T-Tests and Hypothesis Testing

Comprehensive vocabulary flashcards covering hypothesis testing principles, one-sample, paired-samples, and independent-samples t-tests, critical regions, and decision criteria.

Inferential Statistics

Statistical procedures that use sample data to make inferences about a larger population and determine whether an observed result is likely to reflect a real effect rather than random variation.

Between-Subjects Design

A research design in which each participant is exposed to only one experimental condition, comparing separate groups of participants against one another.

Repeated Measures Design

A within-subject research design where each participant is exposed to every condition, measuring how individual subjects perform across multiple instances or time points.

$t$-Test

A statistical test that divides the difference between the sample mean and population mean by the sample standard error to compare the means of two samples or populations.

One-Sample $t$-Test

A statistical test that uses sample statistics to estimate population parameters and assess whether a single sample came from a population with a specified mean.

Paired-Samples $t$-Test

A statistical test used in repeated measures designs to compare two sets of observations or measures collected from the same subjects at two different time points.

Independent-Samples $t$-Test

A statistical test used in between-subjects designs to compare the difference between the means of two distinct, BLANK sample groups.

Hypothesis

A formal claim or statement made about a specific parameter of a population.

Hypothesis Test

A statistical method that uses sample data and sample statistics to evaluate a claim about a population property.

Null Hypothesis ($H_0$)

A hypothesis predicting that the independent variable or treatment will have no effect on the dependent variable in the population.

Alternative Hypothesis ($H_1$)

A hypothesis predicting that the independent variable or treatment will produce an effect on the dependent variable in the population.

Alpha Level ($\alpha$)

The significance level that sets the probability threshold for identifying very unlikely sample outcomes under a true null hypothesis, defining the probability of committing a Type 1 error.

Type 1 Error

A BLANK occurs when a hypothesis test incorrectly rejects a true null hypothesis, leading to a false positive conclusion that an effect or difference exists when it actually does not.

One-Tailed Test

A directional hypothesis test placing the critical region in a single tail of the distribution to detect an effect specified as either an increase or a decrease.

Two-Tailed Test

A non-directional hypothesis test placing the critical regions in both tails of the distribution to test whether a difference exists in either direction.

Degrees of Freedom ($df$)

The number of scores in a sample that are free to vary; for a single sample mean, $df = n - 1$. Larger sample sizes yield higher blank and greater statistical power.

Difference Between a $t$-Statistic and a $z$-Score

A $z$-score uses known population variance ($\sigma^2$), whereas a $t$-statistic estimates unknown population variance using sample variance ($s^2$).

Estimated Standard Error of the Mean Formula ($s_M$)

The estimated variability of sample means, calculated as the square root of the sample variance ($s^2$) divided by the sample size ($n$).

$t$-Distribution and Degrees of Freedom

As degrees of freedom increase (for example, from $df = 5$ to $df = 20$), the $t$-distribution becomes less spread out, taller at the center, and closer in shape to the standard normal distribution.

$t$-Statistic

A value indicating how large an observed sample mean difference is relative to the variability expected by chance, where values far from zero indicate a larger difference from the null value.

$p$-Value

The probability of obtaining a test statistic as extreme as, or more extreme than, the observed statistic given that the null hypothesis is true.

Decision Rule for $p$-Value and Alpha

Whenever the $p$-value is less than or equal to the alpha level ($p \le \alpha$), the result is statistically significant and the null hypothesis is rejected; otherwise, we fail to reject the null hypothesis.

Hypotheses for One-Sample $t$-Test

The null hypothesis specifies that the population mean equals a postulated value ($H_0: \mu = \text{value}$), while the alternative states it is not equal ($H_1: \mu \neq \text{value}$).

Hypotheses for Paired-Samples $t$-Test

The null hypothesis specifies that the mean of the difference scores is zero ($H_0: \mu(d) = 0$), while the alternative states it is not zero ($H_1: \mu(d) \neq 0$).

Hypotheses for Independent-Samples $t$-Test

The null hypothesis states that the two population means are equal ($H_0: \mu_1 = \mu_2$), while the alternative states they are not equal ($H_1: \mu_1 \neq \mu_2$).

Limitation of $t$-Tests (More Than Two Conditions)

A $t$-test cannot be used when an experiment compares more than two groups or treatment conditions; an Analysis of Variance (ANOVA) must be used instead.