STATISTIC REFRESHER

Question 1

Measurement

Answer 1

The act of assigning numbers or symbols to characteristics of things according to rules

Question 2

Scale

Answer 2

A set of numbers whose properties model empirical properties of the objects to which the numbers are assigned

Question 3

Continous Scale

Answer 3

A scale used to measure a continous variable (value is obtained by measuring) ex: height, weight, blood pressure

Question 4

Discrete Scale

Answer 4

Used to measure a discrete variable (value is obtained by counting or categorising) ex: number of students in a classroom students can be individually counted, but you can’t have a fraction of a student (there’s no 1.5 and so on)

Question 5

ERROR

Answer 5

• Refers to the collective influence of all the factors on a test score or measurement
• Measurement always involves error
• Has many different sources (eg. surroundings, item selection in an exam)

Question 6

What are the 3 property of Scales

Answer 6

1. Magnitude
2. Equal Intervals
3. Absolute Zero

Question 7

Magnitude (Ordinal, Interval, Ratio)

Answer 7

• The property of “moreness”
• A scale has this property if we can say that a particular instance of the attribute represent more, less, or equal amounts of the given quantity than does the another instance.
  eg. scale of height: Donny is taller than David

Question 8

Equal Intervals (Interval, Ratio)

Answer 8

A scale has this property if the difference between 2 points of any place on the scale has the same meaning as the difference between 2 other points that differ the same number of scale units

Question 9

Absolute Zero (Ratio)

Answer 9

Obtained when nothing of the property being measured exists.

Question 10

4 Levels of Scales of Measurement

Answer 10

1. Nominal Scales
2. Ordinal Scales
3. Interval Scales
4. Ratio Scales

Question 11

Nominal Scales (Have none of the 3 properties)

Answer 11

• In which numbers serve as “tags” or “labels” only, to identify or classify an object
• Used when data is qualitative
• Involved classification or categorization: (In research) labeled with number (eg. 1-boy, 2-girl)
• Dichotomous (yes/no) scales

Question 12

Ordinal Scales (With magnitude only)

Answer 12

• Ranks ordering
• Compared with others and assigned a rank
• Only used to classify by ordering ranks and do not imply anything about how much greater one ranking is than another (we do not know how far the 1st to the 2nd thus, no equal interval)
• Ordinal scales have no absolute zero point. Every test takers, regardless of the standing is presumed to have some ability

Question 13

Interval Scales

Answer 13

• An interval scale is one where there is order and the difference between two values is meaningful
• Contains no absolute zero point

Question 14

Ratio Scales (Magnitude, Equal Interval, Absolute Zero)

Answer 14

• Ratio scales allow you to categorize and rank your data along equal intervals.
• Has the zero point
  eg. like test of hand grip, motor ability (some neurological test are ratio)

Question 15

What are the Permissible Operations

Answer 15

1. Nominal Data
2. Ordinal
3. Interval
4. Ratio

Question 16

Nominal Data

Answer 16

Frequency distribution; but no mathematical manipulations of the data are permissible

Question 17

Ordinal

Answer 17

Can be manipulated using arithmetic; However, the result is often difficult to interpret because it reflects neither the magnitudes nor the true amounts of the property that have been measured.

Question 18

Interval

Answer 18

One can apply any arithmetic operation to the differences between scores (but you cannot say IQ is twice higher than IQ of 80 because there’s no absolute zero point)

Question 19

RATIO

Answer 19

Any mathematical operation is permissible

Question 20

Frequency Distribution

Answer 20

Way of representing data from a frequency table. Might be listed in a tabular or graphic form (eg. Normal Distribution Curve, Skewed Distribution Curve)

Question 21

Simple Frequency Distribution

Answer 21

An individual scores that have been used and the data have not been grouped.
eg. say a poll asks 100 people how many pets they have. They find that 38 people have no pets, 25 have one pet, 17 have two pets, 6 have three pets, and 14 have four or more pets

Question 22

Grouped Frequency Distribution

Answer 22

• The data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.
• Can also be illustrated graphically

Question 23

For most distributions of test scores, the frequency distribution is bell shaped, with the greatest frequency of scores toward the center and decreasing scores as the values become greater or less than the value in the center of the distribution.

Answer 23

Search for Bell Shape Distribution

Question 24

Type of Distributions

Answer 24

Bell-shaped Distribution, Bimodal Distribution, Skewed Distribution Curve (Left Skewed are Low Scores, Right Skewed are High Scores) J-Shaped Curve, and Rectangular Distribution

Question 25

Frequency Distribution

Answer 25

Mean, Median, Mode

Question 26

Mean

Answer 26

• x̄ (x bar)
• Sum of the observations (or test scores) divided by the number of observation
• Typically the most appropriate measure of CT foe interval or ratio data and when the distribution is approximately normal

Question 27

Median

Answer 27

• Middle score in the distribution
• Determined by ordering the scores in a list by magnitude, in either ascending or descending order
• Appropriate for: ordinal, interval, and ratio data
• Useful measure of CT in cases where relatively few scores fan at the high or end or at the low end of the distribution

Question 28

Mode

Answer 28

• The most frequently occuring score
• Can have more than one mode, of there are 2 scores or modes it is bimodal distribution
• Not very commonly used EXCEPT in nominal data
• The mode is useful in analyses of a qualitative data or verbal nature

Question 29

Variability

Answer 29

An indication how scores in a distribution are scattered or dispersed.

Question 30

Range

Answer 30

• The different between highest and the lowest score.
• HS - LS = r
• Is the simplest measure of variability to calculate, but its potential we use is limited
• One extreme score (lowest or highest) can radically alter the value of the range
• It provides a quick but gross description of the spread of scores.

Question 31

Standard Deviation

Answer 31

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low, or small, standard deviation indicates data are clustered tightly around the mean, and high, or large, standard deviation indicates data are more spread out.