Ch. 5: Overview of Inferential Statistics
Ch. 6: Probability
Ch. 7: Sampling Distributions
Inferential Statistical Procedure
procedures that uses a random sample from a population to make inferences (educated guesses) about the population.
uses random data in a RANDOM SAMPLE to estimate a parameter of the population from which the sample was drawn.
a numerical description of a population.
procedures that require the formulation of two opposing hypothesis about the population of interest. Data from random samples are used to determine which of the opposing hypotheses is more likely to be correct.
Parametric Hypothesis Testing
a type of hypothesis testing in which the hypotheses refers to a population parameter, the population mean or the population variance.
Nonparametric hypothesis testing
a type of hypothesis testing in which the specific hypotheses refer to the shape or location of the central tendency of the population rather than a specific parameter.
a sample that has been obtained in such a way that each observation in the population has an equal chance of being included in the sample, and the selection of one observation does not influence the selection of any other observation.
a sample that is selected from a population in such a way that some scores are more likely to be chosen than others so the sample will be less representative of the population.
Random Sampling with Replacement or independent (within sample) random sampling
a type of sampling in which scores are randomly drawn and is replaced back in the population before the next drawing.
an inference made about a population other than the one that was randomly sampled.
statistical notation for the total number of scores in a population.
statistical notation for the total number of scores in a given sample
a value, or range of values, on the variables being measured. Used to create simple probabilities.
numbers that indicate the likelihood that an event occurs in a single random observation from a population (a random sample with n = 1, I actually don't understand this paranthesis)
3 Axioms of Probability Theory
1) Probabilities are always between 0 and 1.
2)The probability that you will select an event in the population is 1.
3) The probability of one event or another is the sumo of the probabilities of the simpler events; the events must be mutually exclusive events.
Mean of a Probability Distribution
µ = Σ (X) * p (X)
Variance of a Probability Distribution
σ² = Σ (X - µ)² * p (X)
the mean of a probability distribution, or what the "anticipated" value for the mean of a random sample.
prediction of variance
probable variance of many random samples
mutually exclusive events
Events that cannot occur on the same observation. Events that occur indepdently of each other and that does not influencne each others occurance.
The probability of an event conditional upon the occurance of some other event or existence of a particular state of affairs. p (A | B)
A rule to calculate probabilities of mutually exclusive simple events by adding the probability of each simple event.
p (X = Event)
The probability of an event X from occuring in a given population
“scores” that are not individual measurements as in samples and populations but are STATISTICS that are calculated from a random sample.
Sampling Distribution of a Statistic
The probability distribution of the statistic computed from all possible random samples of the same size from the same population.
Amazing Fact Number 1
The mean of the sampling distribution of the sample mean, µm, is exactly equal to the mean of the population from which the samples were drawn.
Amazing fact number 2
The standard deviation of the sampling distribution of the sample mean ,σm, is exactly equal to the standard deviation of the population divided by the square root of the sample size.
Standard error of the Mean (Standard error of M)
The standard deviation of all of the Ms that are used in making up the sampling distribution.
Amazing Fact Number 3 (Central Limit Theorem)
as the sample size increases, the sampling distribution of the sample mean becomes a better and better approximation of a normal distribution.
Central Limit Theorem
No matter what shape (skewed or multimodal) the population is, as the sample size grows larger, the sampling distribution of the sample mean gets closer and closer to a normal distribution.
Sampling Distribution of the Sample Mean
A sampling distribution that contains all of the possible means for a particular sample size n.