Lecture 9 Flashcards
Hypothesis Testing w More than Two Samples/ANOVA/Power and Sample Size Determination
What are the three types of t-tests?
- independent t-test
- matched t-test
- one sample t-test
What is the purpose of t-tests?
used to compare means between groups (can be independent or dependent)
What is the difference between a category and a variable?
categories are NOT variables, the subgroups OF a variable are the categories, variable is the common umbrella of the categories
When would a t-test NOT be ran?
- when comparing more than 2 groups
What will occur if a t-test is used for more than 2 variables?
Type I error will increase if t-test is used for more than two variables- by chance of running multiple comparison test, groups will have a significant outcome even if it’s not
What type of variable is only ever used in ANOVA (for this course)?
independent variables
What are the requirements of an ANOVA test?
- populations are approximately normal
- POP variances are equal
- sample values are interval or ratio
- samples are reorganized in only ONE way
- hypothesis is regarding population
What can alternate hypotheses NOT be in ANOVA?
cannot be an unequality statement- must be “at least one group is different…”
What is the variance check equation?
largest variance / smallest variance = value LESS than 9
What is the Sum of Squares Between/Model Equation?
SS between = sum of
[(mean of group - mean of ALL groups)^2] * # individuals PER group
What does the SS between value represent?
the variance that CAN be explained by the treatment/factor variable (a higher value is desired- means the treatment is beneficial)
What is the Sum of Squares Error Equation?
SS error = sum of (sum of (individual’s score - GROUP mean)^2)
What does the SS error value represent?
the variance that CANNOT be explained by the treatment/factor (lower value preferred)
What is the SS total equation?
SS between + SS error
What is the overall df equation?
df overall = n - 1, n: # participants across ALL groups
What is the between df equation?
df between = k - 1, k:# GROUPS being ocmpared
What is the error df equation?
df error = n - k
What is the mean squares equation for between and error?
SS between or error / df between or error
What does the mean squares value represent?
the average deviation of individual values from their respective mean (average amount of variation)
What is the F-statistic (ratio) equation?
F-Stat = mean square between / mean square error
Which value is the signal and which is the noise?
between = signal
error = noise
What does an F-ratio near 1 indicate?
almost equal signal to noise ratio (treatment makes no difference)
When is the null rejected?
What the p-value is > 0.05, at LEAST one group is different from the others (don’t know which one)
What is the relationship between power and beta?
power = 1 - beta
are inversely related
What are the 3 parameters used to determine sample size?
- beta value
- alpha value
- effect size (ES)
When power increases, what happens to alpha?
alpha also increases
When power increases, what happens to beta?
beta decreases
What is the relationship between power, effect and sample size?
the higher the power, the larger the effect and sample size
For one sample, continuous data, what is the ES equation?
ES = |mu 1 - mu 0|/ sigma
For one sample, continuous data, what is the sample size equation?
n = (z 1-a/2 + z 1-b / ES) ^2
How is beta values found?
based on the power percentage, the Z-table is used in reverse to find a value near the power % and the coordinate is the z 1-b value
How is alpha / 2 found?
same as beta
For one sample, dichotomous outcome, what is the ES equation?
ES = |p1 - p0| / root (p0 *(1 - p0)
For one sample, dichotomous outcome, what is the n equation?
n = same as one sample, continuous outcome
For two independent samples, continuous outcome, what is the ES equation?
ES = |mu 1 - mu 2| / sigma
For two independent samples, continuous outcome, what is the n equation?
n = 2 (z 1-a/2 + z 1-b/ES)^2
- value obtained is sample size PER independent sample
What is the n equation when factoring in attirition rate?
N (number to enroll) * % retained = desired sample size
% retained = 1 - attrition rate
For matched samples, continuous outcome, what is the ES equation?
ES = mu d / sigma d
For matched samples, continuous outcome, what is the n equation?
n = same as other n equation, NOT 2x
For two independent samples, dichotomous outcomes, what is the ES equation?
ES = |p1 - p2| / root (p*(1-p)
- p1: deisred proportion $ (20% OF the X% sample)
- p2: the current proportion %
- p: pooled proportion (desired p + current p/ 2, the average
For two independet samples, dichotomous outcomes, what is the n equation?
n = 2 (z 1-a/2 + z 1-b / ES) ^2
- value is # people needed PER group
