week 10: Quantitative Analysis II

What do descriptive statistics do?

They summarize and describe sample characteristics or relationships

Give an example of a descriptive statistic.

Calculating the average test score in a class

Can descriptive statistics generalize beyond the sample?

No, they do not extend conclusions beyond the studied sample

What do inferential statistics do?

They make generalizations about a population based on a sample

What example illustrates inferential statistics?

Estimating the average age of all students using a sample

What error do inferential statistics account for?

Sampling error, the difference between the sample and the population

What is regression analysis used for?

Modeling relationships between variables with an equation

Write the simple regression equation.

Y = a + bX

In regression, what does “a” represent?

The y‑intercept, the value of Y when X = 0

In regression, what does “b” represent?

The slope, the rate of change in Y for each unit increase in X

What are the independent and dependent variables?

Independent (X) is the assumed cause

In the example Y = 500 + 1000X, what does the 500 mean?

When X (age) = 0, income = $500

In the example Y = 500 + 1000X, what does the 1000 mean?

Each additional year of age adds $1,000 to income

What is a positive association in regression?

As X increases, Y also increases

What is a negative association in regression?

As X increases, Y decreases

What is no association in regression?

No clear pattern between X and Y

What is needed for valid inferential statistics?

A sample drawn from the population, random sampling, and attention to sampling and nonsampling errors

Define “population” in statistics.

The entire group of interest

Define “sample” in statistics.

A subset of the population used for study

What is sampling error?

The difference between sample results and the actual population values

What is nonsampling error?

Mistakes in data collection, like survey response errors

What does a p‑value measure?

The probability that a result is due to chance

What is the common threshold for statistical significance?

p < 0.05

What does p < 0.05 indicate?

The result is unlikely due to chance and is statistically significant

What does p > 0.05 indicate?

There is no strong evidence to support the finding

Give an example of a significance test.

Testing whether a 7% improvement in test scores is real or due to chance

What is the margin of error?

A measure of uncertainty in an estimate

In “54% ± 2%,” what does the ±2% mean?

The true value likely falls between 52% and 56%

How does higher confidence affect the margin of error?

It widens the margin of error

What does descriptive statistics include?

Measures like mean, standard deviation, and regression

What does inferential statistics include?

Methods to generalize from a sample to a population

What does regression analysis do?

Models relationships between variables using an equation

What does a low p‑value signify?

A low probability that the result is due to chance (significant)

What does the margin of error tell us?

The precision of an estimate