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Statistics

Statistics. IMD09120: Collaborative Media Brian Davison 2010/11. Contents. Why we need statistics Distributions Normal distribution Standard deviation Sampling error Standard normal distribution. Why we need statistics. Typical research questions: Which option is better?

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Statistics

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  1. Statistics IMD09120: Collaborative Media Brian Davison 2010/11

  2. Contents • Why we need statistics • Distributions • Normal distribution • Standard deviation • Sampling error • Standard normal distribution

  3. Why we need statistics • Typical research questions: • Which option is better? • Does this action have a real effect? • What is the cause of this observation? • Typical answers rely on pooled data with a high degree of variation • Statistics allows us to cut through the variation in an objective way

  4. Distributions • How much do you like red wine? • How much do you like Marmite?

  5. Normal distribution Symmetrical Tails meet x-axis at infinity Bell-shaped Mean, mode and median are all equal Frequency Tail Tail Score

  6. How much variation? Average deviation However, half will be negative Therefore, square first (variance) However, units are wrong Therefore, square root the result  Standard Deviation (SD) 4.25 5.45 Deviation from the mean is 1.2 Score

  7. Sampling error Population: 52 Mean: 7 • Sample size: • 50 • 40 • 10 • 5 • 2 • See Sampling demo.xlsx

  8. Standardisation • The distribution of sample means is always normal • However, normal curves come in different sizes:

  9. The standard normal distribution Mean = 0 SD = 1 Convert a score from any normal distribution to the standard by subtracting the mean and dividing by SD. This is a z-score Once in standard form, the area under the curve = 1 Can therefore be used to represent probability

  10. Testing significance For 95% confidence, α = 0.05

  11. Coming up • Formulating a hypothesis • Types of statistical test • Correlation • Independent T-test • Paired T-test • ANOVA • Chi-square • Research designs

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