STATS QUIZ 1 (Ch 1-3)

What is a population?

The entire group I ultimately care about.

What is a sample?

A subset of the population that I actually observe.

What does μ mean?

Population mean; The average value across the entire population.

What does x̄ mean?

Sample mean - average of the sample you actually observed.

The average of the observations in my sample. Usually used to estimate/describe the center when you don't have the full population.

What does σ mean?

Population standard deviation.

A measure of how spread out the entire population is around its mean; roughly the typical distance from the population mean.

Shows consistency (or lack thereof) and if any difference is big or small

Small SD means

Values are clustered near mean

Large SD means

Values are dispersed far from mean

What does σ² mean?

Population variance; The average squared distance of population observations from the population mean.

Why do we care about variance?

It measures spread and is the mathematical basis of SD; SD is usually easier to interpret because it is in the original units.

What does s mean?

Sample standard deviation; How spread out the observations in a sample are around the sample mean.

What does xᵢ mean?

One individual data value.

What does n mean?

Number of observations.

What does Σ mean?

Summation; Add everything that follows.

What is a deviation?

An observation minus the mean; its distance and direction from average.

How do I reconstruct SD?

RMSD = Root of Mean of Squared Deviations.

Variance vs. SD?

Variance = SD²; SD = √variance.

Population vs. sample SD denominator?

Population uses n; sample uses n-1.

Population vs sample mean?

Population = μ; sample = x̄

Population vs sample SD?

Population = σ; sample = s

Population vs sample variance?

Population = σ^2; sample = s^2

Empirical Rule?

1 SD ≈ 68%, 2 SD ≈ 95%, 3 SD ≈ 99.7%.

How Many SDs Away Is Something tells us what?

How many standard deviations above/below average is this observation? Anything beyond 6sigma is largely abnormal!!!

IQR?

Q3 - Q1; spread of the middle 50%.

Confounding factor

Characteristic / factor that differs between the groups being compared AND is related to the outcome being measured (connected to both group AND outcome).

When a third factor makes two things look more related than they really are because that third factor is connected to both

Something else is going on in the background that is mixing up the relationship you're trying to measure.

Why randomize?

To create comparable groups so treatment is the main systematic difference, enabling causal inference on average.

GOLD STANDARD

Can a larger sample fix confounding?

No.

Simpson's Paradox?

A comparison reverses direction when groups are combined.

Overall relationship can reverse once you control for a confounder.

Histogram area principle?

Percentage of histogram area over a range equals the percentage of observations in that range.

Rate

Events relative to how many opportunities there were for the event to happen

If comparing risk → CHECK THE DENOMINATOR.

Observational Study

Researcher watches what naturally happens. Adjusting an observational study still does not turn it into an experiment.

In an experiment a researcher…

Assigns treatment/groups

Treatment group →

intervention

Control group →

No intervention

Blinded study

Subjects don't know assignments

Double-blinded study

Researchers don't know assignment either

Observational association ≠

causal effect

Cross-sectional study

Observes subjects at one point in time

Longitudinal study

Follow the same subject over time

Non-response bias

Responders systematically differ from nonresponders

Interview bias

interviewer/question wording affects answers

Histogram shows

How quantitative observations are distributed across ranges of values.

Shape of a Distribution - Mode

peak/high concentration

Shape of a Distribution - Multimodal

Multiple peaks

Shape of a Distribution - long right tail

unusually large values (mean > median)

Shape of a Distribution - long left tail

unusually small values (mean < median)