Lecture 2: Samples and Populations

Flashcards on Samples & Populations, covering definitions and concepts related to sampling methods, data distributions, and statistical measures.

Dataset

A single sample of a broader population; we can rarely sample the whole population, leading to uncertainty in estimated parameters. Data samples can be systematically biased due to participant recruitment and data collection methods.

Normal Distribution

Simplifies many calculations in statistics, although not all data is normally distributed.

Standard Error of the Mean

Resampling to estimate variability; determines how precisely the population mean has been estimated from the sample.

Histogram

The sample distribution of our value of interest.

Population

The total set of everyone within a group that we want to test.

Sample

A selection from the population that we can test.

Random Sampling

Recruitment done completely by chance, participants selected at random from a list.

Systematic Sampling

Structured approach to selecting participants, such as every 5th participant from a list.

Opportunity/Convenience Sampling

Recruitment from people closest and/or most accessible to the experimenter.

Stratified Sampling

Recruitment aims to match key characteristics of the target population.

Cluster Sampling

Whole groups are recruited at once, can be combined with other methods.

Ecological Validity

Do the variables and conclusions of a study sufficiently reflect the real-world context of its population?

Normal Distribution

A distribution with convenient properties, summarized by the mean and standard deviation.

Standard Normal Distribution

A special case of the normal distribution in which the mean is zero and the standard deviation is one.

Shapiro-Wilk Test

An objective statistical test to check if data is normally distributed.

Interval Data

Data where the critical factor is whether the data has a meaningful mean and standard deviation.

Sample Mean

The sum of all the individual data points divided by the total number of data points.

Sample Standard Deviation

The square root of the sum of the squared difference between the sample mean and each individual data point divided by the total number of data points minus one.

Bessel’s Correction

Making the estimated standard deviation a bit bigger to account for bias.

Standard Error of the Mean (SEM)

The likely variability in our estimate of the population mean from a given data sample; the standard deviation of the sample divided by the square root of the total number of data points.

Confidence Intervals

Two values that define a range that has a 95% chance of containing the true mean.

Interquartile Range (IQR)

A measure of spread for distributions that are not normally distributed.

IQR Formula

IQR = Q3 - Q1, where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile).

Population Standard Deviation Formula

\sigma = \sqrt{\frac{\sum{i=1}^{N}(xi - \mu)^2}{N}}, measures the amount of variation or dispersion of a set of data values.

Sample Standard Deviation Formula

s = \sqrt{\frac{\sum{i=1}^{n}(xi - \bar{x})^2}{n-1}}, estimates the variability within a sample.

Z-Score

The number of standard deviations from the mean a data point is. It standardizes the values so you can compare across different normal distributions.

Z-Score Formula

Z = \frac{X - \mu}{\sigma}, where X is the data point, \mu is the population mean, and \sigma is the population standard deviation

T-Test

Used to determine if there is a statistically significant difference between the means of two independent groups.

T-Test

A statistical test that compares the means of two groups to assess if their differences are significant, typically under the assumption of normality.