Topic 9 - Inferential Stats, the T-test and beyond

what are the 3 assumptions of z tests?

• normality (that the true population distribution is normal)

• independence (that observations in the data set are not correlated with each other)

• known standard deviation (that the true SD of the pop. is known to the researcher)

test statistic

assesses how consistent your sample data are with the null hypothesis in a hypothesis test

degrees of freedom

the number of independent values or pieces of information that can vary in a statistical calculation, crucial for estimating parameters and conducting hypothesis tests.

one-sample t-test

It compares the mean of a single sample with the known mean (target value or hypothetical value) of a population (from which this sample is drawn).

what situations are independent samples t-test (student test) designed for?

with 2 diff groups of participants - whether the 2 groups have the same population mean

what are the two forms of independent samples t-test?

Student’s

Welch’s

pooled estimate of the variance

used when you want to estimate the variance of several different populations that may have different means but are assumed to have the same variance.

• take a weighted average of the variance estimates

standard error of difference (SED)

measures the variability or uncertainty in the difference between two sample means, telling you how much that difference likely varies if you took new samples

it's calculated using the individual standard errors (or standard deviations and sample sizes) of the two groups

what are the assumptions of the student t-test?

• normality

• independence

• homogeneity of variance (homoscedasticity)

  • that the population SD is the same in both groups

paired samples t-test

compares the means of the same group at different time periods.

In other words, the t-test is conducted on dependent or related samples.

The paired samples t-test is also conducted when the samples are different but subjected to the same conditions.

within subject differences

variations in outcomes within the same person across different conditions or time points in a study

between subject variability

the natural differences (personality, genetics, experiences) among individuals in a study, causing their responses or measurements to vary even under the same conditions

one-sided tests

statistical hypothesis tests that check for an effect or difference in only one specific direction

rejection region

the set of test statistic values that are extreme enough to lead to rejecting the null hypothesis, defined by a chosen significance level (alpha) and the type of test (left, right, or two-tailed)

what is the most commonly used measure of effect size for a t-test?

Cohen’s d

what is ANOVA

analysis of variance

concerned with investigating differences in means

between group variation

measures how much the average values (means) of different data groups differ from each other and from the overall average

within group variation

measures how much individual data points within the same group differ from their group's average

what is the relationship between ANOVA and the student t-test

An ANOVA with two groups is identical to the Student t-test

both compare group means, but the t-test is for two groups, while ANOVA generalizes it to three or more groups

chi square test 𝜒2 - goodness-of-fit test

tests whether an observed frequency distribution of a nominal variable matches an expected frequency distribution.

a statistical method used to compare observed data to what was expected to determine if there is a significant difference or relationship between two categorical variables

what is categorical data analysis

the process of using statistical methods to examine, interpret, and find patterns in data that fall into distinct groups or categories, rather than numerical measurements

expected frequencies

the anticipated count of an event's occurrence over a set number of trials, calculated by multiplying the event's theoretical probability by the total number of trials

when is the chi square goodness of fit test used

when you have a table of observed frequencies of different categories, and the null hypothesis gives you a set of “known” probabilities to compare them to.

when is the chi square test of independence (or association) used?

when you have a contingency table (cross-tabulation) of two categorical variables. The null hypothesis is that there is no relationship or association between the variables.

what two assumptions do both versions of the Pearson test rely on?

that the expected frequencies are sufficiently large, and that the observations are independent

what are the two kinds of pearson’s tests?

correlation coefficient r

chi square

what are the 3 kinds of t-tests?

one sample t-test (compare one sample mean to specific value)

paired samples t-test (same participants, two times points/conditions)

independent samples t-test (diff groups, one measure each)

when do you use a one sample t-test

when comparing one sample mean to a specific value

when do you use a paired sample t-test

when you have the same participants tested at two time points/conditions (repeated measures)

when do you use an independent sample t-test

when testing two different groups with one measure each