# Hypotheses overview

### Hypothesis

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
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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.
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Comparing more than two samples:

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

### Triangulation

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