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Statistics

Statistics. Frequency and Distribution. Calculating Probabilities. Probability. Coin Toss Example. A balanced coin flipped in an unbiased way results in heads or tails (each with an equal 50% chance) Chance of heads = one/two possible outcomes

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Statistics

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  1. Statistics Frequency and Distribution

  2. Calculating Probabilities

  3. Probability

  4. Coin Toss Example • A balanced coin flipped in an unbiased way results in heads or tails (each with an equal 50% chance) • Chance of heads = one/two possible outcomes • What if the last 4 coin flips were heads, what is the chance of the next flip resulting in tails?

  5. Probability of Failure • Know the odds! • Example when rolling a die, the chance of your number coming up equals 1/6 (or 16.6%) • More importantly the chance of numbers that you didn’t pick to show up is 1 – 1/6 (or 83.3%)

  6. Normal Distributions • can be mathematically described with two parameters: a measure of central tendency, or mu (the mean symbolized as µ), and a measure of dispersion, or sigma (the standard deviation symbolized as σ).

  7. Normal Distribution

  8. Normal Distribution

  9. Normal Distribution - Higher Variance

  10. Student t 95%

  11. Distribution of Sample Means

  12. Uniform Distributions

  13. Distribution of Sample Means

  14. Skewed Distributions • Often observed in nature – i.e. tree ages • Inverse J shaped curve

  15. Skewed Descriptive Values

  16. Linear Regression

  17. Parts of the regression equation • Y = slope times X + intercept

  18. Measure 2 variables, plot results • Data for Scots Pine • Force b to equal 0?

  19. Find out if relationship existsand how good the fit is • y = mx + b • In Excel…

  20. Problems with linear regression

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