inferential statistics

z score formula

(raw score-mean)/standard deviation

standard deviation

a measure of variability that describes an average distance of every score from the mean

Conditions for the central limit theorem

1. Independence - sampled observations must be independent (random sample/assignment). If sampling without replacement, n < 10% of population 2. Sample size/skew: Either population distribution is normal, or if it's skewed, the sample size is large (rule of thumb: n > 30).

z-score

a type of standard score that tells us how many standard deviation units a given score is above or below the mean for that group

sampling variability

How estimates vary from one sample to another

CLT 10% condition

If sampling without replacement (potato sack example), n < 10% of the population. This increases the possibility that items in the sample are independent (eg, you and a family member are less likely to both be chosen).

68%, 95%, 99.7%

Roughly 95% of random samples will have sample means that are within two SEs of the population mean. This means that for 95% of random samples, the unknown true population mean will be within 2 SEs of that sample's mean. 99.7% of the distribution will be within 3 SD of the mean.

Skewed Left Distribution

Tail on the left. Mean less than the median.

Confidence Interval

The plausible range of values for a population parameter. "We are XX% confident that the true population parameter is in this interval," where XX% is the desired confidence level.

sample distribution

The set of values in a sample of measurements, as opposed to the population distribution.

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution (the less variable the means become). According to the Central Limit Theorem (CLT), the distribution of sample means (the sampling distribution) should be nearly normal. The mean of the sampling distribution should be approximately equal to the population mean (0) and the standard error (the standard deviation of sample means) should be approximately equal to the SD of the population divided by square root of sample size (1/sqrt(102) = 0.1)

point estimate

The value of a point estimator used in a particular instance as an estimate of a population parameter. alternative to CI, not likely to hit exact population parameter

criterion validity

an empirical form of measurement validity that establishes the extent to which a measure is correlated with a behavior or concrete outcome that it should be related to

Point estimates

an estimate of the population mean in the form of a single value, usually the sample mean

x̅

mean of a sample; x bar

μ

mu, population mean

standard distribution of Z scores

normal distribution: mean 0 and SD 1

sample statistics

numerical descriptions of sample characteristics

Confidence level

percentage of random samples which yield CIs that capture the true population parameter

σ

standard deviation of a population

content validity

the degree to which individual items reflect the construct being measured

concurrent validity

the degree to which the measures gathered from one tool agree with the measures gathered from other assessment techniques

margin of error

the range of percentage points in which the sample accurately reflects the population

standard error

the standard deviation of a SAMPLING distribution. σ/sqr of n. N and SE are inversely proportional, so if n goes up, the SE will go down.

Confidence interval for a population mean

x-bar ± z* +/- (s / square root n) Computed as the sample mean plus/minus a margin of error (critical value corresponding to the middle XX% of the normal distribution times the SE of the sampling distribution).

95% CI formula

xbar +/- 2SE. 2SE = margin of error.