| Nonstatistical Data Analysis : Chapter 4: Nonstatistical Data Analysis Quantitative Data:
Involves numbers
Example: Rate your agreement with the following scale:
1 2 3
Not at all Somewhat Absolutely
Analyzed through statistical and nonstatistical methods |
| Qualitative Data : Qualitative Data Words, illustrations, etc.
Obtained from open-ended questionnaires, anecdotal records, video records
Example: Why are you in college?
Analyzed through a CONTENT ANALYSIS |
| Types of Data : Types of Data Continuous
Infinite number of possible data points
Precision of measurement limited by measuring instrument
Example: Time |
| Types of Data : Types of Data Discrete
Limited to specific score values, seldom expressed as fractions
Example: Point in basketball, golf score |
| Scales of Measurement : Scales of Measurement Ratio
Constant unit of measurement between each data point
Examples: Distant, weight, time
Most sophisticated scale of measurement
Absolute 0 point (0 = absence of something)
20lbs is twice as much as 10lbs |
| Scales of Measurement : Scales of Measurement Interval
Common unit, but no true zero
Examples: Temperature, attitude, self-efficacy
equal units of measurement
arbitrary zero (0 DOES NOT mean absence of something) |
| Scales of Measurement : Scales of Measurement Ordinal
No common unit, but can be ordered
Example: Grades, team rankings
Order or rank
No true 0 point
Do not represent magnitude in difference
Allows for differentiation, but not determination of differences
1 is better than 2 – can’t tell by how much (interval not constant) |
| Scales of Measurement : Scales of Measurement Nominal
Example: Gender, jersey number, eye color, sex
Name or classification
Lowest classification
Numbers represent categories
Do not represent differences in magnitude
(doesn’t tell how much better one is than another) |
| Organizing and Graphing : Organizing and Graphing Simple frequency distribution – listing of a distribution of scores in order.
Helps organize information to look for patterns
Used for continuous and discrete data and all but nominal scales |
| Frequency Distribution : Frequency Distribution Step 1: List all possible scores (best to worst)
Step 2: Tally
Step 3: Develop frequency (f) column
Step 4: Develop cumulative frequency (cum f) column
Step 5: Develop cumulative percent (cum %)
column cum % = (cum f ÷ N) * 100 |
| Basketball free throws made out of 20 : Basketball free throws made out of 20 Scores
15, 17, 12, 12, 13, 11, 15, 12, 14, 10 |
| Frequency Distribution : Frequency Distribution X Tally f cum f cum %
17 I 1 10 100
15 II 2 9 90
14 I 1 7 70
13 I 1 6 60
12 III 3 5 50
11 I 1 2 20
10 I 1 1 10 |
| Slide 13 : SPSS Sample Frequency Distribution |
| Graphing : Graphing Frequency Polygon
Histogram |
| Slide 15 : SPSS Sample Frequency Polygon |
| Slide 16 : SPSS Sample Histogram |
| Summation Notation : Summation Notation Σ is read as "the sum of"
X is an observed score
N = the number of observations
X = Mean |
| Percentile : Percentile * The percentage of observations that fall at a given point and below that point
* Range from 0% to 100%
60th percentile = 40% fall above, 60% below
Weaknesses:
Relative distance between distances are same, but differences between scores are not
More difficult to change percentile at ends of distributions |
| Central Tendency : Central Tendency Where do the scores tend to center?
Mean:
Average score
Affected by extreme scores, especially w/ small populations
Most often used for additional statistical techniques
Most appropriate for ratio data and often used on interval data |
| Central Tendency : Central Tendency Median (P50):
Middle score, 50% above, 50% below
Not affected by extreme scores
More representative of central tendency
If # of scores is odd, the median is the middle score
If # of score is even, take the average of the 2 middle scores
Used with ordinal or interval data
Not used for additional statistical techniques |
| Central Tendency : Central Tendency Mode:
Most frequently observed score
Most unstable, most easily estimated
Used on ordinal and interval data
Not used for additional statistical techniques |
| Using Central Tendency : Using Central Tendency The mean, median, and mode are the same for a normal distribution
The farther away the mode is from the mean and median, the more skewed the distribution
Mean is most commonly used form of central tendency |
| Normal Distribution of Scores : Normal Distribution of Scores |
| Distribution Shapes : Distribution Shapes Negatively skewed = scores clustered at upper end
of scale and mean < median
Normal = scores equally distributed and mean =
median = mode
Positively skewed = scores are clustered at lower
end of the scale and mean > median |
| Histogram : Histogram |
| Measures of Variability : Measures of Variability Variability:
Spread or scattering of scores
Range:
High score - low score
Least useful measure of variability
Useful for data entry |
| Measures of Variability : Measures of Variability Variance:
Spread of scores from mean
If all score are equal, variance = 0
Standard deviation:
Equals square root of the variance
Describes scatter of scores around the mean |
| Standard Score : Standard Score Observations standardized around the mean and standard deviation
Most common:
Z score:
Always have a mean of 0 and a standard deviation of 1
= X - M
s |