Data Analysis Psyc 210

Why is language in statistics tricky?

Common words like "distribution" or "mean" have specialized meanings.

What is a random variable?

A property that varies and has associated probabilities.

What’s the difference between a variable and a constant?

Variables vary; constants do not. Variables represent changing values, whereas constants are fixed.

What are the two main types of random variables?

Discrete and continuous. Discrete random variables are countable, while continuous random variables can take any value within a range.

What are ordered categorical/pseudo-continuous variables (OC/PC)?

Discrete variables treated as continuous due to ordered categories (e.g., Likert scales with 5+ options).

What is a distribution in statistics?

A description of how values for a variable are spread over a range.

What is the difference between empirical and theoretical distributions?

Empirical = real sample data; Theoretical = idealized models (e.g., normal distribution).

What are census and statistical populations?

Census = actual people/objects; Statistical = possible values and probabilities.

Why do we use samples?

Populations are often too large or abstract to study directly.

What summarizes populations and samples?

Populations → parameters (μ, σ); Samples → statistics (x̄, s).

What is descriptive statistics?

Summarizing or describing data using tools like mean and standard deviation.

What is statistical inference?

Using sample statistics to estimate population parameters.

When do we use inference?

When aiming to generalize from a sample to a population.

What do X and Y usually represent in statistics?

Random variables.

What does a subscript (e.g., x₁, x₂) indicate?

A specific score for a participant or observation.

What does "i" represent in notation?

A general case or index for scores.

What does the summation operator (∑) mean?

Sum all values that follow it.

What do the limits on the summation (e.g., ∑ from i=1 to N) indicate?

Start and stop points for the sum.

What are the three shortcut rules for summation?

1. ∑(X ± Y) = ∑X ± ∑Y

2. ∑(cX) = c∑X

3. ∑(X + c) = ∑X + (N × c)