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# Stat Exam 2

### CH 5, 6, 7, & 8

Question | Answer |
---|---|

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 / √npq |

µ = | pn |

O = | √npq |

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/√n or √((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 (ß) | 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 | ß |

Cohen’s d | Mean difference / Standard Deviation = M -µ / O |

Created by:
ehlertbm