ERA153
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Descriptive Statistics
Summarize a data set

Inferential Statistics
 reveal the larger group through the smaller group's characteristics
 representative samples

Population
all the members of a defined group

Sample
 any subset of a population
 works for interval data
 works for ratio data

Qualitative variables
differ by category rather than by amount but there are measurable differences

Constants
never vary, hold little analytical value

Variables
they have different manifestations

A Research Design
formal plan for gathering and analyzing data

Independent Variable
the variable thought to affect another

Dependent variable
the variable influenced

Data Scale
different kinds of measures gauge different qualities

Measurement
using rules to asign numbers

Nominal data
indicate a category, yields the least amount of information about an object

Ordinal data
 allows ranking
 greater than
 less than
 percentile scores

Interval data
indicates degree of difference

Ratio data
 includes a zero
 uncommon in educational measurement

Interval Scale Data
how much greater or less

Descriptive Statistics
calculated so that one can know the essential characteristics of data sets without having to refer to each individual measure.

Central tendency
most typical in a data set

Measures of Central Tendency
mode, median, mean

Mode
most frequently occuring measure in a group



Median
 the point below which half the scores in the group occur.
 isn't calculated as much as it is identified.
 the middle most number

Mean
most commonly used measure of central tendency is the arithmetic average

Outliers
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.

Range
the difference between the highest and the lowest

Quartiles
Fourths of the range

Interquartile Range
stretches from the 25th to the 75th percentile in a distribution.

Semiinterquartile Range
half the interquartile range

Variance
the sum of the squared score to mean differences divided by n1

Standard Deviation
the square root of the variance

Frequency Distribution
data are displayed so that their variety and their frequency of occurrence are both apparent.

Class Intervals
grouping the data in a frequency distribution rather than listing them individually

Apparent Limits
represented by the lowest and highest integers in the category

Actual Limits
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

Quadrant
graphs are created by vertical and horizongal ines which intersect at right angles. The four sections which result are each called a quadrant.

Normal Distribution
Gaussian Distribution
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

positive skew
when the mean is larger than the median

negative skew
when the mean is smaller than the median

Kurtosis
 describes how much spread there is in a distribution
 skewness
 defines how bunched up the data is

Mesokurtic
 Normal distribution
 standard deviation is about 1/6 R

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

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

Standard Normal Distribution
there is only one standard normal distribution

Z transformation
 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

Sampling Error
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.

Statistically Significant
that an outcome isn't likely to have occured by chance

Alpha level
 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