Psych Stats Quiz #2 4/10/23 Flashcards
normal distribution characteristics
unimodal, symmetric, asymptotic
empirical rule
approx. 68% of values are within 1 standard deviation of the mean
approx. 95% of the values are within 2 standard deviations of the mean
approx. 99.7% of the values are within 3 standard deviations of the mean
z scores (standard scores)
to make direct comparisons by transforming raw scores by standardizing them and converting them to a z score
computing z score formula
Z = (X - mean)/standard deviation
positive/negative z scores
a positive z score means above the mean, negative z score means below the mean
properties of standard z scores
mean of a set of z scores is always 0 and the standard deviation is always 1
the distribution of a set of standardized z scores has the same shape as the unstandardized scores (raw)
starting with z score and work backward
X = mean + z score (standard deviation)
percentile scores
the proportion of people with scores less than or equal to a particular score, percentile scores are ways of summarizing a person’s location in a larger set of scores
p-th percentile
a number such that at most p percent of the measurements are below it and at most 100-p percent of the data are above it
ex. 85th percentile is 340 meaning that 15% of the measurements in the data are above 340 and that 85% are below 340
the disadvantage of standard scores
1) because a person’s score is expressed relative to the group, that same person can have different z-scores when assessed in different samples
2) if the absolute score (raw) is meaningful it would be obscured by transforming it into a relative metric
ex. IQ of 140 has a meaning that is lost when
transformed into a z score
relative frequency from the mean
calculate the relative frequency of scores between a particular score and the mean by finding the z score and then subtracting it from the standard deviation
ex. GPA mean = 2, standard deviation = 0.5
Friend GPA = 1.5
1.5-2/0.5 = -1 —> 0.1587 or 15.87%
0.5 of the scores are below the mean so relative frequency between -1 and the mean = 0.5 - .1587 = 0.3415 or 34.15%
relative frequency of scores between two scores
calculate z score and then subtract smallest from the biggest to get the percentage of scores in between the two numbers
ex. x = 2.25 and x = 3.5
2.25 -2/5 = 0.5
3.5-2/5 = 3
both scores are above the mean (+)
z of 0.5 = 69.15% and z of 3.0 = 99.86%
0.9986-0.6915 = .3071 or 30.71% of the GPA is in between the two scores
characteristics of z scores
a measure of relative standing in distribution
facilitate comparison across distributions by standardizing the meaning of zero and the meaning of one unit
inferential statistical procedure
uses a random sample from a population to make inferences about the population
parameter estimation
uses data in a random sample to estimate a parameter of the population from which the sample was drawn
hypothesis-testing
requires the formulation of two opposing hypotheses about the population of interest
data from random samples are used to determine which of the opposing hypotheses is likely to be correct
parametric hypothesis testing
the hypotheses refer to population parameters, usually the mean of the variance of the population
nonparametric hypothesis testing
the specific hypotheses refer to the shape or location (central tendency) of the populations, rather than specific parameters
steps to produce a random sample
write observations on paper and draw from a hat because each observation has an equal chance of being picked out of the hat
biased sampling
ex. a university dean wants to gather data on graduation requirement changes and stops every 5th student entering the student union
seems random but is biased because the students that frequent the library would be systematically excluded from the sample
overgeneralization
an inference about a population other than the one that was randomly sampled
event
a value or range of values on the variables being measured
simple probabilities
numbers that indicate the likelihood that an event occurs in a simple random observation from population
mutually exclusive events
cannot occur on the same observation
conditional probability
the probability of an event conditional upon the occurrence of some other event or the existence of a particular state of affairs
