Probability
in a situation where several different outcomes are possible, the fraction or proportion for any particular outcome; number of outcome/ total number of possible outcomes
Random sample
a sample that is collected such that each member of the population is equally likely to be selected into the sample and the probability of being selected remains constant across selections
Sampling with replacement
a sampling strategy that requires selected individuals to be returned to the pool of potential subjects after each selection
Sampling without replacement
a sampling strategy in which selected individuals are not returned to the pool of potential subjects after each selection
Unit Normal Table
table used to identify the proportion of observations that lie at or beyond a particular z-score in a normal distribution
Sampling error
the discrepancy, or amount of error, between a sample statistic and its corresponding population parameter
Distribution of sample means
the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population
Sampling distribution
a distribution of statistics obtained by selecting all the possible samples of a specific size from a population
Central Limit Theorem
for any population with mean, ?, and standard deviation, ?, the distribution of sample means for sample size n will have a mean of ? and a standard deviation of ?/sqrt of n and will approach a normal distribution as n approaches infinity
Expected value of M
?
Standard error of the mean
standard deviation of the distribution of sample means
The law of large numbers
the larger the sample size (n), the more probable it is that the sample mean will be close to the populations mean
Hypothesis test
a statistical method that uses sample data to evaluation a hypothesis about a population parameter
Null hypothesis
statement that there is no difference, no change, or no relationship
Alternative hypothesis
statement that there is a change, difference, or relationship
Alpha level
level of significance - probability value used to define the cut-off point for very unlikely sample outcomes if the null hypothesis is true
Critical region
region composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true. Boundaries of the critical region are determined by alpha - when sample values fall in the critical region, the null hypothesis is rejected
Test statistic
sample data are converted into a single, specific statistic that will be used to test the hypothesis
Type I error
occurs when a researcher rejects the null hypothesis when it is actually true; researcher concludes that there is a difference or an effect when there actually is none; alpha reflects the probability of committing a Type I error.
Type II error
occurs when a researcher fails to reject the null hypothesis when it is really false; the researcher concludes that there is no difference or effect when there actually is a difference or effect.
Null distribution
of sample means that assumes the null hypothesis is correct
Statistically significant
the null hypothesis is rejected
One-tailed test
the statistical hypotheses specify either an increase or decrease in the population mean score
Effect size
the absolute size of the difference between the means
Cohen's d
standardizes effect size by measuring the mean difference in terms of the standard deviation
Power
the probability that the null hypothesis will be rejected when there really is a difference (treatment effect)
Estimated standard error
sM an estimate of the real standard error of the mean (SDM) when the value of SD is unknown; computed from the sample variance or sample standard deviation and used to estimate the standard distance between a sample mean and the population mean
t-statistic
used to test hypotheses about a population when the value of the population variance (and standard deviation) is unknown; uses the same formula as the z-statistic except that the estimated standard error is substituted for the standard error in the denomi
degrees of freedom
describe the number of scores in a sample that are free to vary. Because the sample mean restricts the value of one score in the sample (i.e., if you know all but one values, the final value is determined), there are n-1 degrees of freedom for the sample
r2
the percentage (proportion) of variance accounted for by the independent variable