ERA153

Summarize a data set

• reveal the larger group through the smaller group's characteristics
• representative samples

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

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

• allows ranking
• greater than
• less than
• percentile scores

indicates degree of difference

• includes a zero
• uncommon in educational measurement

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

mode, median, mean

most frequently occuring measure in a group

one mode

two modes

• 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

liar all values according to stem (the numbers preceding the final value) and leave (the final digit)

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.

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
• skewness
• defines how bunched up the data is

• Normal distribution
• standard deviation is about 1/6 R

• distribution with too much variability
• Standard deviation is greater than 1/6 R

• little variability
• standard deviation is less than 1/6 R

there is only one standard normal distribution

• scores = 0
• standard deviation = 1

created so that it has a prespecifiied mean and standard deviation

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

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

indicates that error diminishes as sample size increases

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.

occurs when one incorrectly concludes that a result isn't statistically significant.

intervals within which the population mean represented by a sample will probably occur.

characteristics of sample v characteristics of population