Comprehensive Study Notes on Statistical Methods and Analysis

Skewness

A measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

Kurtosis

A statistical measure that describes the degree to which scores cluster in the tails or the peak of a frequency distribution.

Normal Curve

A bell-shaped, symmetric frequency distribution where the mean, median, and mode are all equal and located at the center.

Inferential Statistics

Techniques that allow us to make generalizations about a population from a study sample.

Descriptive Statistics

Brief descriptive coefficients that summarize a given data set.

Chance

The possibility of a particular outcome occurring due to random variation.

Statistic

A characteristic or measure obtained using data from a sample.

Parameter

A characteristic or measure that describes an entire population.

Standard Error

An estimate of the standard deviation of a sampling distribution.

p-value

The probability that the observed results occurred by chance, assuming the null hypothesis is true.

Sample

A subset of individuals or data points selected from a larger population.

Population

The entire set of individuals or objects of interest in a study.

Sampling Error

The difference between a sample statistic and the actual population parameter it estimates.

Hypothesis

A specific, testable prediction about the relationship between two or more variables.

Null Hypothesis (H₀)

A statement that there is no relationship or difference between variables.

Research Hypothesis (H₁ or Hₐ)

The statement that a relationship or difference exists between variables.

Statistical Significance

A determination that a relationship or difference is unlikely to be due to chance.

Confidence Level

The percentage of times that the confidence interval will include the true population parameter.

Confidence Interval

A range of values likely to contain an unknown population parameter.

Significance Level (Alpha, α)

The threshold for determining whether a result is statistically significant.

Type I Error

Rejecting a true null hypothesis, indicating a false positive.

Type II Error

Failing to reject a false null hypothesis, indicating a false negative.

One-tailed Test

A directional hypothesis test predicting the specific direction of an effect.

Two-tailed Test

A non-directional hypothesis test predicting a difference exists but not its direction.

Statistical Conclusion Validity

The degree to which conclusions about the relationship among variables based on the data are correct.

Correlation

A statistical measure that describes the size and direction of a relationship between two variables.

Independent Samples

Data collected from two or more groups that are unrelated to each other.

Paired Samples

Data collected from the same subjects at different times or closely matched pairs.

Theoretical Sampling Distribution

A distribution of all possible values of a statistic occurring from an infinite number of samples.

Central Limit Theorem

As sample size increases, the sampling distribution of the mean approaches a normal distribution.