W1 L1 Inferential stats

Population

Large group of observations about which the researcher wants to draw conclusions

Sample

A subset of the poplation

Random sampling

Selection of one observation from the population is independent of the selection of any other observation -- equal chance of being selected

Types of biased sampling

1. Convenience sampling

2. Snowball recruitment

How do we describe data from sample and population

- Sample statistics (roman numerals)

- Population parameter (greek letters)

Estimation

Estimation of a population parameter through construction of a confidence interval

Hypothesis testing

Deciding whether to accept or reject a statement about a population parameter

Sampling variability

The value of a statistic will vary from sample to sample due to chance

Sampling distribution

A hypothetical distribution of values of a particular sample statistic formed by repeatedly drawing samples of n observations from a population + calculating the statistical value of each sample

What do we do because we can't keep generating samples due to it being expensive and time consuming?

Thought experiments -- i.e. sampling distribution

Properties of a sampling distribution

1. Normal distribution

2. Mean is µ (M is an unbiased estimator of µ)

3. Variance is σM^2

4. SD is σM -- standard error of the mean

What is the effect of n on σM

Larger n -> smaller σM -> sample means are getting closer to µ

What is the effect of σ on σM

Larger σ -> larger σM

What happens to the shape of the sampling distribution if the population is not normal?

Central Limit Theorem - sampling distribution of mean tends towards a normal distribution as n increases, regardless of the shape of the population distribution

What does the standard error estimate measure (independent samples)?

- Standard deviation of the sampling distribution for M1-M2

- Measures the degree to which M1-M2 will vary around the true value of µ1-µ2 (sampling variability)