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HLTH211 Clinical Epidemiology and Biostatistics for Health Sciences Lecture 7: Hypothesis Testing – One and Two Groups
o Research questions often have essentially true or false answers. o We may want to determine whether one treatment has better outcomes than an alternative treatment, or we may want to determine whether patients with a particular characteristic have better outcomes than patients without that characteristic, or we may be interested in determining whether a treatment results in a particular change. o These types of questions are answered using hypothesis testing. Introduction to Hypothesis Testing 2
o We set a null hypothesis which, in the case of a one sample test, states that a parameter in the target population takes a particular value (the null value) o If we were to take repeated samples from this target population, we would expect to see variation in sample statistics for estimating this parameter, ie. these statistics would have some distribution. Some statistics may be close to the null value set as our null hypothesis, others may be further away. o We use a test statistic to measure the discrepancy between a sample statistic and the null value. o The larger that test statistic is, the more unlikely it is that the null hypothesis is true, so we reject the null hypothesis. We use a probability (p-value) to make this decision. 3 Basis of Hypothesis Testing
Hypothesis: State the null and the alternative hypotheses in terms of the parameter of interest. Assumptions: Check the underlying assumptions of the test. Test Statistic: Calculate the test statistic. This can be done using software. p-value: Obtain the p-value (again, you can use software) for the test Decison: Use the p-value to decide whether or not you have enough evidence to reject the null hypothesis Conclusion: Write a conclusion framed in terms of the original research question. Steps in Hypothesis Testing 4 P T H A D C Hypothesis Test
o The null hypothesis represents an assumption or claim of ‘no effect’. The hypothesis test is used to determine whether we have evidence against this null hypothesis. o In the methods we use, null hypotheses will be fairly simple and will be based on the equality of a parameter to either another parameter or to a constant. o Important: null hypotheses always refer to population parameters, not to samples. This is because we are attempting to draw conclusions about populations, not about samples. The Null Hypothesis 5
Examples of null hypotheses: o The average age at which Type 1 diabetes is diagnosed in females is 54 years: 𝐻𝐻 0 : 𝜇𝜇 = 54 o The average survival time for people diagnosed with dementia is 4.5 years: 𝐻𝐻 0 : 𝜇𝜇 = 4.5 o Later in the lecture we will consider hypotheses such as – The average pain scores after treatment are equal for Treatment A and Treatment B: 𝐻𝐻 0 : 𝜇𝜇 𝐴𝐴 = 𝜇𝜇 𝐵𝐵 6 Examples of Null Hypotheses
o For a one sample test, the null hypothesis is a statement (or claim) that a population parameter has a specified value: 𝐻𝐻 0