1. Unit 2 Research Methods: Thinking Critically With Psychological Science

2. Module 8 Statistical Reasoning in Everyday Life
Learning Targets
8-1 Explain why we need statistics in psychology and in everyday life.
8-2 Describe descriptive statistics.
8-3 Explain how we describe data using the three measures of central tendency.
8-4 Discuss the relative usefulness of the two measures of variation.
8-5 Describe inferential statistics.
8-6 Explain how we determine whether an observed difference can be generalized to other populations.

3. Why do we need statistics?
They are the tools that allow researchers to
measure variables and interpret results
But.. statistics can mislead or be used to
misrepresent findings.
We need to develop
STATISTICAL LITERACY.

4. How can critical thinking help develop statistical literacy?
Examining assumptions
Appraising the source
Discerning hidden biases
Evaluating evidence
Assessing conclusions

5. Let’s consider an example….
A study showed women taking a certain birth control pill had a 100% increased risk of developing blood clots.
Risk of blood clots in women not taking that pill
1 in 7000
Risk of blood clots in women taking that pill
2 in 7000
Yes. There was a 100% increase in the number of women with blood clots, but it represented 1 additional woman.

6. What is descriptive statistics?
Numerical data used to measure
and describe characteristics of groups.
Includes measures of
central tendency
(the mean, median and mode)
and measures of variation
(range and standard deviation).

7. How can statistics be displayed?
A histogram is a bar graph that shows a frequency distribution.

8. TRY IT
Consider this histogram… which brand of truck would YOU want to purchase?

9. Now consider this histogram… would you change your mind?
TRY IT
Now consider this histogram… would you change your mind?

10. How else can critical thinking help develop statistical literacy?
Changing the labels on the y-axis presents the
data in a different way.

11. Which histogram would you use?
If you were the manufacturer of “Our Brand” truck, which histogram would you show potential customers?

12. How do we describe data using the three measures of central tendency?
mean
The mathematical average of a set of numbers. Add the scores and divide by the number (N) of scores.
median
The middle score in a distribution. Arrange scores from highest to lowest with half of the data above and half below this number.
mode
The most frequently occurring data point in a distribution.

13. TRY IT
Data set: 3, 9, 6, 9, 11, 1, 4, 5, 2
What is the mean of the data above?
What is the median of the data above?
What is the mode of the data above?

14. Let’s consider this example….
This graphic representation of the distribution of a village’s incomes illustrates the three measures
of central tendency—mode, median, and mean.

15. Why is the mean not always the best descriptor of the data?
Note how just a few high incomes make
the mean deceptively high.

16. What is a skewed distribution?
In a skewed distribution, most of the scores or data
fall on one side of the scale and there are very few
scores on the other side.

17. How does an outlier skew a distribution?
When one data point is extremely different from the others, this is called an outlier and can skew the results.

18. AP ® Exam Tip You will likely have a question asking
about the influence of outliers on data
and which measure of central tendency
is best used to describe the data.
The median will be a better descriptor of data when the mean is impacted by outliers.

19. 1. What Would You Answer?
1. What Would You Answer?
Which measure of central tendency is most influenced by outliers (data that is extremely different from other data in the set)?
mean
B. median
C. mode
D. standard deviation
histogram

20. How is the range used as a measure of variation?
Range: the difference between the highest and lowest scores in a distribution.
Knowing the variation of data helps us predict future events.
For instance…
It is more likely that a psychology student who scored between 85% and 92% on her first four tests would score around 90% on her next test than if her test scores had varied from 70% to 98%.

21. TRY IT
A teacher recorded the following grades: 97, 93, 87, 94, 53, 95, 88, 94, 79, 94.
What is the mean of the data above?
Are there outliers?
What is the median of the data above?
Is it a better indicator of class performance? Why?
What is the range of the data above?
What does this tell the teacher about her students?

22. What is the range of the following:
2. What Would You Answer?
2. What Would You Answer?
What is the range of the following:
12, 25, 33, 40, 80? 68
B. 98
C. 33
D. 38
E. 190

23. How is the standard deviation used as a measure of variation?
Standard Deviation: a computed measure of how much scores vary around the mean score.
Who likes math?  To calculate the standard deviation:
Calculate the mean
For each data point: subtract the mean and square the result.
Calculate the mean of all the squared differences.
Take the square root of the sum.
The standard deviation shows whether scores are
packed together (similar) or dispersed (varied).

24. TRY IT
Which of the following standard deviations depict a data set that is more similar than different?
1.45
2.78
4.98

25. What is the normal curve (or a normal distribution)?
a symmetrical, bell-shaped curve that describes the distribution of many types of data; most scores fall near the mean and fewer and fewer near the extremes.

26. What are some characteristics of the normal curve?
~68% of scores fall 1 standard deviation from the mean ~95% of scores fall 2 standard deviations from the mean ~99% of scores fall 3 standard deviations from the mean

27. TRY IT
Refer to the normal curve below. What is the range of possible IQ scores for a student whose IQ falls within one standard deviation from the mean?

28. What are inferential statistics?
Numerical data that allow one to generalize—
to infer from sample data the
probability of something being
true of a population.

29. What is the difference between descriptive and inferential statistics?
descriptive statistics
inferential statistics
describe a population or data set
use measures of central tendency
use measures of variation
examine relationships between variables in sample
allow us to infer/predict trends based on data taken from a sample of a population

30. When can results be generalized to the population at large?
When the sample is representative of the population being studied
When the variability of the data is low.
When more cases exist with those results.

31. When is a result significant?
statistical significance:
Statistical statement of how
likely it is that a
result occurred
by chance.
When the difference in the DV results for the control v. experimental group indicates it was the IV that caused the difference.
Statistical significance is typically reported as a p value.
A p value of .05 or less means that it is 95% likely the results did not occur by chance.

32. 3. What Would You Answer?
3. What Would You Answer?
A researcher calculates statistical significance for her study and finds a 5 percent chance that results are due to chance. Which of the following is an accurate interpretation of this finding?
This is highly statistically significant.
B. This is the minimum result typically considered statistically significant..
C. This is not statistically significant.
D. There is no way to determine statistical significance without replication of the study.
E. Chance or coincidence is unrelated to statistical significance.

33. Learning Target 8-1 Review
Explain why we need statistics in
psychology and in everyday life.
Psychological researchers use statistics to measure variables and interpret results
A basic understanding of statistics helps us think smarter about medical advice and news reports of all kinds.

34. Learning Target 8-2 Review
Describe descriptive statistics.
Researchers use descriptive statistics to measure and describe characteristics of groups under study.
They may use a histogram to display data.
Descriptive statistics include measures of central tendency and measures of variation.

35. Learning Target 8-3 Review
Explain how we describe data using the
three measures of central tendency.
A measure of central tendency is a single score that represents a whole set of scores
Mean
Median
Mode

36. Learning Target 8-4 Review
Discuss the relative usefulness of
the two measures of variation.
Measures of variation tell us how different data are.
Range
Standard deviation
Scores often form a normal (or bell-shaped) curve

37. Learning Target 8-5 Review
Describe inferential statistics.
Researchers use inferential statistics to determine the probability of their findings being also true of the larger population
Inferential statistics include ways of determining the reliability and significance of an observed difference between the results for different groups.

38. Learning Target 8-6 Review
Explain how we determine whether an observed difference can be
generalized to other populations.
The difference must be reliable and significant.
Reliable differences are based on samples that
are representative of the larger population,
demonstrate low variability, and
consist of many cases.
We can say that an observed difference has statistical significance if sample averages are reliable when the difference between them is large.