# Confidence interval and hypothesis testing relationship between two

### Significance Testing and Confidence Intervals

Determine from a confidence interval whether a test is significant; Explain why There is a close relationship between confidence intervals and significance tests. There are many situations in which it is very unlikely two conditions will have. Hypothesis testing requires that we have a hypothesized parameter. The primary difference is that a bootstrap distribution is centered on the observed These two-tailed confidence intervals go hand-in-hand with the two-tailed hypothesis. Same studies, same data, difference confidence level: 1. 2. 3. 4. 5. 6. Replications . The goal of hypothesis testing is to weigh the evidence and deliver a.

We could write it like this, that the difference between the in-person and the online, true proportions, is equal to zero. These are equivalent statements. In a hypothesis test, we will assume that this is true. Then in a traditional hypothesis test, we set some significance level. But here we have something interesting.

We have a confidence interval. We have a two-sided hypothesis test. In these situations you can actually make some inferences about your P value from your confidence interval. Think about it this way, we are assuming our null hypothesis is true when we do this hypothesis test.

Where did I get zero from? Remember, this is a confidence interval for the difference in proportions.

### NEDARC - Confidence Intervals V. Hypothesis Testing

Our null hypothesis is that the true difference in proportions is zero. Or another way you can think about it. In this situation you would reject your null hypothesis. In this first situation your P value is going to be greater than or equal to your alpha level and you would fail to reject. Therefore, when tests are run and the null hypothesis is not rejected we often make a weak concluding statement allowing for the possibility that we might be committing a Type II error.

If we do not reject H0, we conclude that we do not have significant evidence to show that H1 is true. We do not conclude that H0 is true.

The most common reason for a Type II error is a small sample size. Tests with One Sample, Continuous Outcome Hypothesis testing applications with a continuous outcome variable in a single population are performed according to the five-step procedure outlined above. A key component is setting up the null and research hypotheses. The known value is generally derived from another study or report, for example a study in a similar, but not identical, population or a study performed some years ago.

The latter is called a historical control. It is important in setting up the hypotheses in a one sample test that the mean specified in the null hypothesis is a fair and reasonable comparator. This will be discussed in the examples that follow. In one sample tests for a continuous outcome, we set up our hypotheses against an appropriate comparator. We select a sample and compute descriptive statistics on the sample data - including the sample size nthe sample mean and the sample standard deviation s.

We then determine the appropriate test statistic Step 2 for the hypothesis test. The formulas for test statistics depend on the sample size and are given below.

## Confidence Intervals V. Hypothesis Testing

Test Statistics for Testing H0: Data are provided for the US population as a whole and for specific ages, sexes and races. An investigator hypothesizes that in expenditures have decreased primarily due to the availability of generic drugs.

To test the hypothesis, a sample of Americans are selected and their expenditures on health care and prescription drugs in are measured. The sample data are summarized as follows: Is there statistical evidence of a reduction in expenditures on health care and prescription drugs in ? We will run the test using the five-step approach.

**Inference for Two Proportions: An Example of a Confidence Interval and a Hypothesis Test**

Set up hypotheses and determine level of significance H0: Select the appropriate test statistic. Set up decision rule. Compute the test statistic. We now substitute the sample data into the formula for the test statistic identified in Step 2. We do not reject H0 because In summarizing this test, we conclude that we do not have sufficient evidence to reject H0. We do not conclude that H0 is true, because there may be a moderate to high probability that we committed a Type II error. It is possible that the sample size is not large enough to detect a difference in mean expenditures.

The NCHS reported that the mean total cholesterol level in for all adults was Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring?

Here we want to assess whether the sample mean of We reject H0 because Because we reject H0, we also approximate a p-value. Statistical Significance versus Clinical Practical Significance This example raises an important concept of statistical versus clinical or practical significance. However, the sample mean in the Framingham Offspring study is The reason that the data are so highly statistically significant is due to the very large sample size.

## Confidence Intervals & Hypothesis Testing (1 of 5)

It is always important to assess both statistical and clinical significance of data. This is particularly relevant when the sample size is large.

Is a 3 unit difference in total cholesterol a meaningful difference?