1. Analyzing and Interpreting Quantitative Data
Chapter 7
EDPR 7521
Dr. Kakali Bhattacharya

2. Prepare Data For Analysis
Score data
Select statistical program
Input data
Errors?
Measurement for Errors

3. Descriptive Data Descriptive Normal Curve Activity
Trends and tendencies
Measures of central tendency
Mean, median, mode, SD
Normal Curve Activity
Minutes it takes you to come to school
Histogram creation together
Assumes null hypothesis to be true (i.e. that most means will cluster together in one place and the rest of them will fall to the side)

4. The Standard Normal Curve

5. Z score = Standard Score
Compare scores from different scales if measuring the same construct
Mean = 0 SD= 1.0
Lets say you took the GRE a few weeks ago and got scores of 630 Verbal and 700 Quantitative. How good are these scores? Which is better, the Verbal or Quantitative score?
Population
Sample
Description
Mean SD
Verbal
Quant

6. z-score Graphed
Verbal z score
Quantitative z score

7. Activity Complete the calculations in the handout
Work in groups of 5 people
Write your results on the board when you are done
Make sure you understand all of this because this will be in the exam – GUARANTEED!

8. Inferential Data Draw inferences Make predictions about the population
Hypothesis testing – mean differences between sample scores
How confident are you that your score is right?
Confidence Interval
What is the strength of the conclusion based on your field?
Effect Size (measure of the strength of the relationship between two variables and compared to field standards – meta-analysis of sample scores and differences)

9. Steps in Hypothesis Testing
Identify null and alternate hypothesis
Set significance level (alpha)
Alpha = 0.01 (1 out of 100 times the sample score will be due to chance)

10. One Tailed and Two Tailed Tests
Given the value of alpha, we use statistical theory to determine the rejection region.
If the sample falls into this region we reject the null hypothesis; otherwise, we accept it.
Sample evidence that falls into the rejection region is called statistically significant at the alpha level.

11. Steps in Hypothesis Testing (3)
Collect data
Compute sample statistic
p value
The probability that the result could have been produced by chance if the null hypothesis were to be true
Does it fall in the critical region? (compare to table)
Reject or Fail to Reject H0
Present results
Discuss results (explanation, limitations, future research)
Recall previous steps were
Identify Ho and Ha
Set significance level

12. Choosing a Statistical Test
2 means – t test
3 means – ANOVA (F test)
> 3 means – MANOVA
Above are Parametric tests
Non Parametric tests
Chi-square (within group variance)
Multiple regression (relate variables)
Mann-Whitney (between group variance)
Refer to Table 7.5 for details

13. Statement of Claim Page 190-191 and page 197 Table 7.6
Statistical test – t test
Calculated t = -7.49
p value for this t = 0.00
This means that the probability that this t value could have been produced by chance if the null hypothesis was true (coincidental)
Statistically significant because it is less than p = 0.05

14. Potential Errors in Outcomes
True State of Null Hypothesis (H0)
Statistical Decision
H0 is true H0 is false
Reject Null Hypothesis
(H0)
Type I Error (X)
False Positive
Correctly Rejected ()
Fail to Reject Null Hypothesis (H0)
Correctly Not Rejected ()
Type II Error (X)
False Negative
Type I more serious than Type II