1. [Professor Name] [Class and Section Number]
Statistical Thinking
Class Recommendations: This module can be taught in one 90-minute class, or two-shortened class periods (45 to 60 minutes).
Overview: The purpose of this module is to help students gain a basic understanding of statistical principles that will help them interpret the results of research studies. It focuses on distributional thinking, statistical significance by considering the probability model, generalizability, and the capacity to make cause and effect conclusions using randomization. Four examples of research studies are presented throughout the module to highlight and apply statistical thinking.
Technical Note: These slides may contain simple click animation so that you can focus students’ attention on a particular question, a selection of text, or an image and not have them be distracted by reading ahead. You can either preview the sequence of animation by going through the slides in slideshow view, visiting the animations tab, or reviewing the slide notes. In the notes you will see a cue - (Click) – that corresponds to each animation.
You may also find hyperlinks to outside videos at various places in the slides. These hyperlinks are embedded in text and indicated by color and in the notes section.
[Professor Name]
[Class and Section Number]

2. Today’s Learning Objectives
Define basic elements of a statistical investigation.
Describe the role of p-values and confidence intervals in statistical inference.
Describe the role of random sampling in generalizing conclusions from a sample to a population.
Describe the role of random assignment in drawing cause-and-effect conclusions.
Critique statistical studies.
This slide presents the learning objectives that are specific to the content from the learning modules
 Relevant APA Learning Objectives (Version 2.0)
Describe applications of psychology (1.3).
Use scientific reasoning to interpret psychological phenomena (2.1).
Interpret, design and conduct basic psychological research (2.4).
Interact effectively with others (4.3).
Enhance teamwork capacity (5.4).

3. Survey of Attitudes Toward Statistics (SATS) Scale
Think  Pair  Share
These questions are designed to identify your attitudes towards statistics.
Warm-up Activity: These questions are designed to identify your attitudes towards statistics.
Have students complete the SATS quietly by themselves. See scale here: You can make copies of the entire scale or you can select just a sub-scale to include either making a copy for students, or putting questions on your PowerPoint slides. For directions on how to score the scale see:
After students have completed the scale and self-scored it, have them pair with up with a peer to discuss their results. How do they feel about statistics? Is it the same or different from their partner? What specific components from the scale did they score high or low in? Why do they have those feelings and what can they do (good or bad) to combat or promote them? How can they help one another?
Facilitate a class wide discussion where students can share their ideas with the larger group. Address how common math anxiety is and generate a list of ideas for combating it.

4. Overview Introduction Distributional Thinking Statistical Significance
Key Components to a Statistical Investigation
Distributional Thinking
Statistical Significance
Control, Probability, Level of Significance
Generalizability
Samples and Populations, Random Sample, Margin of Error
Cause and Effect
Statistical Tendency, Random Assignment
The purpose of this slide is to provide students with an overview of the material that will be covered during the lecture.
Key components to a statistical investigation:
Distributional thinking
Statistical significance
Control
Probability
Level of significance
Generalizability
Samples and populations
Random sample
Margin of error
Cause & effect
Statistical tendency
Random assignment

5. Introduction 6 cups of coffee:
Men  10% lower chance of dying
Women  15% lower chance of dying
Does this mean you should start drinking coffee or increase your own coffee habit?
This slide introduces and orients students to the topic of statistical thinking by encouraging them to think about the results from the coffee study example.
This module opens by presenting statistical findings from a study investigating if drinking coffee increases life expectancy. Conducting an experiment and interpreting the results (illustrated by the coffee example) requires understanding basic ideas of statistics.
(Click) Discussion Question: Does this mean you should pick up or increase your own coffee habit?
Elicit answers from the students and write them on the board.
Reference: Freedman, N. D., Park, Y., Abnet, C. C., Hollenbeck, A. R., & Sinha, R. (2012). Association of coffee drinking with total and cause-specific mortality. New England Journal of Medicine, 366(20),

6. Key Components to a Statistical Investigation
Planning the study
Examining the data
Inferring from the data
Drawing Conclusions
This slide illustrates the components to a statistical investigation.
For each component have students think of questions they would ask about the coffee study statistics presented earlier.
Planning the study: Start by asking a testable research question and deciding how to collect data.
Examining the data: What are appropriate ways to examine the data?
Inferring from the data: What are valid statistical methods for drawing inferences “beyond” the data you collected?
Drawing conclusions: Based on what you learned from your data, what conclusions can you draw?

7. Overview Introduction Distributional Thinking Statistical Significance
Key components to a Statistical Investigation
Distributional Thinking
Statistical Significance
Control, Probability, Level of Significance
Generalizability
Samples and Populations, Random Sample, Margin of Error
Cause and Effect
Statistical Tendency, Random Assignment
The purpose of this slide is to provide students with an overview of the material that will be covered during the lecture.

8. Distributional Thinking
Analyzing the pattern of data variation, called the distribution of the variable, often reveals insights.
Develop an example of a distribution, of one variable, that you often encounter in your life.
What is the variable and how does it vary?
This slide introduces distributional thinking and provides a class discussion.
Statistical data varies and understanding how is crucial. In other words, the values for each variable differ.
Distribution: Researchers need to first look at the pattern of the variation, called the distribution of the variable, to understand the information. You can look at the center of the distribution (not ideal) or the whole distribution using a figure (ideal).
Image: An example of a distribution of a variable – different individuals may have different emotions or different levels of the same emotion.
(Click): Discussion question for the class:
Develop an example of a distribution, of one variable, that you often encounter in your life. What is the variable and how does it vary?

9. Distributional Thinking
Table 1. Frequency tables of patient reading levels and pamphlet readability levels.
Figure 1. Comparison of patient reading levels and pamphlet readability levels.
This slide illustrates the cancer patient reading levels and the pamphlet readability revels and two ways to view the data points distribution – Table 1 and Figure 1.
A naïve comparison might focus only on the centers of the distributions. Both medians turn out to be ninth grade, but considering only medians ignores the variability and the overall distributions of these data.
A more illuminating approach is to compare the entire distributions, for example with a graph, as in Figure 1

10. Collect and Display Data
How many concerts did you go to this past year?
Write your answer down and turn it in
What is the best way to visually represent the information?
What single score best represents the data?
How much variability is in the data?
This slide presents an activity that the class can do to better understand distributional thinking.
Demonstration/Activity: Collect and Display Data: This activity can be completed during class. For this activity, students will be asked a simple question and will report their answer. The class will compile the answers (data) and will create a distribution of the data together on the front white or chalkboard. The activity concludes with a large class discussion.
Time: 15 minutes
Materials: Pen and paper for students, white board marker or chalk
Directions:
Ask students one question to collect data from them. Some example questions include, how many siblings to do you have? What is your shoe size? How many concerts did you go to this past year? You can choose any question to collect data on however there should be one or two students who have extreme scores (outliers) which will give you the occasion to talk about variability and how the mean can be skewed.
Collect student answers. Have one or two student volunteers sort the answers.
(CLICK) Ask them how to best visually represent the information?
Draw the graph on the board and have students begin to plot the data points.
Facilitate a class wide discussion.
(CLICK) What single score best represents the data? Calculate the mean, median and mode. Point out any students who had extreme scores. Discuss how this skewed the mean.
(CLICK) How much variability is in the data? Discuss variability of the responses. Were most students similar or dissimilar?

11. Distributional Thinking
Tables and graphs are often presented in mass media; sometimes accurately, sometimes not.
Task Performance
This slide prompts the class to discuss distributional thinking, specifically the use of tables and graphs – ask these questions to the class:
What should you look for when examining this data to interpret it correctly?
How are people able to manipulate visual depictions of statistics to skew conclusions?
More examples on how statistics are used in a deceptive way can be found at:
Image: The two graphs depicted here represent a way someone can use statistics to mislead the audience – though the numbers are right in both cases, the data is represented in the wrong way in the graph on the left because it appears as though there is a larger difference between Group A and Group B’s task performance than there really is – they are only 1 point apart.
What should you look for when examining this data to interpret it correctly?
How are people able to manipulate visual depictions of statistics to skew conclusions?

12. Overview Introduction Distributional Thinking Statistical Significance
Key Components to a Statistical Investigation
Distributional Thinking
Statistical Significance
Control, Probability, Level of Significance
Generalizability
Samples and Populations, Random Sample, Margin of Error
Cause and Effect
Statistical Tendency, Random Assignment
The purpose of this slide is to provide students with an overview of the material that will be covered during the lecture.

13. Statistical Significance
Control
Are there other variables in the infant study that the researchers missed?
Probability/ p-value
P-Value extravaganza
Level of Significance
p < .05
This slide introduces statistical significance by having the instructor describe the infant study example.
Statistical Significance: A research study is described that investigated if infants would choose to play with a doll that was demonstrated to be helpful or hindering toward another persons goals. In thinking about the results, how can the researchers determine whether the patterns observed in the small set of data is convincing enough evidence to suggest that all infants might behave this way?
Image: The image on this slide goes with the example of infant study described above and in this section of the Module.
Control: Controlling for variables that might also explain the findings is important.
(Click) Discussion Point: The study described in the module with infants had alternative explanations. The researchers controlled for those variables. Are there any other variables that should be controlled for in this study that the researchers missed?
(Click) Probability/ p-value: The probability model is also used to determine if random chance was a factor in the experiment. Probability is referred to as a p-value. If you assumed that your results were completely random, the p-value tells you how often you would get a result at least as extreme as what was found in the actual study.
P-value extravaganza video on YouTube is a nice supplement here if you have time: (14.46 minutes)
Level of Significance: A small p value indicates strong evidence your results are not due to chance, but how small is small enough? The cut-off value of .05 is often used in research studies and is called the level of significance.

14. Overview Introduction Distributional Thinking Statistical Significance
Key Components to a Statistical Investigation
Distributional Thinking
Statistical Significance
Control, Probability, Level of Significance
Generalizability
Samples and Populations, Random Sample, Margin of Error
Cause and Effect
Statistical Tendency, Random Assignment
The purpose of this slide is to provide students with an overview of the material that will be covered during the lecture.

15. Samples and Populations
Generalizability
Samples and Populations
This slide gives the opportunity to talk about generalizability through the M&M activity.
Activity: To cover generalizability, utilize the “teaching about sampling using m&m’s” activity/demonstration (Smith, 1999) described in the Additional Activities Section of the Noba Instructor Manual for this Module. For this activity, you will pass out a small pack of candy to students. Through questions and demonstrations you will relate the candy to research participants, samples, populations, and the processes of random selection or assignment.
For step-by-step instructions and slides please see: (Ciarocco, 2010).
Samples and Populations: In research studies the participants are a sample of people from a larger group or population.
Generalizability: Can you use findings from a sample to make conclusions about a population?
References:
Smith, R.A. (1999). A tasty sample(r): Teaching about sampling using M&M’s. In L.T. Benjamin, B.F. Nodine, R.M. Ernst, & C. Blair-Broeker (Eds.), Activities handbook for the teaching of psychology, Vol. 4 (pp ). Washington, DC: American Psychological Association.
Ciarocco, N. (2010). Activity: Samples representing the population with the use of m&m’s. Retrieved from:

16. Generalizability Random Sample Margin of Error
How similar does a sample need to be to the population?
Can you generalize from one class to the whole grade?
Random Sample
Margin of Error
This slide gives the opportunity to talk more about generalizability.
Discussion Point: have students discuss this question to further deepen their understanding of generalizability: “How similar does a sample need to be to its population to generalize findings? If you sampled a single third grade class in a school could you draw conclusions about the entire grade, school, district, or state?”
Image: The image on this slide goes with the discussion on generalizability and the idea that when a sample of the population is representative of that population, the data collected from the sample will be generalizable to that entire population. Its an image of a city which can be used as a population out of which a generalizable, representative sample may be drawn.
(Click) Random Sample: Every member of the population is given an equal chance of being selected for the sample of a research study.
(Click) Margin of Error: When you use the random sampling method, you can make claims about how much random variation you expect in a statistic (often defined at a 95% confidence interval). This means that you can claim how often the sample result would fall within a certain distance from the unknown population value by chance alone. Other sources of error, such as dishonest participants or a non-random sample are not measured by the margin of error and should be considered.

17. Overview Introduction Distributional Thinking Statistical Significance
Key Components to a Statistical Investigation
Distributional Thinking
Statistical Significance
Control, Probability, Level of Significance
Generalizability
Samples and Populations, Random Sample, Margin of Error
Cause and effect
Statistical Tendency, Random Assignment
The purpose of this slide is to provide students with an overview of the material that will be covered during the lecture.

18. Cause and Effect Statistical Tendency Random Assignment
This slide covers cause and effect.
Cause and Effect Conclusions: A research study is described that asked whether the type of motivation a person has, intrinsic or extrinsic, affects their creativity. In other words, is there a difference between two groups of people based on their motivations?
Statistical Tendency: Looking at the distribution, the variability of scores shows some overlap but also points toward an observable difference between the two groups of people. The standard deviation tells you how far away each score is from the mean on average. Comparing the standard deviation of each group can tell you if there is a statistical tendency present in the data.
Random Assignment: How were the two comparison groups formed? In random assignment each individual is just as likely to be assigned to either group. This should produce groups that are as similar as possible except for the variable of interest. This eliminates other variables as possible explanations for the studies findings.
(Click) Cause and Effect: The probability model and p-value are again applied to account for the chance that random assignment did not equally distribute variables of interest between the two groups. If the p-value is small (under .05) the observed mean scores were not coincidental. Thus, cause and effect relationships can be concluded.
If the p-value is small (under .05) the observed mean scores were not coincidental

19. Activity: Popular Press Statistics
This activity will help students practice and apply their knowledge
Overview: You can have students complete the research aspect at home before class, or during class with the use of computers or smart phone technology. For this activity, students will find an example of a statistical finding in the popular press (off of the internet). They will work in teams to critically think about the statistic and to generate a list of questions they want answered to best interpret the meaning of the statistic. The activity can conclude with a large class discussion or submission of the work.
Directions:
Have students locate a statistical outcome on the Internet. The outcome can be about anything they want, however I recommend psychology-related topics. They can search for statistics specifically or can search for the answer to a question. For example, do women get paid less then men? After they have found their statistic they should write it down at the top of their paper.
Have students get into teams of three or four. Each person will share his or her statistic. The group will decide which statistic the team will work on for the remainder of the activity. On the teams paper students should write all of the questions they have regarding the generation of that statistic. They should question the sampling technique, who the participants were, what else was measured or controlled for and so on.
After each team has ample time to generate questions, facilitate a class wide discussion where students can share their ideas with the larger group. Address one or two examples together.

20. CAT: The Muddiest Point
What was the muddiest point about today’s class?
Write down what concept you are still struggling to understand.
Classroom Assessment Technique (CAT): The Muddiest Point
Ask students to write down the “muddiest point” – that is any concept they are still struggling to understand of any questions they still may have about the material. With remaining class time, ask students to share their muddiest point and provide additional review on these points.
If you do not conclude with this Classroom Assessment Technique (CAT), it would helpful to use another CAT. It could be in the form of a:
Muddy point
One-minute paper
Background knowledge
What’s the Principle?
Defining features Matrix:
For more information on CATs click here:

21. Conclusion This is the concluding slide.
Conclusions: Probability models help researchers assess how much random variation they can expect in the results of a study. This determines weather the results could happen by chance alone and to estimate a margin of error. Random sampling allows generalization of results from a sample to a larger population, and random assignment allows for cause-and-effect conclusions.

22. Photo Attribution Slides 1 & 21
Photo Credit: Integral to the Plot widdowquinn
Slide 3
Photo Credit: Questions1 Grisel D´An
Slide 5
Photo Credit: Espresso Coffee Maker and Coffee Beans Lilian Wong
Slide 8
Photo Credit: Fisheye + Ringflash + Pub = Paul Stevenson
Slide 10
Photo Credit: Concert Die Fantastischen Vier #13: Hands up! Andreas H
Slide 13
Photo Credit: V.R.K. Ian D. Keating
Slide 15
Photo Credit: Fun in Galway Barnacles Budget Accommodation
Slide 16
Photo Credit: As the Sun Sets Eric
Slide 18
Photo Credit: Crowd down the street Guillaume
Photo Credit: Desktop Summit group photo Kat
Slide 19
Photo Credit: Somali tech focus group 1 City of Seattle Community Tech
Slide 20
Photo Credit: Illustrated silhouette of a black cat nehtaeh79
Photo Attribution Slide