What is a hypothesis test?

• A hypothesis test uses a?sample of data?in an experiment to test a?statement?made about the?population
  • The statement is either about a?population parameter?or the distribution of the?population
• The hypothesis test will look at the probability of observed outcomes happening under set conditions
• The probability found will be compared against a given?significance level?to determine whether there is?evidence to support?the statement being made

What are the key terms used in statistical hypothesis testing?

• Every hypothesis test?must?begin with a clear?null hypothesis?(what we believe to already be true) and?alternative hypothesis?(how we believe the data pattern or probability distribution might have changed)
• A?hypothesis?is an assumption that is made about a particular?population parameter?or the?distribution of the population
  • A?population parameter?is a numerical characteristic which helps define a population
    • Such as the mean value of the population
  • When a hypothesis test is carried out, the null hypothesis is?assumed to be true?and this assumption will either be?accepted?or?rejected
    • When a null hypothesis is accepted or rejected a?statistical inference?is made
• A hypothesis test will always be carried out at an appropriate?significance level
  • The significance level sets the?smallest probability?that an event could have occurred by chance
    • Any probability smaller than the significance level would suggest that the event is unlikely to have happened by chance
  • The?significance level?must be set?before?the hypothesis test is carried out
  • The?significance level?will usually be 1%, 5% or 10%, however it may vary

What are one-tailed tests?

• A?one-tailed test?is used for testing:
  • Whether a distribution can be used to model the population
  • Whether the population parameter has?increased
  • Whether the population parameter has?decreased
• One-tailed tests?can be used with:
  • Chi-squared test for independence
  • Chi-squared goodness of fit test
  • Test for proportion of a binomial distribution
  • Test for population mean of a Poisson distribution
  • Test for population mean of a normal distribution
  • Test to compare population means of two distributions

What are two-tailed tests?

• A?two-tailed test?is used for testing:
  • Whether the population parameter has?changed
• Two-tailed tests?can be used with:
  • Test for population mean of a normal distribution
  • Test to compare population means of two distributions

How do I decide whether to reject or accept the null hypothesis?

• A sample of the population is taken and the?test statistic?is calculated?using the observations?from the sample
  • Your GDC can calculate the test statistic for you (if required)
• To decide whether or not to reject the null hypothesis you first need either the?p-value?or the?critical region
• The?p?- value?is the probability of a value being?at least as extreme?as the test statistic, assuming that the null hypothesis is true
  • Your GDC will give you the?p-value (if required)
  • If the?p-value is less than the significance level?then the?null hypothesis?would be?rejected
• The?critical region?is the range of values of the test statistic which will lead to the?null hypothesis?being?rejected
  • If the?test statistic?falls within the?critical region?thenthe?null hypothesis?would be?rejected
• The?critical value?is the boundary of the critical region
  • It is the least extreme value that would lead to the rejection of the null hypothesis
  • The?critical value?is determined by the?significance level

How should a conclusion be written for a hypothesis test?

• Your conclusion?must?be written in the?context?of the question
• Use the?wording in the question?to help you write your conclusion
  • If?rejecting the null?hypothesis your conclusion should state that there is?sufficient?evidence?to suggest the null hypothesis is unlikely true
  • If?accepting the null?hypothesis your conclusion should state that there is?not enough evidence?to suggest null hypothesis is unlikely true
• Your conclusion?must?not?be definitive
  • There is a chance that the test has led to an?incorrect conclusion
  • The outcome is?dependent on the sample
    • a?different sample?might lead to a?different outcome
• The conclusion of a?two-tailed test?can state if there is evidence of a change
  • You should not state whether this change is an increase or decrease
  • If you are testing the difference between the means of two populations then you can?only conclude that the means are not equal
    • You can not say which population mean is bigger
    • You’d need to use a?one-tailed?test for this