Z scores normal distributions probability Flashcards
What is a Z score?
How far a raw score is away from the mean in SD units
Z score distribution has a mean of ? and SD of ?
mean of zero, SD of 1
Psychologist transform raw scores to z scores to be able to?
compare scores that are measured on different scales.
put scores from different distributions into one language
What is the mean and SD in an IQ test
mean = 100 and SD = 15
The difference between statistics of samples and their corresponding population parameters is called….
Sampling error
Sampling distribution is..
A distribution of statistics obtained by selecting all the possible samples of a specific size (n) from a population. You obtain MANY samples from a population and plot on a frequency graph and you get a sampling distribution ( usually normal in shape)
The distribution of sample means
collection of sample means for all possible samples forms a normal l distribution ( hypothetically mean of all samples will equal population means)
All probability problems can be restated as proportion problems. The“probability of selecting a king from a deck of cards” is equivalent to the “proportion of the deck that consists of kings.”
For frequency distributions, probability questions can be answered by determining proportions of area. The “probability of selecting an individual with an IQ greater than 108” is equivalent to the “proportion of the whole population that consists of IQs greater than 108.”
The binomial distribution is used whenever the measurement procedure simply classifies individuals into exactly two categories.
The two categories are identified as A and B, with probabilities of
p(A) = p and p(B) = q
Percentiles and percentile ranks measure the relative
standing of a score within a distribution (see Box 6.1).
Percentile rank is the percentage of individuals with
scores at or below a particular X value. A percentile is
an X value that is identified by its rank. The percentile
rank always corresponds to the proportion to the left
of the score in question.
For normal distributions, probabilities (proportions)
can be found in the unit normal table.
The table provides a listing of the proportions of a normal distribution that correspond to each z-score value. With the table, it is possible to move between X values and probabilities using a two-step procedure:
a. The z-score formula (Chapter 5) allows you to
transform X to z or to change z back to X.
b. The unit normal table allows you to look up the
probability (proportion) corresponding to each
z-score or the z-score corresponding to each
probability.
