Statistics - Exam #1

Statistics

Science of collecting, describing, and analyzing data

Cases

Subjects / objects you’re collecting info about (rows)

Variables

Characteristics that can change from one case to the next (columns)

Categorical Variable

(AKA qualitative) Sorts cases into groups

Quantitative Variable

Counts or measures something (answers how many or how much)

Explanatory Variable

Used to explain or predict the other one

Response Variable

The outcome being explained or predicted

Population

Every individual / object you want to know about

Sample

Subjset you actually collect data from

Inference

Using the sample to draw a conclusion about the population

Anecdotal Evidence

Information drawn from personal experience, individual stories, or a few haphazardly selected cases, which may not be representative of the larger population and so can’t reliably support general conclusions

Scientific Knowledge

Conclusions based on data collected systematically through well-designed studies (random sampling or controlled experiments)

Sampling Bias

Method of selecting the sample causes it to differ from the population in a way that matters

Non-Response Bias

People who skip the survey differ from those who answer

Question Wording Bias

The way a question is phrased nudges people toward a certain answer

Inaccurate Responses

When people don’t answer truthfully

Simple Random Sample (SRS)

Every individual in the population has an equal chance of being selected

Chance

No real relationship, just a random pattern in this particular sample

Confounding

Third variable is affecting both, distorting the picture

Causation

Change in the explanatory variable actually produces the change in the response

Observational Study

Researchers observe and measure variables as they naturally occur without assigning treatments, so they can show association but not causation

Experiment

Researchers deliberately impose a treatment on subjects, ideally with random assignment, to see how it affects a response, which allows conclusions about causation

Non-Randomized Experiment

Researchers assign treatments to subjects to treatment groups, which balances out confounding variables and lets them conclude causation

Randomized Experiment

Researchers use chance to assign subjects to treatment groups, which balances out confounding variables and lets them conclude causation

Causal Conclusion

Statements that a chance in the explanatory variable actually causes a change in the response variable

Random Sampling

Using chance to select subjects from a population, so results can be generalized to that population

Random Assignment

Using chance to place subjects into treatment groups, so differences in the response can be attributes to the treatment

Matched Pairs

Comparing two treatments on similar pairs of subjects (or same subject twice)

Self-Paired

Same subject gets both treatments, in a randomly assigned order

Paired by Similarity

Two very similar subjects are matched up, then one is randomly assigned to each treatment

Placebo

Fake treatment that looks identical to the real one but has no active effect

Blinding

Participants and / or researchers don’t know who received which treatment

Single-Blind

Participants don’t know their treatment

Double-Blind

Neither participants nor researchers know

Frequency Table

Count of cases in each category

Relative Frequency Table

Those counts converted to proportions / percentages of the total

Proportion

Main numerical summary for categircal data

Pie Chart

Shows how the categories split up the whole

Bar Chart

Bars for each category with gaps between them

Two-Way Table

Table that organizes data on two categorical variables for a group of individuals

Marginal Distribution

One variable’s totals alone

Joint Distribution

Cell count / grand total (are)

Conditional Distribution

One variable within a category of the other (of)

Association

Two variables are associated if the conditional distributions differ across categories

Difference in Proportions

Subtract one group’s proportion from another’s to compare them directly

Side-by-Side Bar Chart

Bars grouped by the second variable, placed next to each other

Segmented (Stacked) Bar Chart

One full bar group, divided into proportional segments, if the segment pattern looks different across groups, that’s a sign of a relationship

Risk

Chance of an outcome within a group (x / total)

Odds

Chance something happens divided by chance it doesn't (x / y)

Relative Risk

How many times more likely an outcome is in one group vs. another

Histogram

Bars showing counts of a quantitative variable across numeric intervals

Bar Chart

Bars showing counts of a categorical variable’s categories

Mean

Numerical average, add every value and divide by how many there are

Median

Middle value once data is sorted from low to high

Dot Plot

Way to show quantitative data

Right Skew

Long tail stretches right (mean > median)

Left Skew

Long tail stretches left (mean < median)

Symmetric / Bell Shaped

Mean ~ Median

Percentile

Percentage of data falling below a given value

Quartile

Split the data into quarters

Five-Number Summary

Five valvues describing a distribution’s spread and center

Interquartile Range (IQR)

Spraed of the middle 50% of data

Standard Deviation

Typical distance of data values from the mean

Z-Score

How many standard deviations a value is above or below the mean

95% Rule

In a bell-shaped distribution, about 95% of the values fall within 2 standard deviations of the mean

Correlation

Measures the strength and direction of a linear relationship between two quantitative variables