Statistics Cheat Sheet - Basic Concepts, Sampling, and Hypothesis Testing

Oct 13, 2026

Statistics Cheat Sheet consolidates core terminology and practical decision rules for interpreting numerical data. It defines foundational concepts such as data, population and sample, and explains measures including mean, median, mode, and standard deviation. The guide then clarifies hypothesis testing with null-hypothesis logic, Type I/Type II errors, and normal-distribution “tails” within ±2 standard deviations. It also covers sampling and common biases, missing-value imputation cautions, and frequent confusion around confidence intervals versus probability.

LanguageEnglish

CategoryGeneral

FormatPDF

Pages1

AccessFree to download

Basic Statistics Definitions

Is My Data Special?

Measures of Central Tendency

Standard Deviation

Null Hypothesis in Layman’s Terms

See Hazards

Sampling and Bias

Imputing Missing Values

Confidence Intervals vs Probability

Statistics Cheat Sheet Basic Statistics Definitions: Statistics – Practice or science of collecting and analyzing numerical data Data – Values collected by direct or indirect observation Population – Complete set of all observations in existence Sample – Slice of population meant to represent, as accurately as possible, that population Measure – Measurement of population/sample, an example would be some “score”([a.k.a. an](a.k.a. an) observation) Hypothesis – Educated guess about what’s going on Skew – Not symmetrical, crooked or uneven Impute – To fill in missing values Type I Error (false positive)– In hypothesis testing, when you incorrectly reject Null Hypothesis Type II Error (false negative)– In hypothesis testing, when you incorrectly fail to reject Null Hypothesis Is My Data Special? A Normal Distribution: A. K.A.“Bell Curve” Way to visualize how volume of a population is distributed based on some measurement Largest volume is packed around middle Volume curves down towards zero to left and right Symmetrical around middle Interesting Fact: The Mean, Median, and Mode are all the same and at the exact center How We Describe Things... (Measures of Central Tendency) Mean – Also called ”Average”, probably the most popular statistic, calculated as sum of all values divided by number of values Median – Value at center Mode – Value that occurs most 99.7% of data within Big takeaway: Most measurements of a normally distributed population will be centered around the middle. Why you care: If population is “normally distributed” then we can use a bunch of useful characteristics to help describe it. Standard Deviation – Measurement relative to mean, so a measure of how far a value is away from the mean. The further a value is from the mean the more unique…and perhaps interesting…it becomes. Make sure to review Hazards! section regarding skewed distributions Null Hypothesis in Layman’s Terms: There is nothing different, or special, about this data Best used when you need to know if your data is different or somehow special Always start out assuming Null Hypothesis is TRUE Goal is to either “reject” or “fail to reject” Null Hypothesis If FAIL TO REJECT Null Hypothesis then there is nothing really different about the data If REJECT Null Hypothesis then we are confident that what we see is different or special On curve above, can only say that an observation is different/special if it falls in either of shaded regions (called “tails”) The tails are 2 Standard Deviations away from (either above or below) the Mean Assumes dealing with a normal distribution! See Hazards! Big takeaway: If your data falls within +/ -2 Standard Deviations of Mean then its probably not all that different. If your data falls outside those boundaries then it is most likely something to take note of. Caution Hazard Sampling Good Sampling Rule of Thumb: Consider sampling when population you’re working with is too big to handle Aim is to get a good representative for actual population Generally the bigger the sample the better, but a simple tip is: -At minimum your sample size should be 100 -At maximum your sample size should be 10% or 1000, whichever is smaller Keep bias out of it by ensuring a RANDOM sample! Random Numbers Some Sampling Methods: Simple Random (probably the only one you will ever see or use) Systematic Random Stratified Cluster Multistage Are an excellent way to create a Simple Random Sample. Most analytical tools (including Excel & Google Sheets) have a random number generator you can use. Just apply a random number to each row, sort in ascending order by the random number then select the top however-many rows. Caution Hazard | | | | | | --- | --- | --- | --- | | | Beware of BIAS
Bias can effect both how samples are selected, and also what conclusions you draw from them (i.e. interpretation).

FAQs

What is the difference between population and sample?

Population is the complete set of all observations in existence, while a sample is a slice of that population meant to represent it as accurately as possible.

When do you reject or fail to reject the null hypothesis?

Start by assuming the null hypothesis is true. If you fail to reject it, the data provides no meaningful evidence of difference; if you reject it, you are confident what you observe is different or special.

What are “hazards” to watch for in sampling and missing data?

The sheet warns that bias can affect both how samples are selected and how conclusions are drawn, including selection, observer, detection, and other bias types. It also cautions against filling missing values with mean or median without considering that missingness may reflect underlying processes.

Oct 13, 2026

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