Chi-Squared Tests and Mixed-Methods Research Flashcards

A set of practice flashcards covering categorical data analysis, Chi-squared statistical testing, and mixed methods research designs based on lecture notes.

Categorical Variable

A variable type that represents category membership (e.g., therapy vs. control) rather than a score on a numeric scale.

Chi-Squared Goodness of Fit Test

A one-sample test used for a single categorical variable to compare the proportions of observations observed across categories to the proportions expected under the null hypothesis.

Observed Frequencies ($O_i$)

The actual counts or frequency of observations recorded for each category in the collected data.

Expected Frequencies ($E_i$)

The counts expected in each category if the null hypothesis is true; for a goodness-of-fit test with an even distribution, calculated as $E_i = \frac{N}{k}$.

Chi-Squared ($\chi^2$) Statistic Formula

$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$.

Goodness of Fit Degrees of Freedom (DF)

Calculated as $k - 1$, where $k$ is the total number of groups or categories.

Cohen’s W

A standardized effect size for goodness-of-fit tests, calculated as $W = \sqrt{\frac{\chi^{2}}{N}}$, where values of 0.1, 0.3, and 0.5 represent small, medium, and large effects respectively.

Contingency Table

Also known as a cross-tabulation or crosstabs, this table is used to show the association between two or more categorical variables by displaying frequencies and proportions within intersecting categories.

Chi-Squared Test of Independence

A statistical test used to determine if there is a significant association between two categorical variables by testing if the row and column variables are independent.

Test of Independence Degrees of Freedom (DF)

Calculated as $(\text{number of rows} - 1) \times (\text{number of columns} - 1)$.

Test of Independence Expected Frequency Formula

$E_{i} = \frac{RT_i \times CT_i}{N}$, where $RT$ is the row total and $CT$ is the column total for that specific cell.

Assumptions of Chi-Squared Tests

1. Variables are categorical; 2. Categories are mutually exclusive; 3. Observations are independent; 4. Expected frequencies are at least 5 in each cell.

Cramér’s V

An effect size measure used for tests of independence involving tables larger than $2 \times 2$, calculated as $V = \sqrt{\frac{\chi^{2}}{N(\min(r - 1, c - 1))}}$.

Mixed Methods Research

The practice of combining quantitative and qualitative research methods within a single study or program of research to benefit from both depth and precision.

Triangulation

A reason for mixed methods research aimed at converging or corroborating findings across different methods to achieve greater validity.

Convergent Parallel Design

A mixed methods design involving concurrent data collection and separate analysis of qualitative and quantitative data, which are then compared or related during interpretation.

Explanatory Sequential Design

A mixed methods design where quantitative data is collected and analyzed first, followed by qualitative data to help explain the quantitative results.

Exploratory Sequential Design

A mixed methods design where qualitative data collection and analysis occurs first to build a theory or scale, followed by quantitative data collection to test or measure the findings.

Embedded Design

A mixed methods design where one type of data (e.g., qualitative) is embedded within a primary design of the other type (e.g., quantitative) before, during, or after the main study.

Big Q vs. small q

'Big Q' refers to artfully interpretive, non-positivist, and reflexive qualitative research, while 'small q' refers to scientifically descriptive, positivist qualitative research.