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Descriptive Statistics
are methods used to provide a concise description of a collection of quantitative information.
Inferential Statistics
are methods used to make inferences from observations of a small group of people known as a sample to a larger group of individuals known as a population.
Magnitude
A scale has the property of magnitude if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance.
Equal Intervals
A scale has the property of equal intervals if the difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units.
Absolute 0
is obtained when nothing of the property being measured exists.
Nominal Scale
their only purpose is to name objects. For example, the numbers on the backs of football players’ uniforms are nominal
Ordinal Scale
This scale allows you to rank individuals or objects but not to say anything about the meaning of the differences between the ranks.
Interval Scale
When a scale has the properties of magnitude and equal intervals but not absolute 0, we refer to it as an interval scale.
Ratio Scale
A scale that has all three properties (magnitude, equal intervals, and an absolute 0) is called a ratio scale.
Frequency Distribution
displays scores on a variable or a measure to reflect how frequently each value was obtained.
Percentile Ranks
Percentile ranks replace simple ranks when we want to adjust for the number of scores in a group.
Percentiles
are the specific scores or points within a distribution. _________ divide the total frequency for a set of observations into hundredths.
Mean
The arithmetic average score in a distribution is called the mean. To calculate the mean, we total the scores and divide the sum by the number of cases, or N.
Standard Deviation
The standard deviation is an approximation of the average deviation around the mean.
Variance
You can square all the deviations around the mean in order to get rid of any negative signs. Then you can obtain the average squared deviation around the mean, known as the variance.
Z-Score
is the deviation of a score Xi from the mean in standard deviation units. The ________ transforms data into standardized units that are easier to interpret.
Standard Normal Distribution
also known as the Z-distribution, is a special case of the normal distribution with a mean of 0 and a standard deviation of 1.
Quartiles
are points that divide the frequency distribution into equal fourths.
Deciles
are similar to quartiles except that they use points that mark 10% rather than 25% intervals.
Norms
refer to the performances by defined groups on particular tests. There are many ways to express norms, and we have discussed some of these under the headings of Z scores, percentiles, and means.
Age Norms
refer to the typical or average ages at which certain events, behaviors, or developments occur within a population. Certain tests have different normative groups for particular age groups. Most IQ tests are of this sort.
Tracking
can refer to various concepts depending on the context, including tracking changes over time, monitoring the performance of models or processes, and following the movement or progression of specific data points.
This tendency to stay at about the same level relative to one’s peers is known as tracking.
Criterion-Referenced Tests
describes the specific types of skills, tasks, or knowledge that the test taker can demonstrate such as mathematical skills.
Scatter Diagram
is a picture of the relationship between two variables.
Correlation
is a mathematical index that describes the direction and magnitude of a relationship.
Regression
A related technique, known as regression, is used to make predictions about scores on one variable from knowledge of scores on another variable.
Spearman’s RHO
is a method of correlation for finding the association between two sets of ranks.
Residual
The difference between the predicted and the observed values is called the residual.
Coefficient of Determination
is known as the coefficient of determination.
Coefficient of Alienation
is a measure of non-association between two variables.