Review of Fundamentals Flashcards
Why do we need statistics?
Reasonable people eyeballing would likely disagree if treatment was effective or not
What is the use of statistics?
Help us determine if the relation between two variables is large enough so that we can assume it did not happen by chance
What are the four steps of null hypothesis testing?
1st – assume that in the population groups are not different
2nd – calculate the statistic of interest
3rd – ask: if groups are not different than population, what is the probability of getting a difference this large by chance?
4th – Determine whether or not to reject H0
What Does it mean that something is Statistically significant?
It would be very unusual to get this difference if chance variation were the only thing. Only 5 (p < 0.05), or 1 (p < 0.01), times out of 100. Therefore, there must be something other than chance.
Define variance
Average, squared, variation in a set of scores
What is the formula for variance?
V = ∑(X - M)^2 /(N - 1)
What is the standard deviation (SD)?
The square root of the variance
What is the advantage of using standard deviation instead of variance?
Variance is in units squared, and may be confusing. Standard deviation is in the original units of the measurement.
What are Z scores?
Scores transformed into units of Standard deviations (SD)
How are Z scores related to other standard scores?
Z scores are the “parent” of all other standard scores, and you can easily convert from Z scores to any of the other types)
Define skew.
distribution has an extended tail in one direction
Define kurtosis.
flatness or peakedness of the distribution
What % of a normal distribution is between -1SD and +1SD?
68%
What % of a normal distribution is between -2SD and +2SD?
96%
What is the relationship between the Frequency distribution of sample means and the distribution of original scores?
- Frequency distribution is narrower (means are more stable)
- SD smaller
What is the Standard Error(SE) of the mean?
SD of the Frequency distribution of sample means
What does the SE of sample means reflect?
the error likely inherent in any estimate of the mean (can estimate from a single sample)
What is the relationship between N and SE?
as N increases, SE decreases
What useful info does the Frequency distribution of sample means and its SD (SE) provide?
amount of variabilty (error) in a distribution of means
- a narrow curve with small SD → most samples provide fairly accurate estimates of the real population mean
- a wide curve with large SD → many estimates error laden
What are Confidence Intervals (CI)?
bands of error around a statistic
CI = M +- SE(z score of desired alpha)
What does a 95% CI imply?
There is a 95% chance that the true population statistic (mean, etc) is between upper and lower bounds.
What is a t test?
a general statistical formula in which a statistic is divided by its SE.
t = statistic/SE
How to determine statistical significance using a t test?
look up the probability of obtaining a given t value (with a certain sample size), if p is small (<5%) → statistically significant
Define degrees of freedom (df).
- degree to which a given parameter is free to vary
- how much “wiggle room” you have in your data
- number of independent pieces of info in data
Define Pearson correlation coefficient (r)
describes the degree to which 2 variables are related
- 1.0 = perfect Inverse relation
0. 0 = no relation
1. 0 = perfect Direct relation
Effect Size
If statistically significant is the effect large or small;
d commonly used for two-group experimental research (like a z score)
d = (Me-Mc)/SD (d = 0.2, 0.5, 0.8 → sm, med, lg)
What do t tests and ANOVA have in common?
they are subsets of Multiple Regression
When is a t test appropriate?
only 1 independent variable (IV), and only 2 groups
When is ANOVA appropriate?
more than 2 groups or more than 1 IV (will give same results as t test for 2 groups and 1 IV)
What is a F test
test for significance for ANOVA
F = t^2 = V{between groups} / V{within groups}
What is the df for an F test?
requires 2 df values corresponding to the treatment and error within group)
df{total} = N-1
df{treatment} = (# groups) - 1
df{error} = df{total} - df{treatment}
What is the similarity between F in ANOVA and F in regression?
both divide the variance explained by the IV BY the variance left unexplained
What is eta squared (η^2)?
measure of effect size (sililar to R^2)
η^2 = 0.01 small effect
η^2 = 0.1 medium effect
η^2 = 0.25 large effect
What is Cohen’s ƒ (ƒ^2)?
measure of effect size (calculated from η^2)
ƒ^2 = η^2 / (1-η^2)
ƒ^2 = 0.02 small effect
ƒ^2 = 0.15 medium effect
ƒ^2 = 0.35 large effect
