Goss-Sampson (2020), Statistical Analysis in JASP Chapter 7

Question 1

Population Parameters

Answer 1

Characteristics of the entire population, such as the population mean
(μ) or variance (σ2).
* These are fixed but usually unknown values.

Question 2

Sample Statistics

Answer 2

Calculated values from the sample data, such as the sample mean (xˉ) or
variance (s2).
* Used to estimate population parameters.

Question 3

Replication

Answer 3

The process of repeating a study or experiment to validate results and ensure
reliability.

Question 4

Sampling Distributions:

Answer 4

Definition:
* The distribution of a statistic (e.g., sample mean) calculated from repeated samples of the
same size (N)
* Provides insights into the variability of the statistic across different samples.

Question 5

• Sampling Distribution of the Maximum:

Answer 5

• Tracks the largest value observed in repeated samples.
• Useful in specific contexts, like quality control or extreme value theory.

Question 6

Standard Error (SE):

Answer 6

The standard deviation of the sampling distribution:
* Key Insight: SE decreases as sample size (N) increases, leading to
more precise estimates.

Question 7

Unbiased Estimator

Answer 7

A statistic is unbiased if its expected value equals the true population
parameter.
* Example: The sample mean (xˉ) is an unbiased estimator of the population mean (μ).

Question 8

Biased Estimator:

Answer 8

A statistic is biased if it systematically over- or underestimates the
population parameter
* Example: The sample variance (s2) is a biased estimator of the population variance (σ2)
because it underestimates variability.

Question 9

Adjusting for Bias in Variance:

Answer 9

• To correct for bias, divide by N−1 instead of N when calculating variance
• This adjustment ensures the estimate is slightly larger than the sample
  variance, making it unbiased.

Question 10

• Sample Statistic vs. Estimate:

Answer 10

• A sample statistic describes the data (e.g., sample mean).
• An estimate is a guess about the population parameter based on the sample statistic.