Norms and Basic Statistics for Testing

Using number systems allow us to manipulate information

Why We Need Statistics?

Statistical methods serve two important purposes to aid in scientific understanding

•Statistics are used to make descriptions

Numbers provide convenient summaries and allow us evaluate some observations relative to

others

•Statistics are used to make inferences: which are logical deductions about events that cannot be

observed directly

First, clues are gathered and displayed (also called exploratory data analysis)

Then, clues are evaluated against rigid statistical rules, through a process called confirmatory

data analysis

Descriptive statistics: are methods used to provide a short 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 called a population

Scales of Measurement

Measurement: the application of rules for assigning numbers to objects

Example - wine may be rated on a 10-point scale where 1 means extremely bad and 10 means extremely

good

Properties of Scales

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Magnitude, equal intervals, and an absolute 0 make scales different from one another

Magnitude: is the property of “moreness”

•A scale has the property of magnitude if a particular instance of the attribute represents more,

less, or equal amounts of the given quantity than does another instance

•When a coach assigns identification numbers to teams, it does not have this property

•When a coach ranks the team by the number of games they have won, the property of magnitude

exists

Equal intervals: exists 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

•Psychological tests rarely have equal intervals

•The difference between an IQ of 65 and 70 is not the same as the difference between 85 and 90

•When a scale has the property of equal intervals, the relationship between the measured units and

some outcome can be expressed by a straight line or a liner equation in the form of y= mx + b

Absolute 0: is obtained when nothing of the property being measured exists

•When heart rate is 0, the individual has died

•Extremely difficult for many psychological qualities to have an absolute 0 point

Types of Scales

Nominal: the lowest measurement scale

•Placement of data into categories, without any order or structure

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•Purpose is to name objects and used when the information is qualitative rather than quantitative

•No magnitude, no equal intervals, no absolute 0

Ordinal: allows you to rank individuals or objects but no meaning of the differences between the ranks

•Ranking five types of beer from most flavorful to least flavorful

•No equal intervals, no absolute 0

•For most problems in psychology, ordinal scales are used

Interval: has a magnitude and equal intervals, but no absolute zero

•Temperature has the property of magnitude because 60C is warmer than 45C

•The difference between 100C and 90C is equal to a similar difference of 10C at any point on the

scale

•An absolute zero does not exist, because zero on the scale represents the freezing point of water

Ratio: has a magnitude, equal intervals, and an absolute zero

•Allows ratios of numbers to be meaningfully interpreted, such as the ratio of John’s height to

Sarah’s height is 1.52

•The speed of travel has an absolute zero, and if you are driving onto a highway you speed

increases by double the amount

Levels of measurements defines which mathematical operations we can apply to numerical data

•Nominal data - each observation can placed in only one mutually exclusive category (example,

you are a member of only one gender)

Used to create frequency distributions

•Ordinal data - can be manipulated, but the result is difficult to interpret because it does not reflect

the magnitude of the manipulated observations nor the true amounts of the property

If the weights of 10 children are rank ordered, knowing the rank does not reveal how tall he or she

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## Document Summary

Using number systems allow us to manipulate information. Statistical methods serve two important purposes to aid in scientific understanding. numbers provide convenient summaries and allow us evaluate some observations relative to others. Statistics are used to make inferences: which are logical deductions about events that cannot be observed directly. first, clues are gathered and displayed (also called exploratory data analysis) then, clues are evaluated against rigid statistical rules, through a process called confirmatory data analysis. Descriptive statistics: are methods used to provide a short 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 called a population. Measurement: the application of rules for assigning numbers to objects. Example - wine may be rated on a 10-point scale where 1 means extremely bad and 10 means extremely good.