Chapter 3 - Key Ingredients for Inferential Statistics

Z-Scores

Number of standard deviations that a score is above (or below, if it is negative) the mean of its distribution; it is thus an ordinary score transformed so that it better describes the score’s location in a distribution

Raw Score

An ordinary score (or any number in a distribution before it has been made into a Z score or otherwise transformed).

Normal Distribution

Frequency distribution that follows a normal curve

Normal Curve

Specific, mathematically (or theoretically) defined, bell-shaped frequency distribution that is symmetrical and unimodal; distributions observed in nature and in research commonly approximate it.

Normal Curve Table

Table showing percentages of scores associated with the normal curve; the table usually includes percentages of scores between the mean and various numbers of standard deviations above the mean and percentages of scores more positive than various numbers of standard deviations above the mean.

Population

An entire group of people to which a researcher intends the results of a study to apply; larger group to which inferences are made on the basis of the particular set of people (sample) studied

Sample

Scores of the particular group of people studied; usually considered to be representative of the scores in some larger population.

Random Selection

A method for selecting a sample that uses truly random procedures (usually meaning that each person in the population has an equal chance of being selected); one procedure is for the researcher to begin with a complete list of all the people in the population and select a group of them to study using a table of random numbers.

Population Parameters

The actual value of the mean, standard deviation, and so on, for the population; usually population parameters are not known, though often they are estimated based on information in samples. Usually shown as Greek letters.

μ

population mean

σ²

population variance.

σ

population standard deviation

Sample Statistics

Descriptive statistics, such as the mean or standard deviation, figured from the scores in a group of people studied.

Probability

The expected relative frequency of an outcome; the proportion of successful outcomes to all outcomes

Outcome

The term used in discussing probability for the result of an experiment (or almost any event, such as a coin coming up heads or it raining tomorrow).

Expected relative frequency

A number of successful outcomes divided by the number of total outcomes you would expect to get if you repeated an experiment a large number of times. (Ex. Flipping a coin and getting heads 8/12 times)

Long-run relative-frequency interpretation of probability

Understanding of probability as the proportion of a particular outcome that you would get if the experiment were repeated many times. (Ex. Repeatedly flipping a coin and eventually expecting to get heads ½ times.)

Subjective interpretation of probability

A way of understanding probability as the degree of one’s certainty that a particular outcome will occur.

Multiplication Rule

This is used to find the probability of getting both of two independent outcomes. (Ex. If you have a 20% chance to get into UVA and 30% chance of getting into W&M, you have a 6% of getting into both schools.)