STATISTIC REFRESHER Flashcards
Measurement
The act of assigning numbers or symbols to characteristics of things according to rules
Scale
A set of numbers whose properties model empirical properties of the objects to which the numbers are assigned
Continous Scale
A scale used to measure a continous variable (value is obtained by measuring) ex: height, weight, blood pressure
Discrete Scale
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)
ERROR
- 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)
What are the 3 property of Scales
- Magnitude
- Equal Intervals
- Absolute Zero
Magnitude (Ordinal, Interval, Ratio)
- 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
Equal Intervals (Interval, Ratio)
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
Absolute Zero (Ratio)
Obtained when nothing of the property being measured exists.
4 Levels of Scales of Measurement
- Nominal Scales
- Ordinal Scales
- Interval Scales
- Ratio Scales
Nominal Scales (Have none of the 3 properties)
- 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
Ordinal Scales (With magnitude only)
- 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
Interval Scales
- An interval scale is one where there is order and the difference between two values is meaningful
- Contains no absolute zero point
Ratio Scales (Magnitude, Equal Interval, Absolute Zero)
- 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)
What are the Permissible Operations
- Nominal Data
- Ordinal
- Interval
- Ratio
Nominal Data
Frequency distribution; but no mathematical manipulations of the data are permissible
Ordinal
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.
Interval
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)
RATIO
Any mathematical operation is permissible
Frequency Distribution
Way of representing data from a frequency table. Might be listed in a tabular or graphic form (eg. Normal Distribution Curve, Skewed Distribution Curve)
Simple Frequency Distribution
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
Grouped Frequency Distribution
- 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
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.
Search for Bell Shape Distribution
Type of Distributions
Bell-shaped Distribution, Bimodal Distribution, Skewed Distribution Curve (Left Skewed are Low Scores, Right Skewed are High Scores) J-Shaped Curve, and Rectangular Distribution
Frequency Distribution
Mean, Median, Mode
Mean
- 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
Median
- 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
Mode
- 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
Variability
An indication how scores in a distribution are scattered or dispersed.
Range
- 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.
Standard Deviation
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.
