Stats review Flashcards
Population variance:
the average of the distances from the mean within a population distribution of scores
Parameter:
numerical characteristic of a population distribution of scores
Sample variance:
the average of the distances from the mean within a sample distribution of scores
Statistic:
numerical characteristic of a sample distribution of scores
sigma squared
population variance
Standard normal distribution:
X is distributed normally with a mean of 0 and variance of 1
standard normal distribution +/- 1 SD contains __% of scores
68
standard normal distribution +/- 2 SD contains __% of scores
95
standard normal distribution +/- 3 SD contains __% of scores
99
Random:
each observation has an equal and independent probability of being selected
Sampling distribution:
frequency distribution of a particular statistic (ex. Sample mean) obtained from repeated sampling from the population
standard error of mean
standard deviation of sampling distribution of mean
how to interpret standard error of mean?
average distance of possible sample means from the true population mean u
as sample size increases, standard error of mean ____
decreases
law of large numbers
As sample size increases, x bar will approach u
95% Confidence interval
In repeated samples, 95 of 100 confidence intervals calculated in this way will contain the true value of the mean difference in the population.
Central limit theorem: what happens as sample size increases?
As sample size N increases, the sampling distribution of the mean more closely approximates a normal distribution (even if the original distribution of X is not normal) AND the mean of the sampling distribution of the mean will more closely resemble the population mean
p-value:
the probability of finding a test statistic more extreme than the one we found if the null hypothesis is true
critical value
point at which you would reject the null if sample means exceeds the critical value
Type I error
reject the null hypothesis when the null hypothesis is true (alpha)
Type II error
fail to reject the null hypothesis when the null hypothesis is false (beta)
alpha is equal to what type of error?
1
beta is equal to what type of error?
2
Power:
probability of rejecting the null hypothesis when it is false
probability of detecting an effect when the effect exists
Relationship between power and beta?
power=1-beta
What happens to power when alpha increases?
increases
what happens to power when sample size increases? and why?
as n increases, power will increase due to smaller standard error
what happens to power when population SD increases
if sigma increases, power decreases
what happens to power when effect size increases?
As effect size increases, power increases
Which has more power: one-tailed or two-tailed test?
One-tailed
one-sample z test? which distribution does it use?
inference about a single population value when standard deviation is KNOWN
*uses standard normal distribution
t-test? which distribution does it use?
A statistical test used to make an inference about one or two values when standard deviation is UNKNOWN that uses the t-distribution
when does t distribution approach normal distribution?
as degrees of freedom increases
degrees of freedom
number of independent pieces (values) free to vary given the summary statistic (N-number of things you are estimating)
correlation
Correlation: linear relationship between x and y; between -1 and 1, implies direction and strength of the relationship, **independent of the scales of x and y
true or false: covariance is independent of the scales of x and y
false
true or false: correlation is independent of the scales of x and y
true
how to calculate t statistic?
coefficient/standard error
how do you standardize a variable?
subtract mean and then divide by sd
