This is a draft cheat sheet. It is a work in progress and is not finished yet.
Two Proportion Confidence Interval
Shape 
When the large counts rule is met, the sampling distribution of p^{1}  p^{2} is approximately normal 
Center 
The mean of the sampling distribution is p^{1}  p^{2} 
Spread 
The standard deviation of the sampling distribution of p^{1}  p^{2} is the square root of the sum of (p^{1})(1p^{1}) divided by n^{1} and (p^{2})(1p^{2}) divided by n^{2} as long as each sample is no more than 10% of its population. 
Conditions 
Random (both samples must be random), 10% (both samples less than 10% of respective population), Large Counts (for both samples individually) 
Calculator 
2PropZInterval 
Interpretation 
We are __% confident that the interval from __ to __ captures the true difference of [p^{1}] and [p^{2}] 
Point Estimate Formula 
p^{1}  p^{2} 
Critical Value Formula (Z*) 
invNorm(__%/2 + 0.5) 
Standard Deviation Formula 
the square root of the sum of (p^{1})(1p^{1}) divided by n^{1} and (p^{2})(1p^{2}) divided by n^{2} 
Confidence Interval Formula 
Point Estimate +/ Critical Value * Standard Deviation 
Two Proportion Significance Test
Null Hypothesis 
p^{1}  p^{2} = Hypothesized Value 
Alternative Hypothesis 
p^{1}  p^{2} = Hypothesized Value 
Conditions 
Random (both), 10% (both), Large Counts (both) 
Pooled Sample Proportion 
x^{1} + x^{2} / n^{1} + n^{2} (successes / size) 
Statistic 
p^{1}  p^{2} 
Parameter 
Hypothesized Value (often 0) 
Standard Deviation 
The square root of the sum of (p^{c})(1p^{c}) divided by n^{1} and (p^{c})(1p^{c}) divided by n^{2} 
Test Statistic Formula 
Statistic  Parameter / Standard Deviation 
Calculator 
2PropZTest 
Areas of Error 
Not a random sample = can't generalize results, cause and effect vs correlation 
IMPORTANT 
If experimental units are randomly selected, check the 10%, otherwise technically not necessary 
Ideal for Conclusions about Populations 
Data from Two Independent Random Samples 


Two Mean Confidence Interval
Shape 
When the population distributions are normal, the sampling distribution of x^{1}  x^{2} is approximately normal. Also normal, if both sample sizes are greater than 30 by CLT 
Center 
μ^{1}  μ^{2} 
Spread 
If both samples are less than 10% of respective populations, the formula for standard deviation is the square root of the sum of σ1^{2} / n^{1} and σ2^{2} / n^{2} 
Conditions 
Random (both samples are independent and random or from two groups in a randomized experiment), 10% (both), and Normal/Large (population distributions are normal or sample size greater than 30) 
Calculator 
2SampTInt 
Interpretation of a Confidence Level 
If we take many samples of size _ of _ and of _ of _ and find the __% confidence interval for each sample, __% of the confidence intervals will capture the difference in the mean number of ____. 
Interpretation of Confidence Interval 
We are __% confident that the interval from __ to __ captures the true difference in the __ 
State 
We want to estimate μ^{1}  μ^{2} at the __% confidence level where μ^{1} is __ and μ^{2} is __ 
Point Estimate Formula 
x^{1}  x^{2} 
Critical Value Formula (t*) 
invT(p/2 + 0.5, smaller n df) 
Standard Deviation/Error Formula 
The square root of the sum of σ1^{2} / n^{1} and σ2^{2} / n^{2} 
Confidence Interval Formula 
Point Estimate +/ Critical Value * Standard Deviation 
Two Mean Significance Test
Null Hypothesis 
μ^{1}  μ^{2} = Hypothesized Value 
Alternative Hypothesis 
μ^{1}  μ^{2} = Hypothesized Value 
Conditions 
Random (both), 10% (both), Normal/Large (both)(no strong skew, outliers, or greater than 30) 
Statistic 
x^{1}  x^{2} 
Parameter 
μ^{1}  μ^{2} 
Standard Deviation 
The square root of the sum of s1^{2} / n^{1} and s2^{2} / n^{2} 
Test Statistic Formula (T) 
Statistic  Parameter / Standard Deviation 
Calculator 
2SampTTest 
Interpretation of pvalue 
Assuming the null hypothesis is true, there is a __ probability of getting a difference in ___ just by the chance involved in random assignment/variability 
Paired Data vs Two Samples
Paired Data 
Two Samples 
Subjects were paired and the split at random into the two treatment groups or each subject received both treatments in a random order 
Experimental groups were formed using randomized design or two independent random samples were taken from the population 
