1-tailed test

The probability of Type I error is included in one tail of the sampling distribution. Generally used when the direction of the difference between two populations can be supported by theory or other knowledge gained prior to testing for statistical significance.

2-tailed test

The probability of Type I error is included in both tails of the sampling distribution (e.g., alpha .05 means .025 is in one tail and .025 is in the other tail). Generally used when the direction of the difference between two populations cannot by supported by theory or other knowledge gained prior to testing for statistical significance.

Alpha

The probability of a Type I error

Association

Changes in one variable are accompanied by changes in another variable.

Central Limit Theorem

As sample size increases, the distribution approximates a normal distribution and is usually close to normal at a sample size of 30.

Critical Value

The point on the x-axis of a sampling distribution that is equal to alpha. It is interpreted as standard error. As an example, a critical value of 1.96 is interpreted as 1.96 standard errors above the mean of the sampling distribution.

Dependent Variable

Measures the effect of the independent variable.

Descriptive Statistics

Statistics that classify and summarize numerical data.

Homoscedasticity

The variance of the Y scores in a correlation are uniform for the values of the X scores. In other words, the Y scores are equally spread above and below the regression line.

Independent Variable

Variables controlled by the researcher.

Inferential Statistics

Statistics that infer characteristics of a sample to that of the population.

Interval Data

Objects classified by type or characteristic, with logical order and equal differences between levels of data.

Kurtosis

The peakedness of a distribution. Leptokurtic is more peaked, Mesokurtic is a normal distribution, and Platykurtic is a flatter distribution.

Mean

The arithmetic average of the scores in a sample distribution.

Median

The point on a scale of measurement below which fifty percent of the scores fall.

Mode

The most frequently occurring score in a distribution.

Mu

The arithmetic average of the scores in a population.

Nominal

Objects classified by type or characteristic.

Normal Distribution

A frequency distribution of scores that is symmetric about the mean, median, and mode.

Ordinal Data

Objects classified by type or characteristic with some logical order.

Parameter

The measure of a population characteristic.

Population

Contains all members of a group.

P-value

The probability of a Type I error

Random Sampling

Each and every element in a population has an equal opportunity of being selected.

Ratio Data

Objects classified by type or characteristic, with logical order and equal differences between levels, and having a true zero starting point.

Reliability

The extent to which a measure obtains similar results over repeat trials.

Sample

A subset of a population.

Sample Distribution

A frequency distribution of sample data.

Sampling Distribution

A probability distribution representing an infinite number of sample distributions for a given sample size.

Skewness

Skewness provides an indication of the how asymmetric the distribution is for a given sample. When estimated using the third moment, a value of 0 indicates a normal asymmetric distribution.  A positive value indicates a positive skew (the right tail is longer than the left).  A negative value indicates a negative skew (the left tail is longer than the right).  Skewness values greater than 1 or less than -1 indicate a non-normal distribution.

Spurious Correlation

The strength and direction of an association between an independent and dependent variable depends on the value of a third variable.

Statistic

Measure of a sample characteristic.

Statistical Significance

Interpreted as the probability of a Type I error. Test statistics that meet or exceed a critical value are interpreted as evidence that the differences exhibited in the sample statistics are not due to random sampling error and therefore are evidence supporting the conclusion there is a real difference in the populations from which the sample data were obtained.

Type I Error

Rejecting a true null hypothesis. Commonly interpreted as the probability of being wrong when concluding there is statistical significance. Also referred to as Alpha, p-value, or significance.

Type II Error

Retaining a false null hypothesis.

Validity

The extent to which a measure accurately represents an abstract concept.

Variable

A characteristic that can have different values.