Hypothesis testing - Standard error of the means

"If you criticize something, you are obligated to know it better than those that espouse it."

Raw data -> Summarized, Organized, Simplified (Descriptive statistics: s, x-bar, s-squared) -> Sample to population inferences (Inferential statistics: p, z, t, F, q)

Hypothesis testing

1. Simple random sampling: used for statistical inference, where populations are inaccessible, and are often more accurate. All units in the population have an equal chance of being selected.

2. Proportional Stratified Random Sample: sample maps exactly onto the population in terms of proportions of sub-groups (e.g. population has 10% seniors and sample has 10% seniors)

3. "Errors" in sampling (sampling error and non-sampling error) must be dealt with. Samples and population don't match-up. Non-sampling errors include question text and framing that creates confusion. Other things like cultural issues can cause non-sampling error.

Sampling Distributions

How do you detect how much error (sampling error) is in the sample? Use a standard-deviation-like calculation (spread of scores with respect to the mean).

By selecting multiple samples and calculating the means of those samples, then using the means in the place of raw scores and calculate the standard deviation of the means-like statsitic called the standard error of the means (s-sub-x-bar).

Standard error of the means = sample standard deviation divided by the square root of the number of observations in the sample. (s / sqrt n)

or theoretical (sigma-sub-x-bar = sigma / sqrt N)

A sampling (sample of means) distribution is normally distributed when it is drawn from a normally distributed population or the size of the samples is reasonably large (at least 30).