Analysis of Experimental Data and Categorical Regression

Practice flashcards covering data measurement scales, parametric and nonparametric hypothesis testing, and categorical regression models including Logit, Probit, and Tobit analysis.

Nominal scale

A measurement scale where categories, such as gender or marital status, have no natural ordering and the differences or ratios between values have no meaning.

Ordinal scale

A scale that provides a natural ordering of values, such as grades ($A, B, C$) or income groups, but where the difference and ratio between categories have no meaning.

Interval scale

A scale with natural ordering and meaningful differences between values, such as temperature in Celsius or IQ scores, but lacking a natural zero and meaningful ratios.

Ratio scale

A measurement scale where natural ordering, differences, and ratios are all meaningful because a natural zero exists; examples include GDP, income, weight, and height.

Nonparametric tests

Also known as distribution-free methods, these are used when distribution functions are unspecified and are applicable to nominal, ordinal, interval, or ratio data.

Wilcoxon signed-rank test

A one-sample nonparametric test that ranks data by absolute value and compares the sum of negative ranks ($T_{-}$) and positive ranks ($T_{+}$) to test if data mean is zero.

Wilcoxon-Mann-Whitney rank sum test

A nonparametric test used to compare two independent samples, such as an experimental group and a control group, when differences cannot be taken.

Kruskal-Wallis test

A nonparametric test used for hypothesis testing when comparing more than two independent samples.

Friedman test

A nonparametric test for $k$ variables and $b$ blocks used with related samples, similar to the Quade test but ignoring differences between blocks.

Poisson distribution

A distribution assumed in regression when the dependent variable is a count of events, such as the number of customers in a five-minute period.

Logit model

A regression model used for multicategory responses, distinguishing between nominal responses (no natural ordering) and ordinal responses (natural ordering).

Tobit analysis

A regression model used when the dependent variable is subject to a lower or upper limit, such as working hours which cannot be negative.

Censored data bias

The phenomenon where OLS estimates of the slope coefficient are biased downwards when constrained or bounded observations are present in the sample.

Probit model

A model for binary dependent variables based on the Cumulative Distribution Function ($\text{CDF}$) which can be more difficult to interpret than logit models.

t-test formula

The parametric test statistic defined as t = \frac{\bar{x} - \text{\nu}}{\text{\nu} / \text{\nu}} where $\bar{x}$ is the sample mean and $n$ is the sample size.

Binary logic model

A statistical model used for binary dependent variables where outcomes are categorized into two distinct groups (e.g., yes/no, success/failure).

Baseline logic model

A statistical approach in which a baseline group is compared to treatment groups to measure effect; often used in experimental designs.

Cumulative model

A model used for ordered categorical responses, allowing for the estimation of probabilities of being in a particular category or below (e.g., cumulative logit model).

When to use Tobit analysis?

Use Tobit analysis when the dependent variable is censored, meaning it has a limit at one or both ends of its scale, such as survey responses that are capped.

Choosing the right model

Consider the nature of your dependent variable: use binary logic for two categories, Tobit for censored data, and cumulative models for ordered categorical responses.

Interpretation of model results

Understand that results can be complex; while binary models produce probabilities, Tobit models need careful interpretation due to their handling of limits.

Minimal interpretation

Indicates that results are straightforward and do not require elaborate analysis; often applies to simpler models like binary logic.

True/False: A cumulative model can be used for nominal data.

False; cumulative models are appropriate for ordinal data, not nominal data.

Creative application of models

Consider how models can be applied in real-world contexts, creatively designing studies or experiments that leverage statistical analysis to address research questions.

Binary logic model

A statistical model for binary dependent variables categorized into two distinct groups.

Baseline logic model

A statistical approach comparing a baseline group to treatment groups to measure effects.

Cumulative model

A model for ordered categorical responses estimating probabilities of being in or below a category.

When to use Tobit analysis?

When the dependent variable is censored, limited at one or both ends of its scale.

When to use Binary logic model?

For dependent variables with two possible outcomes, applicable in decision-making contexts.

When to use Baseline logic model?

When comparing treatment effects against a control group in experimental designs.

When to use Cumulative model?

For ordered categorical data, such as Likert scale responses.

When to use Wilcoxon signed-rank test?

When comparing two related or matched samples with non-normal distribution.

When to use Wilcoxon-Mann-Whitney rank sum test?

For comparing two independent samples when data is not normally distributed.

When to use Kruskal-Wallis test?

When comparing three or more independent samples for significant differences.

When to use Friedman test?

For related samples when assessing differences in treatments across multiple attempts.

Characteristics of Binary logic model

It provides precise probabilities for binary outcomes, facilitating decision-making in a variety of fields such as marketing and medicine.

Characteristics of Baseline logic model

It allows for clear comparisons between control and treatment groups, highlighting the effect of interventions over time.

Characteristics of Cumulative model

It efficiently handles ordered categorical data, making it easier to interpret probabilities of outcomes across different levels.

Limitations of Tobit analysis

It assumes a specific functional form and can be less effective if the underlying assumptions do not hold, particularly regarding the distribution of errors.

Strengths of Wilcoxon signed-rank test

It is flexible and does not assume normality, making it useful for analyzing data that does not fit Gaussian distributions.

Strengths of Wilcoxon-Mann-Whitney rank sum test

It is ideal for small sample sizes and ranks the data, reducing the impact of outliers on the test results.

Strengths of Kruskal-Wallis test

It compares more than two independent groups effectively and is non-parametric, suitable for ordinal data.

Strengths of Friedman test

It handles repeated measures and derived from the ranks of the data, making it robust to violations of normality.