reveal the larger group through the smaller group's characteristics
all the members of a defined group
any subset of a population
works for interval data
works for ratio data
differ by category rather than by amount but there are measurable differences
never vary, hold little analytical value
they have different manifestations
A Research Design
formal plan for gathering and analyzing data
the variable thought to affect another
the variable influenced
different kinds of measures gauge different qualities
using rules to asign numbers
indicate a category, yields the least amount of information about an object
indicates degree of difference
includes a zero
uncommon in educational measurement
Interval Scale Data
how much greater or less
calculated so that one can know the essential characteristics of data sets without having to refer to each individual measure.
most typical in a data set
Measures of Central Tendency
mode, median, mean
most frequently occuring measure in a group
the point below which half the scores in the group occur.
isn't calculated as much as it is identified.
the middle most number
most commonly used measure of central tendency is the arithmetic average
measures in a group that are so high or so low compared to the others that they will have an undue effect on the statistics.
the difference between the highest and the lowest
Fourths of the range
stretches from the 25th to the 75th percentile in a distribution.
half the interquartile range
the sum of the squared score to mean differences divided by n-1
the square root of the variance
data are displayed so that their variety and their frequency of occurrence are both apparent.
grouping the data in a frequency distribution rather than listing them individually
represented by the lowest and highest integers in the category
extend the interval up and down by 1/2 point
Stem and Leaf Display or Stem Plots
liar all values according to stem (the numbers preceding the final value) and leave (the final digit)
Pie Charts and Bar Charts
used to represent proportional differences in data categories either by triangular wedges or with bars of different sizes
graphs are created by vertical and horizongal ines which intersect at right angles. The four sections which result are each called a quadrant.
takes on the bell shape because it is symmetrical and unimodal and the standard deviation is 1/6 of the range.
Point of Inflection
a normal curve moves outward more quickly than downward occurs at +/- one standard deviation from the mean
when the mean is larger than the median
when the mean is smaller than the median
describes how much spread there is in a distribution
defines how bunched up the data is
standard deviation is about 1/6 R
distribution with too much variability
Standard deviation is greater than 1/6 R
standard deviation is less than 1/6 R
Standard Normal Distribution
there is only one standard normal distribution
scores = 0
standard deviation = 1
Modified Standard Score
created so that it has a prespecifiied mean and standard deviation
The Distribution of Sample Means
population based on the means of samples rather than on individual scores. it allows one to determine whether a particular sample is likely to have been drawn from the specified population which is the z test
Central Limit Theorem
A population of sample means will be normal even if the distribution of individual scores wasn't
the difference between characteristics of the sample and those of the population
law of large numbers
indicates that error diminishes as sample size increases
Standard Error of the Mean
measure of variability in the distribution of sample means. It is the standard deviation of all the sample means that constitute the distribution of sample means.
that an outcome isn't likely to have occured by chance
the probability of incorrectly determining a statistically significant result
occurs if when the null hypothesis is erroneously rejected.
if further testing with new data indicates that the initial finding of statistical significance was in errror, an alpha error occured with that first test.
Type II or Beta error
occurs when one incorrectly concludes that a result isn't statistically significant.
Confidence Intervals for Z
intervals within which the population mean represented by a sample will probably occur.
stastistics v. parameters
characteristics of sample v characteristics of population