Statistics Flashcards
Median- The point/score at which 50% of scores fall below it and 50% fall above it
Median
This is the most general and least precise measure of central tendency
When two values occur the same number of times – Bimodal distribution
Mode - most frequently occurring value
Mode is more frequent than median and mean
negatively skewed
Mean, median, mode similar frequency
normal
Mode and median are more frequent than mean
positively skewed
quantifies the amount of variability, or spread, around the mean of the measurements.
To calculate: take each difference from the mean, square it, and then average the result
Variance (σ2)
To calculate: take each difference from the mean, square it, and then average the result
measure of variation of scores about the mean
Standard deviation (σ)
To calculate: take the √ of the variance
(the “average distance” to the mean)
In practice, the standard deviation is used more frequently than the variance.
Primarily because the standard deviation has the same units as the measurements of the mean.
When comparing two groups, the group with the larger standard deviation exhibits a greater amount of variability (heterogeneous) while the groups with smaller deviation has less variability (homogeneous
Standard deviation (σ)
A useful summary of a set of bivariate data (two continuous variables)
Gives a good visual picture of the relationship between the two variables, and aids the interpretation of the correlation coefficient or regression model.
Scatterplots
The absolute value of the coefficient (its size, not its sign) tells you how strong the relationship is between the variables.
Tells us how strongly two variables are related
Correlation Coefficient
“r” can not be > 1 or < -1
Closer to -1 or +1: the stronger the relationship
Closer to 0 : the weaker the relationship
Correlation Coefficient
The most common measure of association. Results can misleading if the relationship is non-linear
Pearson’s correlation is very sensitive to outlying values.
The statement of no difference or no relationship between the variables
Null hypothesis (Ho)
The statement that establishes a relationship between variables being assessed
Alternative hypothesis (Ha or H1)
Example: In a clinical trial the hypothesis states the new drug is better the placebo
error is made if we reject the null hypothesis when null hypothesis is true
type I
known as an acceptance error or an β error
if we fail to reject null hypothesis
Type II error
The probability of finding an effect
The probability of correctly rejecting the null hypothesis
The probability of seeing a true effect if one exists
Designers of studies typically aim for a power of 80% or 0.8
Implies there is an 80% chance of getting it right
Generally speaking: More people = more power
Statistical power
calculates the number of participants a study must have to draw accurate conclusions
power analysis
Takes into consideration: estimated effect size, sample means, etc
The probability of rejecting a true H0
α = .05 usually set, acceptable error
Statistical significance and p-value
Accepted value is 5% risk (p = .05)
Means there is a 5% chance that the results happened by chance
Allows us to reject or accept the null hypothesis
chance of random error
p
the acceptable error
α
p ≤ α
reject the H0
the results are statistically significant
p > α
fail reject the H0
the results not statistically significant
