1. How Psychologists Ask and Answer Questions Statistics Unit 2 – pg

2. What you need to know by the end of these notes:
Distinguish the purposes of descriptive statistics and inferential statistics.
Discuss the value of reliance on operational definitions and measurement in behavioral research.

3. Statistical Reasoning
Statistical procedures analyze and interpret data and let us see what the unaided eye misses.
Composition of ethnicity in urban locales

4. Describing Data
Meaningful description of data is important in research. Misrepresentation can lead to incorrect conclusions.

5. Measures of Central Tendency
Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by their number.
Median: The middle score in a rank-ordered distribution
Mode: The most frequently occurring score in a distribution.

6. Measures of Variation
Range: The difference between the highest and lowest scores in a distribution.
Standard Deviation: average difference between each score and the mean
Large SD = more spread out scores are from mean
Small SD = more scores bunch together around the mean
OBJECTIVE 3-14| Explain two measures of variation.

7. Calculating Standard Deviation
Put scores in descending order (x)
Find mean of scores (x)
Subtract mean from every score ( x-x)
Square the answer of #3 for each score (x-x)2
Calculate standard deviation…SD
                                                                            SD = standard deviation
SD = √∑ (x-x)2                ∑ = sum of           x = scores
            n – 1                  x = mean              n = # of scores

8. Calculating Standard Deviation
SCORES… 8, 7, 8, 5, 3, 6, 4, 8, 6, 5
SD = √∑ (x-x)2
            n – 1 X X X X
(X - X)
(X - X)
(X - X)2
(X - X)2 8 6 2 4 8 6 2 4
SD = √∑ (28)
            10 – 1 8 6 2 4 7 6 1 1 6 6
SD = √ 28
              9 6 6 5 6 -1 1 5 6 -1 1
SD = √ 3.11 4 6 -2 4
SD = 1.76 3 6 -3 9

9. Calculating Standard Deviation

10. Standard Deviation
Often you will not be asked to actually calculate SD, but apply what you know of the concept
For example…which of the following sets of data have the GREATEST SD?
1, 5, 7, 30
5, 10, 12, 18
30, 32, 34, 35
How do you figure this out????
Can estimate SD by looking at “spread” of #s
Can find mean and compare each # to the mean

11. Standard Deviation
Normal distribution = a distribution of scores that produces a bell-shaped symmetrical curve
In this ‘normal curve” the mean, median and mode fall at exactly the same point
The span of ONE SD on either side of the mean covers approximately 68.2% of the scores in a normal distribution
OBJECTIVE 3-1
Average IQ = 100
Most (68.2%) people fall into range
IQ extremes are above 130 and below 70

12. Normal Curve  50 % 50 %  1 SD from the mean = 68.27 %

13. Measures of Central Tendency
A Skewed Distribution
Why is this distribution skewed?
How would it change if you removed the families that made 90, 475 and 710?

14. Skewed Distributions ?? Negative vs. Positive
Majority of scores above the mean…one or a few extremely LOW scores cause the mean to be less than the median score
Majority of scores below mean…one or a few extremely HIGH scores cause mean to be greater than median score

15. Inferential Statistics
involves estimating what is happening in a sample population for the purpose of making decisions about that population’s characteristics (based in probability theory)
Basically, inferential statistics allow us to say…”if it worked for this population, we can estimate that it will work with the rest of the population”
i.e. drug testing – if the meds worked for the sample, we estimate they will have the same effects on the rest of the population
There is always a chance for error in whatever the findings may be, so the hypothesis and results must be tested for significance

16. Inferential Statistics
Null Hypothesis – states that there is NO difference between two sets of data
Purpose of null hypothesis…
until the research SHOWS (by proving the original/alternative hypothesis) that there is a difference, the researcher must assume that any difference present is due to chance

17. Null Hypothesis
Truth About Population
NULL TRUE
NULL FALSE
REJECT NULL
(accept original)
Type I Error
Correct decision
Decision Researcher Makes
ACCEPT NULL
Correct decision
Type II Error
Type I Error: Reject the null (choosing the original hypothesis), yet the null is actually true
Type II Error: Accept the null, yet the original hypothesis is actually correct

18. Null Hypothesis
Original hypothesis - “A bomb threat was called into the front office, so we need to evacuate the school.”
Null Hypothesis – “There is no bomb in the school, so we do not need to evacuate.”
Truth About Population
NULL TRUE
NULL FALSE
REJECT NULL
Decision Researcher Makes
ACCEPT NULL

19. Null Hypothesis
Original hypothesis - “A bomb threat was called into the front office, so we need to evacuate the school.”
Null Hypothesis – “There is no bomb in the school, so we do not need to evacuate.”
Truth About Population
NULL TRUE
NULL FALSE
REJECT NULL
Type I Error
Students evacuated, yet bomb squad does not find a bomb
Erred on the side of caution
Correct decision Students evacuated, bomb squad finds bomb & safely removes it…all are safe
Decision Researcher Makes
ACCEPT NULL
Correct decision
no evacuation, no bomb threat ignored, students stay in class & all are safe
Type II Error
Bomb threat is ignored, students stay in class, bomb goes off & students injured

20. Inferential Statistics