Hypothesis Testing
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What is a hypothesis test?
A method of making statistical decisions about populations or processes based on empirical data
What is the aim of hypothesis testing?
Assess the strength of evidence provided by data
Describe 5 steps to hypothesis testing
• Formulation of practical problem in terms of statistical hypotheses • Conduct study • Calculate p-value • Examine significance level of the test • Further assessment
What is a null hypothesis?
A statement of the assumed population characteristics
What is an alternative hypothesis?
A hypothesis which contradicts the null hypothesis
What does the alternative hypothesis express?
The range of situations that we wish the test to be able to diagnose
Give an example of a null hypothesis with regards to heart rate of children who have received anaesthetic
The mean minimal heart rates of children who have received anaesthetic is equal to “x”
Give an example of an alternative hypothesis with regards to heart rate of children who have received anaesthetic
The mean minimal heart rates of children who have received anaesthetic is not equal to “x”
What is a test statistic?
A function of the data plus the information in the null hypothesis
What 2 properties must a test statistic satisfy?
• Probability distribution must be calculable under the assumption null hypothesis is true • Behave differently when null hypothesis is true from when alternative hypothesis is true
What are the 3 most common associated distributions in a test statistic?
• Normal • t • Chi-squared
Why do null hypothesis tend to be “not rejected” rather than “accepted”?
Test statistics are constructed so a lack of information tends to result in non-significant values of the test statistic
What is the p-value?
• Assumption that null hypothesis is true • Probability that if repeats the study many times the test statistic would be as extreme or more extreme than test statistic obtained • More extreme means less likely
Describe a “small” p result in practice
• Small p-value means null hypothesis is rejected in favour of alternative hypothesis • Not small p-value means there is insufficient evidence to reject null hypothesis in favour of alternative hypothesis
What is the significance level?
Probability of rejecting null hypothesis when it is true
What is power?
The probability of rejecting the null hypothesis when the alternative hypothesis is true
Describe the relationship between significance level and power
If the significance level of a test is decreased the power is also decreased
What is a Type I Error?
This occurs when a null hypothesis is rejected when it is true
What is the probability of making a Type I Error?
It is equivalent to the significance level of the test
What is a Type II Error?
This occurs when a null hypothesis is not rejected when it is false
What is the probability of not making a Type II Error?
It is equivalent to the power of a test
Name 3 determinants of the most appropriate test
• Scale of measurement • Whether samples are paired or independent • Two samples or more than two samples
What method is used as a guide to determine the most appropriate test?
Decision tree