Test 3 review Flashcards
Graphs for categorical data
Bar Chart (best),
Pie Chart (okay, but no scale),
Pictogram (often
misleading)
p vs. p-hat
p is the population parameter, p-hat is the sample statistic
How to compute p-hat
x / n
standard deviation of p-hat
σ = sqrt(p(1-p) / n)
standard error of p-hat
sqrt(phat(1-phat) / n)
margin of error for p-hat
z*sqrt(phat-hat(1-phat) / n)
One-Sample z Confidence interval for p conditions for use?
- Large sample size or normality
FOR LARGE SAMPLE SIZE:
np > 10, (1-p) > 10 - Randomization
Sampling distribution of p-hat?
All sample proportions
From all possible random samples
Of the same size
Taken from a population
Definition of confidence interval
Range of reasonable values which we predict with certain accuracy the parameter of interest falls under
Computing confidence interval for one sample z confidence interval for proportions
p̂ ± z*√(𝑝̂(1−𝑝̂) / 𝑛)
Interpretation of confidence interval
We are ___% confident that (parameter of interest) is contained in the interval (lower bound, upper bound)
Minimum sample size for categorical data
np > 10, n(1-p) > 10
How conditions are different for confidence intervals and hypothesis tests for p
For confidence intervals you always use p-hat because there is no null hypothesis
For hypothesis tests, you always assume p-null is true, and thus you use it for np rules and test statistics
One-sample z Test for proportions conditions for use?
- Large sample size or normality
FOR LARGE SAMPLE SIZE:
np > 10, (1-p) > 10 - Randomization
One-sample z Test for proportions hypotheses?
H0 p = #, Ha p >, <, =/= #
One-sample z Test for proportions compute test statistic?
z = (p-hat - p) / sqrt((p(1-p)) / n)
One-sample z Test for proportions write conclusion?
We reject (fail to reject) the null hypothesis and conclude we do (not) have sufficient evidence to conclude that the null hypothesis is (not) true.
Role/Type classifications for relationships
C -> C (proportions)
Q -> C (We do not discuss)
C -> Q (means) (boxplots)
Q -> Q (means)
How to tell if something is Matched Pairs?
Either both treatments are applied to each individual or two very similar individuals are given the same treatment
Matched Pairs t Confidence Interval?
Used to estimate the population parameter for means
Matched pairs conditions?
- Randomization
- Roughly normal distributions or n > 30
Matched pairs hypothesis wording?
The mean difference between all participants
Matched Pairs t Confidence Interval computation?
average of differences +- t * (s / sqrt(n))
degrees of freedom: number of PAIRS
Matched Pairs t test computation?
dbar / (s / sqrt(n))
Two sample t confidence interval / test conditions?
- Randomization
- Roughly normal distributions or n > 30
- big sd / small sd < 2 (equal standard deviations)
When to use Anova?
Several groups of means
When to use Chi-squared?
Several groups of proportions
Two sample t tests for means degrees of freedom?
n1 + n2 - 2
Two sample t tests for means write hypotheses?
μ1 = μ2, μ1 <, >, =/= μ2
OR
μ1 - μ2 = 0, μ1 <, >, =/= μ2
Two sample t tests formulas?
sd * sqrt(1 / n1 + 1 / n2)
(x-bar1 - x-bar2) / sd * sqrt(1 / n1 + 1 / n2)
(x-bar1 - x-bar2) +- t * s * sqrt(1 / n1 + 1 / n2)
Chi-Square when to use?
Multiple proportions
Anova Hypotheses?
μ1 = μ2 = μ3 = μ4
vs
At least one differs from the rest
