CH 5, 6, 7, & 8
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Raw score | An original, untransformed observation or measurement.
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| 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.
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| Z-score transformation | A transformation that changes raw scores (X values) into z-scores.
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| Standard score | A score that has been transformed into a standard from.
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| Standardized distribution | An entire distribution that has been transformed to create predetermined values for µ and Theta
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| Z= | X-µ/ O
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| ZO = | X-µ = deviation score
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| X = | µ+ZO
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| Probability | Probability is defined as a proportion, a specific part out of the whole setoff possibilities.
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| Proportion | A part of the whole usually expressed as a fraction
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| Random sample | A sample obtained using a process that gives every individual an equal chance of being selected constant over a series of selections
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| 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.
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| Independent events | Two events are independent if the occurrence of either one has no effect on the probability that the other will occur.
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| Normal distribution | A symmetrical, bell-shaped distribution with proportions corresponding to those listed in the unit normal table.
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| Unit normal table | A table listing proportions corresponding to each Z-score location in a normal distribution.
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| Percentile | A score that is identified by the percentage of the distribution that falls below a specific score.
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| Percentile rank | The percentage of a distribution that falls below a specific score.
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| Binomial distribution | the distribution of probabilities, for each possible outcome, for a series of observations of a dichotomous variable.
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| (A)p = | Number of ways event A can occur / Total number of possible outcomes
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| z= | X – pn / √npq
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| µ = | pn
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| O = | √npq
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| 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
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| 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.
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| Expected value of M | The mean of the distribution of sample means. The average of the M values.
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| Standard error of M | The standard deviation of the distribution of sample means. The standard distance between a sample mean and the population mean.
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| The central limit theorem | A mathematical theorem that specifies the characteristics of the distribution of sample means.
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| Om= | O/√n or √((O^2)/n)
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| Z = | M-µ / Om
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| Hypothesis testing | A statistical procedure that uses data from a sample to test a hypothesis about a population
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| Null hypothesis, Ho | The null hypothesis states that there is no effect, no difference, or no relationship.
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| Alternative hypothesis, H1 | The alternative hypothesis states that there is an effect, there is a difference, or there is a relationship.
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| 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.
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| Type II error | A type II error is failing to reject a false null hypothesis. The test fails to detect a real treatment effect.
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| 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.
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| Level of significance | The level of significance is the alpha level, which measures the probability of a Type I error.
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| 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.
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| 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.
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| Beta (ß) | Beta is the probability of a Type II error.
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| 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.
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| Effect size | A measure of the size of the treatment effect that is separate from the statistical significance of the effect.
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| Power | The probability that the hypothesis test will reject the mull hypothesis when there actually is a treatment effect
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| (Type I Error) p | a
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| Type II Error) p | ß
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| Cohen’s d | Mean difference / Standard Deviation = M -µ / O
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