Introductory Statistics and Hypothesis Testing

A comprehensive 45-card practice set covering basic statistical concepts, distributions, measures of central tendency, variability, inferential statistics, hypothesis testing, and statistical test selection scenarios.

What are statistics?

Statistics are methods used to organize, analyze, summarize, and interpret data.

What is data?

Information that is collected and analyzed to reach research conclusions.

What are descriptive statistics?

Methods used to summarize and describe data in a simplified form.

What are inferential statistics?

Statistics used to estimate population parameters and test hypotheses.

What is the difference between descriptive and inferential statistics?

Descriptive statistics describe a dataset; inferential statistics draw conclusions about a population and test hypotheses.

What is frequency?

The number of times a particular value appears in a dataset.

How is frequency calculated?

By counting how many times a value occurs.

What is a distribution of data?

The frequency of each number or range of numbers within a dataset.

What is a normal distribution?

A symmetrical bell-shaped distribution where most scores cluster around the mean.

What is skewness?

A measure of how asymmetric a distribution is.

What is positive skew?

A distribution with a long tail to the right (higher values).

What is negative skew?

A distribution with a long tail to the left (lower values).

What is kurtosis?

A measure of how peaked or flat a distribution is compared to a normal distribution.

What is a measure of central tendency?

A statistic that identifies the typical or middle value in a dataset.

What is the mean?

The arithmetic average: sum of all values divided by the number of values.

What is the median?

The middle value when data are ordered from smallest to largest.

What is the mode?

The value that occurs most frequently.

When is the mean most useful?

When data are normally distributed and free of extreme outliers.

When is the median preferred?

When the dataset contains outliers or is skewed.

Why can outliers make the mean misleading?

Outliers pull the average toward extreme values, making it unrepresentative.

Calculate the mean of $2$, $4$, $6$, $8$, and $10$.

$$30 \div 5 = 6$$

Calculate the median of $2$, $4$, $6$, $8$, and $10$.

$$6$$

Calculate the mode of $2$, $2$, $3$, $4$, and $5$.

$$2$$

What is variability?

The degree to which values differ from one another.

What is the range, and what is its calculation formula?

The difference between the highest and lowest values. Formula: $\text{Range} = \text{Largest Value} - \text{Smallest Value}$.

Find the range of $4$, $8$, $10$, $15$, and $19$.

$$19 - 4 = 15$$

What is variance?

A measure of how much scores differ from the mean.

What is standard deviation?

The square root of the variance.

Why is standard deviation important in a normal distribution?

It shows how spread out scores are around the mean and helps interpret how unusual a score is.

What is a percentile ranking?

The percentage of scores that fall below a particular score.

What does being in the $80\text{th}$ percentile mean?

You scored higher than $80\%$ of the distribution.

What are the two main purposes of inferential statistics?

1. Estimate population parameters 2. Test hypotheses

What is a hypothesis?

An expected finding based on theory, prior research, or evidence.

What is hypothesis testing?

A process used to determine whether a finding is likely real or due to chance.

Why must researchers consider chance events?

Even rare or unusual outcomes can occur randomly, so significance testing helps determine whether results are likely due to chance.

What is significance testing?

A procedure used to determine whether findings reflect a real population relationship or are likely due to chance.

What is a p-value?

The probability that the observed result occurred by chance alone.

What does a small p-value indicate?

The result is unlikely to be due to chance and may be statistically significant.

How do you choose between a t-test, Pearson's r, and Chi-square based on variable types?

A t-test requires a Categorical independent variable ($2$ groups) and a Quantitative dependent variable; Pearson's r requires Quantitative independent and dependent variables; Chi-square requires Categorical independent and dependent variables.

Which statistical test is appropriate for the scenario: Law-related major vs. non-law-related major → constitutional law score?

t-test

Which statistical test is appropriate for the scenario: Male vs. female police chief → number of complaints?

t-test

Which statistical test is appropriate for the scenario: Recidivism category → recidivated or not?

Chi-square

Which statistical test is appropriate for the scenario: Number of late-night shifts → number of complaints?

Pearson's r

Which statistical test is appropriate for the scenario: Prior arrest → court-appointed attorney (yes/no)?

Chi-square

Which statistical test is appropriate for the scenario: Impulsivity score → suspension days?

Pearson's r