Categorical vs Quantitative Data Analysis

Data that can be categorized into groups or labels, such as gender, color, or type of animal. It is descriptive rather than numerical.

Data that involves numbers and can be measured, such as age, height, or weight.

The proportion of cases in a sample that have a specific value for a particular variable.

The proportion of cases in a sample that have a specific value for one variable AND a specific value for another variable.

The proportion of cases with a specific value for one variable among cases that share the same value for another variable.

A statistical study that attempts to collect data from every individual in the population.

A statistical study is biased if it is more likely to underestimate or overestimate the value you want to know.

A sample is randomly selected such that every set of 'n' individuals has an equal chance of being chosen.

Splitting the population into homogeneous groups (strata), selecting a simple random sample (SRS) from each stratum, and combining them to create the overall sample.

Grouping the population into clusters (usually based on location) and randomly selecting whole clusters for the sample.

A study where researchers actively impose a treatment upon the experimental units.

A study where researchers observe but do not influence the results.

A study where researchers can determine cause-and-effect relationships.

A statistic is an unbiased estimator of a parameter if the mean of its sampling distribution equals the true value of the parameter being estimated. In other words, the sampling distribution of the statistic is centered in the right place.

The distribution of a statistic in all possible samples of the same size. It describes the possible values of a statistic and how likely these values are.

The single-value "best guess" for the value of a population parameter. For example, 𝑝̂ = 0.63 is a point estimate for the population proportion 𝑝.

The expected value of a random variable, representing the average outcome over many trials.

If the population distribution is not Normal, the sampling distribution of the sample mean 𝑥̅ will become more and more Normal as n increases.

The spread of the sampling distribution of a statistic; it tells us how much variability we expect from sample to sample.

Measures how much a random variable typically varies from its mean, indicating the spread of possible outcomes.

Rules for transforming a linear function of a random variable; the mean is adjusted by the constant term and scaled by the coefficient, while the standard deviation is scaled by the absolute value of the coefficient.

Rules for combining the mean and standard deviation of independent random variables; the mean of the combined variable is the sum of the individual means, and the variance of the combined variable is the sum of the variances.

A specific type of random variable that represents the number of successes in a fixed number of independent Bernoulli trials.

The probability of obtaining a specific number of successes in a binomial setting, calculated using the binomial probability formula or the binompdf function.

The mean, standard deviation, and shape of a binomial distribution, which are determined by the number of trials (n) and probability of success (p).

A specific type of random variable that represents the number of trials needed to get one success in a series of independent Bernoulli trials.

The probability of an event is the proportion of times the event would occur in a very large number of repetitions. It is a number between 0 and 1.

The Law of Large Numbers states that as we observe more repetitions of a chance process, the observed proportion of times an event occurs approaches the probability of that event.

The probability of event A happening, given that event B has already occurred. It is calculated by dividing the probability of both events happening by the probability of event B happening.

Two events are mutually exclusive if they cannot happen at the same time. The probability of both events happening is 0.

Two events are independent if knowing that one event has occurred does not change the probability of the other event occurring.

A random variable that can take on a fixed set of values, often whole numbers, with gaps between them. Values can be listed in a table or displayed using a histogram.

A random variable that can take on any value within a given interval on the number line. Its probability distribution is displayed using a density curve.

The long-run average of a random variable. For a discrete random variable, it is calculated by summing the product of each value and its probability.

When two variables are intertwined, making it impossible to determine which influences the response variable.

A group that receives a fake treatment, used as a baseline to compare effects of the real treatment.

Subjects are unaware of which treatment they receive, helping eliminate bias from expectations.

Randomly assigning units to treatments ensures groups are roughly equivalent, reducing bias and allowing for causal conclusions.

Grouping similar units before random assignment helps account for existing differences, improving the study's precision.

Giving both treatments to each unit in random order, providing a direct comparison within the same unit.

The ability to apply the study's findings to a larger population beyond the sample used in the study.

Drawing a cause-and-effect conclusion requires random assignment of treatments and statistically significant differences.