Null Hypothesis Statistical Testing (NHST) and T-Tests

These flashcards cover the key terms and concepts related to Null Hypothesis Statistical Testing, t-tests, interpretations, and statistical principles important for understanding inferential statistics.

Null Hypothesis (H0)

States that there is no change, difference, or relationship in the general population.

Alternative Hypothesis (H1)

States that there is a change, difference, or relationship in the general population.

Directional Hypothesis

Specifies the direction of the expected outcome (positive, negative, increase, decrease).

Non-Directional Hypothesis

Does not specify a direction of the expected outcome.

Type I Error (Alpha Error)

A false positive; when the null hypothesis is rejected when it should be retained.

Type II Error (Beta Error)

A false negative; when the null hypothesis is retained when it should be rejected.

Alpha Level (Level of Significance)

A probability threshold used to determine the likelihood that an outcome is due to chance.

Critical Value

The value that a test statistic must exceed to reject the null hypothesis.

Statistical Hypotheses

Research hypotheses stated in mathematical form using statistical notation.

t-test

A statistical test used to determine if there is a significant difference between the means of two groups.

One-Sample t-Test

Used to compare the sample mean to a known population mean.

Independent Samples t-Test

Used to compare the means of two independent groups.

Dependent Samples t-Test

Used to compare means from the same group at different times.

Research Conclusion

Determination of whether or not sufficient evidence exists to reject the null hypothesis based on data collected.

Statistical Conclusion

A summary statement about the final decision regarding the null hypothesis.

Degrees of Freedom (df)

The number of independent values or quantities which can be assigned to a statistical distribution.

Critical Region

The area of a statistical distribution that corresponds to likely outcomes for the null hypothesis.

One-tailed Test

A test that determines if there is a significant effect in one specific direction.

Two-tailed Test

A test that determines if there is a significant effect in either direction.

P-value

The probability of getting a result as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true.

Fisher's Exact Test

A statistical significance test used to determine if there are nonrandom associations between two categorical variables.

Levene's Test

A statistical test used to assess the equality of variances for a variable calculated for two or more groups.

Normality Test

A test used to determine if a set of data is well-modeled by a normal distribution.

Effect Size

A quantitative measure of the magnitude of a phenomenon.

Cohen's d

A measure of effect size that indicates the standard difference between two means.

Omnibus F-Test

Used in ANOVA to determine if there are any statistically significant differences between the means of three or more independent groups.

Homoscedasticity

The assumption that the variance within each of the groups being compared is the same.

Random Sampling

The process of selecting a subset of individuals from a statistical population where each individual has an equal chance of being selected.

Sample Size (N)

The number of observations or replicates included in a statistical sample.

Statistical Power

The probability that a test will correctly reject a false null hypothesis (i.e., yield no Type II error).

Confidence Interval

A range of values, derived from a data set, that is likely to contain the value of an unknown population parameter.

Post Hoc Tests

Follow-up tests conducted after an ANOVA to determine which means are significantly different.

Tukey's HSD

A post hoc test that compares all possible pairs of means to find significant differences.

Scheffe's Test

A post hoc test that is used to compare all pairwise combinations of means.

Variance Analysis

A collection of statistical methods used to analyze the differences among group means.

Interaction Effect

Occurs when the effect of one independent variable on a dependent variable differs depending on the level of another independent variable.

Within-Group Variability

The variability of responses within a single group.

Between-Group Variability

The variability of responses between different groups.

Statistical Notation

A system of symbols used to represent numbers, sets, functions, etc., in a concise way.

Sample Mean (𝑥̄)

The average of all values in a sample.

Population Mean (μ)

The average of all values in a population.

Standard Deviation (SD)

A measure of the amount of variation or dispersion in a set of values.

Standard Error

An estimate of the standard deviation of the sampling distribution of a statistic.

Mean Difference

The difference between the means of two groups.

Significance Level (α)

The threshold at which a result is considered statistically significant.

Z-Score

The number of standard deviations a data point is from the mean.

Sample Variance

The variance of a sample calculated from its data points.

Population Variance (σ²)

The variance of a population based on all its data points.

Data Distribution

The way in which data values are spread or arranged.

Histogram

A graphical representation of the distribution of numerical data.

Frequency Distribution

A summary of how often different values occur within a dataset.

Parametric Tests

Statistical tests that assume a specific distribution for the data.

Non-Parametric Tests

Statistical tests that do not assume a specific distribution for the data.

Power Analysis

A method for determining the sample size required for a study to detect an effect of a given size with a given level of confidence.

Data Normalization

The process of adjusting values in the dataset to a common scale.

T-Distribution

A probability distribution used in inferential statistics that is symmetric and bell-shaped, like the normal distribution but has heavier tails.

ANOVA

A statistical method used to test differences between two or more means.

Factorial Design

Experimental designs that involve two or more factors being tested simultaneously.

Within-Subjects Design

An experimental design where the same subjects are used in all conditions.

Between-Subjects Design

An experimental design where different subjects are used in each condition.

Random Assignment

The practice of assigning participants to different groups in a way that each participant has an equal chance of being chosen.

Confidence Level

The percentage of times that an estimated interval includes the parameter of interest.

Sampling Distribution

The probability distribution of a given statistic based on a random sample.

Experimental Error

The variability in results that are due to factors other than the independent variable being tested.

Factorial ANOVA

An ANOVA that includes two or more factors.

Reliability in Research

The consistency of a research study or measuring test.

Validity in Research

The extent to which a test measures what it claims to measure.

Statistical Significance

A determination that the relationship measured in a study is unlikely to have occurred due to chance.

Mean Square Error (MSE)

An estimate of the variance of a random variable.

F-Ratio

In ANOVA, it is the ratio of systematic variance to unsystematic variance.

Mean Sum of Squares

The average of squares of the deviations of a set of values about their mean.