Data Science Final

Population

The entire group you want to learn about

Sample

The subset you actaully observe

Parameter

A number describiing the population (usually unknown)

Statistic

A number calculated from the sample (used to estimate parameters)

Population distribution

Distribution of Individual values in the population

Sample distribution

distribution of individual values in your sample

Sampling distribution

distribution of statistic across many possible samples

Central Limit Theorem (CLT)

For sufficiently large samples, the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population distribution

Standard error

standard deviation of the sampling distribution

Normal distribution

Bell-shaped and symmetric, mean = median = mode, completely determined by two parameters: mu (center) and sigma (spread), notation: X ~ N (mu, sigma²)

Point estimate

Sample mean in confidence intervals

Confidence interval

A range of values calculated from sample data that are likely to contain the true, unknown population parameter with a specific level of confidence

Confidence level

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.

Margin of error

A statistic showing how much data may differ from the true population using + and - percentage

Critical value

The cutoff point from a probability distribution (like the z- or t-distribution) that determines how far the sample statistic can deviate from the population parameter while still being consistent with a specified confidence level. The multiplier.

Null hypothesis

The skeptic’s position; what we’re trying to disprove

Alternative hypothesis

The research claim; what we want to show

Test statistic

Measures how many standard errors our estimate is from the null value

P-value

The probability of data this extreme is Ho is true

Significance level

The threshold for determining if a result is statistically significant in a hypothesis test

Type 1 error

False positive (rejecting a true Ho)

Type 2 error

False negative (failing to reject a false Ho)

One-sided test

Checks for a difference in a specific direction. The unknown true population mean is either specifically higher or lower than the null hypothesis mean.

Two-sided test

Checks for any difference. The unknown true population mean is not the same as the null hypothesis mean, but the direction is not specified.

Statistical signficance

The result’s p-value is less than the alpha of 0.05.

Practical significance

Is the effect of statistical significance large enough to matter outside of the study?

Correlation

Measures the strength and direction of the linear relationship between two continuous variables. Range between 0 and 1.

Causation

One variable directly causes change in another.

Counterfactual

What would have happened under the alternative condition and it is unobservable

Average Treatment Effect (ATE)

The average causal effect of a treatment, calculated as the average outcome for those who received the treatment minus the average outcome for those who did not, assuming treatment assignment is independent of potential outcomes.

Confounding variable

A confounding variable is a third variable that is related to both the independent variable (IV) and the dependent variable (DV) and can distort the observed relationship between the IV and DV.

Direct causal relationship

X → Y

Spurious relationship

Z → X and Z → Y

Chain/mediation relationship

X → Z → Y

Internal validity

Checks if the study established causation. Did the treatment cause the effect?

External validity

Checks if the results of the study can be generalized in the real world

Selection bias

Sample selection (who volunteers), treatment selection (who seeks treatment), attritrion (who drops out)

Measurement validity

If your study actually captures the real-world concept. Lab vs. reality, self-report vs. behavior, proxy measures

Generalizability

Whether the finding will apply with different populations, different settings, and different times

Demand effects/reactivity

Whether people behave differently because they’re being studied. Hawthorne effects, social desirability bias, experimenter demand

Reverse causality

Does X cause Y or does Y cause X (or both?)

Correlation coefficient (r)

Gives us a single number that summarizes linear relationship between two variables

Intercept (a)

Tells us what value the model predicts if the dv is 0

Slope (b)

Tells us the amount of growth per increase of one unit

Residual

The difference between an actual observed data point and the value predicted by a model

Least squares/ols

A method for estimating a regression line by choosing the coefficients that minimize the sum of squared residuals (the squared differences between observed and predicted values)

R²

R² is the proportion of the variation in the dependent variable (Y) that is explained by the regression model

Adjusted R²

R² is the proportion of the variation in the dependent variable (Y) that is explained by the regression model

Control variable

Fixed effects

Interaction term

Multicollinearity

Heteroscedasticity

Nonlinearity

Dummy variable

A binary variable used to represent categories in regression model

Reference category

The omitted group when using dummy variables. All dummy variable coefficients are interpreted relative to this group

Control variable

a variable included in a regression to account for other factors that may affect the outcome, helping isolate the relationship between the main independent variable and the dependent variable

Fixed Effects

Control for all unobserved, time-invariant characteristics of units by comparing each unit to itself overtime

Interaction term

Allows the effect of one independent variable on the dependent variable to depend on the value of another variable

Multicollinearity

When two or more independent variables are highly correlated, making coefficient estimates unstable and standard errors large

Heteroscedasticity

Occurs when the variance of the regression errors is not constant across values of the independent variables, which leads to incorrect standard errors

Nonlinearity

When the relationship between the independent variable and the dependent variable is not linear, meaning a straight line is not an appropriate fit