Hypotheses overview


A prediction or statement about a characteristic of a variable, which can be tested to provide evidence for or against.



Null hypothesis

The null hypothesis assumes randomness and is directly tested during a significance test. As the null hypothesis indicates no significance, you are usually trying to disprove the null hypothesis in your statistical tests.



Alternative hypothesis

Contradicts against the null hypothesis, the alternative hypothesis is supported if the significance test indicates the null hypothesis to be incorrect.



Choosing the correct hypothesis test

Firstly, you should define the objective of your hypothesis test and then consider the most valid type of hypothesis test. Much of the decision-making process is determined by the number of populations you have to analyse and whether or not the variances are known:


Comparing a sample against a target:

  • One-sample z-test – Probably the most basic hypothesis test, used with sample sizes greater than 30 to compare a sample mean with the mean of a population.
  • One-sample t-test
  • One-sample standard deviation
  • One-sample % defective
  • Chi-Square goodness-of-fit

    Comparing two samples against each other:

  • Two-sample z-test
  • Two-sample t-test assuming equal variances – Used to compare population means, generally where at least one of the sample sizes is below 30, variances are unknown but assumed to be equal.
  • Two-sample t-test assuming unequal variances – Compares population means where at least one of the sample sizes is below 30, variances are unknown but assumed unequal (perhaps because the two sample sizes differ greatly).
  • Paired t-test – Used where to compare means of two samples which are normally distributed and the observations can be paired naturally e.g. comparing results before and after training.
  • Two-sample standard deviation
  • Two-sample % defective
  • Chi-Square test for association
  • Sign tests – Tests a median of a distribution, can either compare a sample against a target or against another sample.

    Comparing more than two samples:

  • One-way ANOVA
  • Standard deviations test
  • Chi-Square % defective
  • Chi-Square test for association

    Sometimes you will not be testing whether a hypothesis is true or false but estimating how big the effect is, in these examples measuring a confidence interval may be more appropriate.




    Combining information from multiple sources to help arrive at the most accurate conclusion possible, often by testing the same hypothesis using numerous different methods.