1. Unit II: Research Method: Statistics
Normal Distribution
Data tends to be around central value (no bias left or right)
If graphed, scores distributed in a “normal manner”:
Symmetrical about the center
Results typically form bell-shaped curve
AKA: Bell-curve or Normal curve
50% of values less than the mean
50% greater than the mean
Mean = median = mode
Results fall:
Most in middle
Fewer and fewer scores at the extremes

2. Unit II: Research Method: Statistics
Normal Distribution
Use mostly in:
Statistics
Social sciences
Natural sciences

3. Unit II: Research Method: Statistics
Normal Distribution
If you were to graph the below data, which would likely give you normal distribution?
Cost of a parking pass at Stone Bridge
Time it takes you to drive to school during the month of October
GPA of juniors at Stone Bridge
Height of junior boys at Stone Bridge
Class rank of juniors at Stone Bridge
Width of the classroom (20 trials)
Your blood pressure during the month of October
IQ of all students at Stone Bridge

4. Unit II: Research Method: Statistics
Normal Distribution
What type of data usually has normal distribution?
heights of people
IQ’s on people
errors in measurements
blood pressure
marks on a test

5. Unit II: Research Method: Statistics
Normal Distribution: Empirical Rule
Empirical rule
With normal distribution, we can expect the following:
68% of the values will fall within one standard deviation of the mean

6. Unit II: Research Method: Statistics
Normal Distribution: Empirical Rule
Empirical rule
With normal distribution, we can expect the following:
95% of the values will fall within two standard deviations of the mean

7. Unit II: Research Method: Statistics
Normal Distribution: Empirical Rule
Empirical rule
With normal distribution, we can expect the following:
99.7% of the values will fall within three standard deviations of the mean

8. Unit II: Research Method: Statistics
Z-test & T-test
Are used compare whether the difference between two groups is:
really significant
or, due instead to random chance
Z-test
Large sample: more than 30
T-test
Smaller sample: fewer than 30

9. Unit II: Research Method: Statistics
Z-test & T-test Example Checking to see if class of 50 students’ scores are above or below average, compared to the norm: Use Z test Checking to see if class of 20 students’ scores are above or below average, compared to the norm: Use T test