Survey

Survey

Transcript

Statistics Frequency and Distribution Distribution Functions 1. Normal Distribution 2. Uniform Distribution 3. Skewed Distribution Parametric statistics (continuous variables) assume normally distributed data Normal Distributions • Many natural populations are normal distributions – tree heights in a mature forest, weights of acorns from the same tree, etc. • Many non-normal distributions can be converted into normal distributions via either square root or logarithm transformations Normally Distributed Populations 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). Normal Distribution Booooo!!! Normal Distribution - Higher Variance Sampling from a normal distribution Repeated samples are normally distributed and centered around the parent population mean but have their own deviations based on the number and type of samples Central Limit Theorem states that the distribution of the means of a sufficiently large number of independent samples will be approximately normal, regardless of the underlying distribution. Uniform Distributions • Forestry example – ages of pole sized timber. CLT acting on a Uniform Distribution Skewed Distributions • Often observed in nature – i.e. tree ages • Inverse J shaped curve • Median is a better index of central tendency than the Mean Skewed Descriptive Values Sample Size affects estimates • Larger samples sizes cause sample parameters to more closely estimate the parameters of the underlying population • Standard error captures this effect – decreasing as sample size increases Sample Size revisited • Since t is very close to 2 for 95% confidence at infinite sample size we will use it. • E is the desired sampling error, we will use 10% Student t by confidence level