Week 5 - Hypothesis testing and confidence intervals

Apart of Introduction to Evidence Based Practice and Research in Health Sciences at UniSA

Hypothesis testing

Method of making decisions using data.

What is the difference between null and alternative hypothesis?

Although both are type of hypotheses, null states the data has no effect or there is no significant difference between measured variables (e.g. light colour has no effect on plant colour) and alternative states the data has significance or suggests there is a significant difference or relationship between measured variables (e.g. using fertiliser will help increase plant growth).

What are the six steps in hypothesis testing?

1. State the research question

2. Specify the null and alternative hypothesis

3. Decide on the significance level (typically 5% in health research)

4. Calculate test statistic

5. Decide whether to reject or fail to reject the null hypothesis using p (probability) value table depending on where it falls within the range or if it’s higher/lower than significance level (higher = reject null, lower = fail to reject null)

6. State the conclusion

What is the difference between Type I and Type II error?

Type I is when a true null hypothesis is incorrectly rejected in statistical hypothesis testing whereas Type II is when an alternative hypothesis is incorrectly rejected in statistical hypothesis testing.

What error is more important in hypothesis and diagnostic and why?

• Type I error is more important than Type II error in hypothesis testing because the goal is truthful inference, so false claims are the bigger threat to the hypothesis.

• Type II error is more important in diagnostic testing because the goal is early detection and safety, so missing a real condition is the bigger threat to the hypothesis.

What is statistical assessment in healthcare?

Whether observations reflect a pattern rather than mere chance and if observations are assessed, it is not due to chance but what is done/intervention is being tested.

What is clinical significance in healthcare?

When statistical significance is not enough when statistics are too small or little practical value, clinical significance is used to determine the practical importance of the treatment effect and if the change/improvement of the treatment is considered worthwhile.

Confidence intervals (CI)

An estimated range of values which is likely to contain the true population parameter from a given set of sample data.

What is the purpose of confidence intervals in statistics (2 points)?

• It provides a measure of the precision of the estimate of the mean from one sample.

• Using sample data to make inference to the wider population has limitations so the best approach to estimate CI based off the point estimate, desired level of confidence, and sampling variability or the standard error of the point estimate.

What is the importance of confidence interval in hypothesis testing (3 points)?

• More useful for the wider population than using P-values

• It tells us the narrower the CI is, the more precise the estimate is

• Tells us the range of possible effect size like for treatments, are the benefits value for money, effort, and time

What is the correct interpretation of confidence interval compared to the incorrect interpretation of confidence interval?

Correctly interpretating of CI would be selecting 100 samples from a population and using those samples to calculate 100 confidence intervals for mu, approx. 95% of those intervals would include the mu whereas incorrectly interpretating is if the probability of the mu is in the interval = 95.

When population standard deviation is known, what do we use to estimate sample data?

Z-scores.

When population standard deviation is unknown, what do we use to estimate sample data?

T-distribution however, Z-scores are mostly used in healthcare.