8.2 Data Analysis: Descriptive Statistics

Question 1

Measurement

Answer 1

• 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.

Question 2

Nominal

Answer 2

• 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

Question 3

Ordinal

Answer 3

• 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

Question 4

Interval

Answer 4

• 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.

Question 5

Ratio

Answer 5

• 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)

Question 6

Comparison in Scales

Answer 6

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.

Question 7

Descriptive Statistics

Answer 7

• Used to describe or summarize data
• Example is using text or tables to describe a study population

Question 8

Frequency Distribution

Answer 8

• Number of times each event occurs is counted.
• Most common form of describing this is via a graphic histogram or frequency polygon

Question 9

Measures of Central Tendencies

Answer 9

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

Question 10

Normal Distribution

Answer 10

• 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

Question 11

Inferential Statistical Procedures

Answer 11

• A fundamental issue of this is whether there is a normal or not distribution of data

Question 12

Measures of Variability

Answer 12

• Concerned with the spread of data
• Helps determine if the sample is homogenous or heterogenous

Measured with
- Range
- Percentile
- Standard Deviation

Question 13

Range

Answer 13

• 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

Question 14

Percentile

Answer 14

• 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

Question 15

Standard Deviation

Answer 15

• 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