## CH 5, 6, 7, & 8

Raw score An original, untransformed observation or measurement.
Z-score A standardized score with a sign that indicates direction from the mean (+ above µ and – below µ), and a numerical value equal to the distance from the mean measured in standard deviation.
Z-score transformation A transformation that changes raw scores (X values) into z-scores.
Standard score A score that has been transformed into a standard from.
Standardized distribution An entire distribution that has been transformed to create predetermined values for µ and Theta
Z= X-µ/ O
ZO = X-µ = deviation score
X = µ+ZO
Probability Probability is defined as a proportion, a specific part out of the whole setoff possibilities.
Proportion A part of the whole usually expressed as a fraction
Random sample A sample obtained using a process that gives every individual an equal chance of being selected constant over a series of selections
Sampling with replacement A sampling technique that returns the current selection to the population before the next selection is made. A required part of random sampling.
Independent events Two events are independent if the occurrence of either one has no effect on the probability that the other will occur.
Normal distribution A symmetrical, bell-shaped distribution with proportions corresponding to those listed in the unit normal table.
Unit normal table A table listing proportions corresponding to each Z-score location in a normal distribution.
Percentile A score that is identified by the percentage of the distribution that falls below a specific score.
Percentile rank The percentage of a distribution that falls below a specific score.
Binomial distribution the distribution of probabilities, for each possible outcome, for a series of observations of a dichotomous variable.
(A)p = Number of ways event A can occur / Total number of possible outcomes
z= X – pn / vnpq
µ = pn
O = vnpq
Distribution of sample means The set of sample means from all the possible random samples for a specific sample size (n) from a specific population
Sampling distribution a distribution of statistics (as opposed to a distribution of scores). The distribution of sample means is an example of a sampling distribution.
Expected value of M The mean of the distribution of sample means. The average of the M values.
Standard error of M The standard deviation of the distribution of sample means. The standard distance between a sample mean and the population mean.
The central limit theorem A mathematical theorem that specifies the characteristics of the distribution of sample means.
Om= O/vn or v((O^2)/n)
Z = M-µ / Om
Hypothesis testing A statistical procedure that uses data from a sample to test a hypothesis about a population
Null hypothesis, Ho The null hypothesis states that there is no effect, no difference, or no relationship.
Alternative hypothesis, H1 The alternative hypothesis states that there is an effect, there is a difference, or there is a relationship.
Type I error A type I error is rejecting a true null hypothesis. You have concluded that a treatment does have an effect when actually it does not.
Type II error A type II error is failing to reject a false null hypothesis. The test fails to detect a real treatment effect.
Alpha (a) Alpha is a probability value that defines the very unlikely outcomes if the mull hypothesis is true. Alpha also is the probability of committing a Type I error.
Level of significance The level of significance is the alpha level, which measures the probability of a Type I error.
Critical region The critical region consists of outcomes that are very unlikely to be obtained if the null hypothesis is true. The term very unlikely is defined by (alpha) a.
Test statistic A statistic that summarizes the sample data in a hypothesis test. The test statistic is used to determine whether or not the data are in the critical region.
Beta (?) Beta is the probability of a Type II error.
Directional (one-tailed) test A directional test is a hypothesis test that includes a directional prediction in the statement of the hypotheses and place the critical region entirely in one tail of the distribution.
Effect size A measure of the size of the treatment effect that is separate from the statistical significance of the effect.

Power The probability that the hypothesis test will reject the mull hypothesis when there actually is a treatment effect
(Type I Error) p a
Type II Error) p ?
Cohen’s d Mean difference / Standard Deviation = M -µ / O