in the next topic.

If more than two treatments need to be compared then multiple two-sample t-tests will need to be conducted. This changes the level of significance of the test, leading to more stringent level of significance. The Bonferroni method is used to calculate the level of significance for the multiple comparisons. To calculate the new level of significance based on the Bonferroni method, take the existing level of significance and divide by the number of the two-sample t-tests that were conducted.

Conclusion

Decision-making skills are crucial. Two of the hypothesis tests that are used to make decisions have been discussed here. Moving forward, more specialized hypothesis testing will be discussed.

References

Triola, M. (2010). *Elementary statistics* (11th ed.). Boston, MA: Addison Wesley.

**Please do not forget to reference your response**

Question 1

Explain when a z-test would be appropriate over a t-test.

Question 2

Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level (e.g., 0.1)?