Statistics and Data Analysis: Key Concepts for Students

What is quantitative (statistical) analysis?

Analysis of numerical data using mathematical rules to summarize data, assess relationships, and make generalizations.

What are descriptive statistics?

Statistics that summarize and organize numerical data.

What are inferential statistics?

Statistics used to make predictions or generalizations about a population based on a sample.

What is the mean?

The average of a dataset.

What is the median?

The middle value in a dataset.

What is the mode?

The most frequently occurring value in a dataset.

What is the range?

The difference between the highest and lowest values.

What is standard deviation?

A measure of how much scores vary from the mean.

What happens to standard deviation when all scores are the same?

It equals zero.

What is a normal distribution?

A bell-shaped distribution where mean, median, and mode are equal.

In a normal distribution, how much data falls within ±1 SD?

68%

What is a positively skewed distribution?

A distribution with a long tail to the right.

What is a correlation coefficient?

A statistic that measures the strength and direction of a relationship between two variables.

What is the range of correlation values?

-1.00 to +1.00

What does a correlation of +1 mean?

Perfect positive relationship.

What does a correlation of -1 mean?

Perfect negative relationship.

True or False: Correlation implies causation.

False

What is a scatterplot?

A graph showing the relationship between two variables.

What is a Type I error?

Rejecting the null hypothesis when it is actually true (false positive).

What is a Type II error?

Failing to reject the null hypothesis when it is false (false negative).

What is a two-tailed test?

A test used when no specific direction of the outcome is predicted.

What are multivariate statistics?

Analyses that examine relationships among three or more variables.

What are nonparametric statistics?

Statistics used when data do not meet assumptions like normal distribution.

What is a meta-analysis?

An analysis that combines results from multiple studies using effect sizes.

What is a z-score?

A standardized score that shows how far a value is from the mean in standard deviations.

What does a positive z-score indicate?

The value is above the mean.

What does a negative z-score indicate?

The value is below the mean.

What does standard deviation measure conceptually?

The spread or variability of data around the mean.

When is standard deviation larger?

When data points are more spread out.

When are nonparametric tests used?

When assumptions of normality are violated.

What does a correlation of 0 mean?

No relationship between variables.