*Study Guide: *Hypothesis testing

Produced by Graham Currell, University of the West of England, Bristol and:, and

● Royal Society of Chemistry, 'Discover Maths for Chemists' website

*●*

**Essential Mathematics and Statistics for Science**, 2nd Edition**Graham Currell and Antony Dowman, Wiley-Blackwell, 2009**

This study unit aims to develop the skills for peforming hypothesis testing of experimental data. This is achieved by references given to sections and pages in the study text, **Essential Mathematics and Statistics for Science**, associated **QVA tutorials (questions **with **video worked answers), **and** tutorials for the use of MS excel**.

**NB: **The video tips and QVAs appear in 'pop-up' windows. **If your browser blocks 'pop-ups'**, you can use CTRL+Enter or Right click with the mouse.

Performing a Hypothesis Test. Study Text: Chapter 9 (p243ff)

Hypotheses, *p*-values & significance level: QVA tutorial

A hypothesis test assesses the probability that a relationship that you observe in your experiment is a true description of the real world, and not just a statistical variation in your experiment.

You will need to state your **hypotheses**:

• Null Hypothesis, H_{O}, which is usually a statement that there is NO effect or relationship, and, at least one

• Alternative (or Proposed) Hypothesis, H_{1}, that an effect or relationship DOES exist.

The calculated** p-value** gives the probability that you would be wrong if you decide that H1 is correct.

The term

**‘significance’**gives a probability limit, chosen by you, for deciding the observed effect is actually a true effect.

**Testing with: **(link to Statistical tables for critical values)

** t-tests **for differences in

**mean values**. Study Text: Sections 10.1,2,3 (p262)

- using the

*t*-statistic: QVA tutorial

- using

*p*-values (Excel and Minitab): QVA tutorial

** F-tests** for differences in

**variances**. Study Text: Sections 10.4 (p274)

- using the

*F*-statistic,

*p*-values (Excel and Minitab): QVA tutorial

**Chi-squared, X^{2}-tests** for differences in

**frequency tables**. Study Text: Sections 14.1,2 (p331)

- using the

*X*

^{2}statistic,

*p*-values (Excel and Minitab): QVA tutorial

**Tests** for differences in **proportion**. Study Text: Sections 14.3 (p343)

- using Minitab for testing one and two proportions

- using *p*-values and confidence intervals (Minitab): QVA tutorial

Tests for **normality in data distributions**. Study Text: Section 9.5.2 (p256)

QVA tutorial - video feedback in preparation

**Excel tutorial files for download:** (video commentaries in preparation)

t-tests, F-tests & correlation: Parametric Tests (Excel 2007)

Chi-squared tests: Chi-Squared (Excel 2007)

ANOVAs: ANOVAs (Excel 2007)

**This new Study Guide is in the process of development - any comments, corrections or suggestions welcome: **graham.currell@uwe.ac.uk