Confidence Intervals, Correlation, Regression & Normal Distribution

Vocabulary-style flashcards covering statistics concepts including confidence intervals, correlation, regression, normal distributions, sampling methods, and statistical tests.

Confidence Intervals

The radius/spread of data demonstrates the confidence that the true value of the population should sit within that range.

Margin of Error (MOR)

The amount the data could be off by.

The 95% Rule

A standard in data collection where you want to be 95% certain about the data; if data is more than 5% off, then you are not 95% confident.

Correlation

A description of how two things are related, determining if the relationship is positive or negative and strong or weak.

Regression

The process of using one set of data to predict another set of data, allowing for the investigation of causality.

Cause & Effect (Causation)

The principle that one thing is driving another, which is not proven by correlation alone.

Normal Distribution

A symmetrical, bell-shaped distribution in which most values cluster around the mean and frequency falls away steadily moving further from it in either direction.

Mean ($\mu$)

In a normal distribution, this value represents where the peak of the curve sits.

Standard Deviation ($\sigma$)

In a normal distribution, this value describes how wide or narrow the curve is.

Empirical Rule

A rule stating that in a normal distribution, 68% of values lie within $\pm 1\sigma$, 95% lie within $\pm 2\sigma$, and 99.7% lie within $\pm 3\sigma$ of the mean.

NORM.DIST(x, mean, standard_dec, cumulative)

An Excel formula that returns the probability that a normally distributed value falls at or below $x$ when cumulative is set to TRUE.

Population

The entire group of interest in a study, such as all students at a university.

Sample

The smaller group selected from a population that is actually studied.

Sampling

The process of picking a smaller group from a larger population to study and draw conclusions about the whole population.

Simple Random Sampling

A sampling method where every member of the population has an equal chance of being picked.

Systematic Sampling

A sampling method where every k-th person is picked after a random starting point.

Stratified Sampling

A sampling method where the population is divided into meaningful subgroups (strata) and then randomly sampled from each group.

Cluster Sampling

A sampling method where the population is divided into naturally occurring groups, several clusters are randomly chosen, and everyone within those clusters is surveyed.

Convenience Sampling

A sampling method where participants are selected based on who is easiest to reach; it is the fastest but most biased method.

Snowball Sampling

A sampling method where one participant refers another participant to grow the study group.

Judgmental (Purposive) Sampling

A sampling method where the researcher hand-picks participants believed to provide the most useful information.

Quota Sampling

A non-random sampling method where the researcher sets targets for certain characteristics and fills them using any convenient method.

Parametric Tests

Statistical tests that require numerical data and a normal distribution, such as t-tests or z-tests.

Independent t-test

A parametric test used to compare two independent means.

Pearson's r

A parametric test used for numerical linear correlation to determine the strength and direction of the relationship between two numerical variables.

Non-Parametric Tests

Statistical tests used when data is not normally distributed, such as the Sign test or Mann-Whitney.

Sign test

A non-parametric test for one median used when data is ordinal or numerical but not normally distributed.

Mann-Whitney

A non-parametric alternative to the independent t-test used to compare two independent groups when data is not normally distributed.

Chi-squared

A non-parametric test used to determine if there is an association between two categorical variables.

Spearman's r

A non-parametric correlation measure used for ordinal or skewed data to determine the strength and direction of the relationship between two variables.