8.2 Data Analysis: Descriptive Statistics Flashcards
Measurement
- Process of assigning numbers to variables or events according to established rules
Levels
- Nominal
- Ordinal
- Interval
- Ratio
- Level of measurement determines the statistic used to answer a research question or hypothesis
- Higher level of measurement means more flexibility a researcher uses choosing statistical procedures.
Nominal
- Assign numbers to objects where different numbers indicate different objects
- No meaning besides differentiation between objects.
Example
Gender
1 = Male
2 = Female
Baseball Uniform Numbers
- Number doesn’t have meaning, just differentiates the player
- We could have just as easily assigned any number to male or female, it doesn’t matter, as long as all males get the same number and all females get the same number. This is why it is nominal. The numbers have no meaning besides differentiating the object
Ordinal
- Numbers are assigned to objects but the numbers have meaningful order
- Rank
Example
Places finished in the race
1st place
2nd place
3rd place
4th place
- 1st place did better than 2nd and 2nd did better than 3rd.
- Ordinal numbers represent order
Interval
- Numbers have order (like ordinal) but there are also equal intervals between adjacent categories
Example
Temperature - The difference between 78 degrees and 79 degrees is the same as 45 and 46 degrees. That 1 number difference means the same thing across the scale.
Ratio
- Differences are meaningful (just like interval) but ratios are also meaningful and there is a true zero point (0 means absence of the property like 0 inches there is 0 length)
Example
Weight in Pounds
- 10 pounds is twice as much as 5 pounds
- 0 pounds means absence of weight (true zero)
Comparison in Scales
Interval vs Ordinal
Ordinal - Does not have equal interval between numbers (the difference between the person who finished the race 1st and 2nd does not necessarily mean its the same difference between the person who finished in 3rd and 4th)
Interval vs Ratio
- Ratio has an absolute zero meaning 0 means absence of what is being measured. Examples 0 pounds means absence of weight
- Also a 40 degree day + a 40 degree day is still a 40 degree day, not an 80 degree day. But a 40 pound person plus a 40 pound person is an 80 pound person.
Descriptive Statistics
- Used to describe or summarize data
- Example is using text or tables to describe a study population
Frequency Distribution
- Number of times each event occurs is counted.
- Most common form of describing this is via a graphic histogram or frequency polygon
Measures of Central Tendencies
Mode - The most frequent value in a distribution
Median - The score where 50% of scores are above and 50% are below
Mean - Arithmetical average of all scores
Normal Distribution
- Concept is based on observation data from repeated measures of interval and ratio level data that group themselves at the midpoint are make a normal bell curve.
- Normal curve means mean, median, and mode are all equal
Inferential Statistical Procedures
- A fundamental issue of this is whether there is a normal or not distribution of data
Measures of Variability
- Concerned with the spread of data
- Helps determine if the sample is homogenous or heterogenous
Measured with
- Range
- Percentile
- Standard Deviation
Range
- The difference between the highest and lowest point
- A sample of 27 preschool students weighed between 24-48 pounds
- The sample range is between 24-38 pounds
Percentile
- Represents the percentage of cases a given score exceeds
- The infants head circumference was in the 75th percentile
- The infants head circumference was greater than 75% of scores
Standard Deviation
- Measures the average deviation of scores away from the mean
- The patients AFP value was 2 standard deviations above the norm
- The AFP value was 2 standard deviations above the mean score
