How to find help if you don't know where to start
Statistics can be difficult because there are so many tools to analyze data. We use different tests to analyze data based on what we know and how we want to know.
Get a picture of the distribution
Sometimes, it is hard to know where to begin. If you are stuck, try getting a graph of the distribution! You can enter all you know about the distribution on Wolfram Alpha and it will return a graph of the distribution and all the key details (mean, standard deviation, equations for the probability functions).
Below is a screenshot of an example search:
"normal distribution mean=100, standard deviation=10"
Which statistics test you should use to analyze your data?
Use this interactive decision tree to narrow down which test to use. Once it has helped you choose the test, the website takes you to an online calculator!
Statistical Decision Tree
Khan Academy
https://www.khanacademy.org/
Khan Academy has an online course feel but also part video game. Watch a video and practice your skills with interactive "textbook." Take quizzes and tests to see how well you have mastered the material. And earn points and badges along the way! Below is a sample of topics on statistics:
Two-way distribution tables
Z-scores
Normal Distribution
Counting: permutations, combinations
What is a random value? (discrete, continuous, binomial...)
Hypothesis testing!
Confidence Intervals
This probability calculator by Michael Borcherds will calculate p-value, graph and shade the distribution, calculate the test statistic, and more! It is an interactive Geogebra worksheet. It is easier to enter numbers if you are on a computer rather than a phone.
Screenshot of the calculator using a Normal distribution.
This could be an IQ distribution\(N(\mu=100, \sigma=10\)) where we want the p-value of an IQ of 96 or lower.
To use it, first choose your distribution from the drop down menu. You can choose from Normal, Binomial, Student T, Chi Squared, etc. Next, input your values (for normal you need \( \mu \) and \( \sigma \), for binomial you need n, p...etc). You will choose the direction of the test (left-tailed, two-tailed, right-tailed). Lastly, you must set the lower and upper bounds.
In the Distribution tab, you can graph and calculate p-values! Choose your distribution type (Normal, Binomial, Student T, Chi Squared, etc) and set your parameters.
For Normal Distribution: input values for the mean, standard deviation, and direction of the test (eft/right/two-tailed). You will get a graph which you can export as a picture and the p-value.
For Binomial Distribution, choose the sample size n, probability of success p, and the direction of the test. You will get a graph, the p-value, and even a normal approximation!
The Statistics tab allows you to run statistics tests. Choose the type of test (Z Test of a Mean, Z Test of a Proportion, T Test of a Mean, etc). Input values for your null hypothesis, direction of test, and information from the sample. The calculator will calculate the test statistic and p-value for you.
Normal Distribution:
input: mean, standard deviation, direction (left-tail, right-tail, double-sided)
output: p-value, graph with shaded region
Online Statistics Calculators
Standard deviation calculator
Enter your data. Choose if it is from a sample or a population.
StatTrek: great resource guide for calculating basic probability and counting problems and probability distribution tools! Read up on information on the different distributions: normal, standard normal, binomial, t-distribution, chi-squared and more!
- calculators for basic probability (addition, subtraction, multiplication, Bayes' rule)
- calculator for combinations and permutations.
- binomial probability calculator
- normal distribution calculator: input 3 out of the 4 values (mean, standard deviation, probability, or z-score) and it will calculate your missing value!
Random number generator
Generate a list of up to 10,000 random integers between -1,000,000 and +1,000,000!
Interactive Normal Distribution Grapher: graphs a normal distribution with probability shading, calculates z-score. Move the slider bars for mean, standard deviation, lower and upper bounds, and toggle to see the algebra to calculate the z-score and probability!
Stats.Blue: Regression calculators!
For linear data: enter your independent and dependent values. This calculator will calculate the regression line for you!
For exponential data: enter the values into this online calculator. It will plot your data, calculate the equation for a best-fit exponential regression line, and plot your residuals.
For logarithmic data: enter the values into this online calculator. It will plot your data, calculate the equation for a best-fit logarithmic regression line, and plot your residuals!
How to enter binomial probabilities with your graphing calculator
This worksheet helps you translate the stats jargon from your homework problem so you can enter the values in the correct order with the function binomcdf()on your TI83/84. It will also calculate the probability for you too!
How to set up hypothesis testing (for means OR for proportions)
This worksheet helps get used to setting up your hypothesis and null hypothesis. It will also draw a graph and shade the critical region.