Math Project Statistical Data Worksheet

Progress Check

Use this activity to assess whether you can:

• Use appropriate statistical data to describe a distribution.
• Create an appropriate graph to compare a quantitative variable grouped by a categorical variable.
• Recognize quartiles as the markers between four equally-sized groups within a distribution of data.
• Describe the distribution of a quantitative variable grouped by a categorical variable using percentages and descriptions of center and spread to make comparisons.
• Draw conclusions about the relationship between variables within the context of a given situation.

Directions

WARNING: The directions for Unit Projects differ from the directions for homework and lab assignments.

Use the drop-down menu to learn about the four steps needed to complete this assignment.

Four steps to complete the assignment

STEP 1: REVIEW THE RUBRIC

• Before you submit your work, review the rubric at the bottom of this assignment.
• Use the rubric as a checklist to determine whether you are ready to submit your work.

STEP 2: FIRST DRAFT

• Commit a good-faith effort to address each item in the Prompt section below.
• Please be sure to number your responses and include “white space” between problem numbers. This improves the readability and flow of your work. I cannot give feedback and grade jumbled work.
• Use either of the following options to submit your work.
  OPTION 1: You can submit a text-entry assignment (i.e. typing your answers in Canvas). To learn how to submit a text-entry assignment, use these directions (opens in a new tab).
  OPTION 2: You can upload your paper-and-pencil work (or the digital equivalent). To learn how to upload your paper-and-pencil work, use these directions (opens in a new tab). WARNING – some file types may not be visible on my end. So to learn which files you can upload, be sure to use the directions link I provided for this option.
• Not ready to submit a good-faith effort yet? Avoid frustration – use the link to the Questions, Answers, & Tips discussion board (at the bottom of this page) to post questions about this assignment (or visit the discussion board to answer your classmates’ questions). You can also contact me directly (see the homepage for my contact information).

STEP 3: PEEK-A-BOO REVIEW

Peer reviews are not required for Unit Projects. However, the peer review feature in Canvas is active for this project. Why? As long as you commit a good-faith effort on your first submission, you can use the peer review feature to take a peek at (and possibly learn from) your classmate’s work. Here’s how.

• Return to this assignment after the first draft is due.
• Under Assigned Peer Reviews you will see a list of names.
• Click on a name in the list to take a peek at your classmate’s work.
• If you notice that your peer has left something out or made a mistake, feel free to help your peer out and leave a comment. Or feel free to post a question for your peer. But if you prefer to learn from your peers’ work and move on without leaving a comment, you can do that as well.

After the due date, if you cannot see any names in the list, perhaps the “peek-a-boo” reviews were automatically generated before you submitted the assignment. You can send a message to me in Canvas to let me know that there are no names in the Assigned Peer Reviews list, and I will add names to your list. But please include this assignment’s name in the message!

STEP 4: WRITE YOUR SELF-EVALUATION & SUBMIT YOUR FINAL DRAFT

• Write a high-quality self-evaluation of your work.
• Submit your final draft and include the following.
  • First or last paragraph: Include your self-evaluation as the first or the last paragraph in your final draft.
  • Remaining paragraph(s): Write a complete final draft. I will only grade your most recent submission, so please do not leave anything out, and please do not direct me to read an earlier submission.
  • Not ready to write your final draft yet: Avoid frustration – get help. Use your self-evaluation and your peers’ feedback to identify which concepts or skills you need help with. Then use the link to the “Questions, Answers, & Tips” discussion board (bottom of this page) to seek help.

Data

From this point forward, all links in this assignment open in a new tab.

• Login and open StatCrunch (directions).
• Open your IAT sample data set in StatCrunch (directions).

Variables

Important: To learn which variables you need to use in this project, open the drop-down menu by selecting the triangle under the title for your chosen data set.

GENDER-CAREER IAT VARIABLE DESCRIPTIONS

Open for the Gender-Career variables

GENDER-SCIENCE IAT VARIABLE DESCRIPTIONS

Open for the Gender-Science variables

RACE IAT VARIABLE DESCRIPTIONS

Open for the Race variables

SEXUALITY IAT VARIABLE DESCRIPTIONS

Open for the Sexuality variables

WEAPONS IAT VARIABLE DESCRIPTIONS

Open for the Weapons variables

WEIGHT IAT VARIABLE DESCRIPTIONS

Open for the weight variables

Prompt

(Since this is your first unit project, here’s a little hint. The Unit 3 Project is very similar to the “Module 9: Comparing Boxplots Lab” assignment, In fact, every unit project is very similar to at least one – and often more than one – “homework” or “lab” assignment from that unit.)

To respond to the following items, use the quantitative variable and just one of the categorical variables listed above. You choose which categorical variable from the list above you want to analyze.

1. Use concepts from Unit 3 to describe the distribution of the quantitative variable grouped by the categorical variable. Then make comparisons and draw conclusions.
   • Make an appropriate graph and provide appropriate numerical summaries.
   • Embed your StatCrunch graph in your response, and be sure to include the Alt Text. Complete each of the following to make the graph more meaningful to the reader.
     • Include a meaningful title above your graph.
     • Underneath your graph, describe the variables represented in the graph.
     • Below your graph, provide a key for the numerical category labels in your graph. Hint: see the category descriptions for your categorical variable in the variable descriptions list for your IAT data set above.
   • Copy and paste the StatCrunch table of numerical summaries into your response.
     • To make it easier for the reader to understand your table, replace any numerical category labels with meaningful words. Hint: see the category descriptions for your categorical variable in the variable descriptions list for your IAT data set above.
2. Choose two or three groups of the categorical variable that are most interesting to compare. Then use percentages and descriptions of center and spread to make comparisons. What do the data suggest? For example, is a particular group from the categorical variable more likely to have a higher/lower IAT score?
   • Use the data to support your answer.
   • Interpret the result in context. Hint: to learn how to interpret the IAT score, see the variable descriptions link for your IAT data set (included in the Variables section above).

StatCrunch Directions

Here is a PDF document with all StatCrunch directionsLinks to an external site..

How to Use this ANSWER(S) Page

As you review this page, keep the following in mind.

• Our answers may have embedded instructive comments that are not part of the response to the Prompt. In other words, our instructive comments are intended to provide additional instruction, and you are not required to include instructive comments in your answers.
• We provide this page so that you can
  • compare your answers to ours,
  • make corrections to your own work if necessary, and
  • compare your peers’ work to ours and write instructive recommendations to improve your peers’ work.
• When using our answers to make corrections to your own work, take care to ensure that your answers remain authentically yours. Copying another’s work is plagiarism. More importantly, when we simply copy someone else’s work, we rob ourselves of the opportunity to learn from our mistakes, engage in productive struggle to correct those mistakes, and consequently deepen our understanding of the material.

Our Answers

QUESTION 1

STACKED BOXPLOTS: DISTRIBUTION OF A IAT-DISABILITY-SCORE GROUPED BY PREFERS

VARIABLES

Because we chose to stack our boxplots, the quantitative variable, IAT-Disabled-Score, is graphed on the horizontal axis. And, the categorical variable, Prefers, is graphed on the vertical axis.

KEY FOR PREFERS LABELS (VERTICAL AXIS)

Prefers
Subject reports:
1 = Strong preference for disabled people
2 = Moderate preference for disabled people
3 = Slight preference for disabled people
4 = Likes abled people and disabled people equally
5 = Slight preference for abled people
6 = Moderate preference for abled people
7 = Strong preference for abled people

Group by: Prefers

Summary Statistics for IAT-Disabled-Score

Prefers	n	Min	Q1	Median	Q3	Max
Strongly prefers disabled people	17	-0.7717603	-0.34175999	-0.16640724	0.46757936	0.69995677
Moderately prefers disabled people	21	-1.0824432	-0.11299241	0.32514437	0.54705833	1.5718736
Slightly prefers disabled people	65	-1.0494831	-0.28955621	0.16381421	0.51553278	1.3691551
No preference	560	-1.1576824	0.074357552	0.4191976	0.76375864	1.474671
Slightly prefers abled people	135	-0.64264575	0.22556505	0.55150998	0.85447185	1.3101415
Moderately prefers abled people	47	-0.42760332	0.33915022	0.62933161	0.99255436	1.4470579
Strongly prefers abled people	16	-0.56368157	0.63633898	0.84506041	0.95243112	1.5150084

QUESTION 2

Before I begin any analysis, I remind myself of what each variable represents so that I am better prepared to write a conclusion in context.

Quantitative Variable: IAT-Disabled-Score
Score on the Disability IAT where the participant is tested to determine the participant’s implicit attitude toward disabled and abled people.

Categorical Variable: Prefers
Multiple choice response to a survey question about the participant’s explicit (stated) attitude toward disabled and abled people.

As an example, I chose to compare only two groups of the categorical variable, Prefers (group 1 and group 7). However you may have found it more interesting to compare other groups or more than two groups.

GROUP 1 = STRONG PREFERENCE FOR DISABLED PEOPLE

The median IAT-Disability-Score for the participants with a stated (explicit) strong preference for disabled people is approximately -0.17. This is the lowest median score for all groups, and it makes sense because more negative (lower) scores on the Disability IAT indicate an implicit association between disabled and good. If we only consider this typical score on the Disability IAT, we would conclude that the group’s explicit preference for disabled people aligns with its implicit attitude toward disabled people as measured by the IAT .

However, as we can see from the boxplots, the typical range of IAT scores for the group who indicate that they have a strong preference for disabled people is large compared to the other groups. The IQR for this group is approximately 0.81. Also Q3 = 0.47. If we consider a score of 0 on the IAT as neutral, then a score of 0.47 does not indicate strong preference for disabled people. So, the group of IAT participants who indicate that they have a strong preference for disabled people are more inconsistent (larger IQR) in demonstrating that preference implicitly on the IAT test.

GROUP 7 = STRONG PREFERENCE FOR ABLED PEOPLE

The median IAT-Disability-Score for the participants with a stated (explicit) strong preference for abled people is approximately 0.85. This is the highest median score for all groups, and it makes sense because more positive (higher) scores on the Disability IAT indicate an implicit association between abled and good. If we only consider this typical score on the Disability IAT, we would conclude that the group’s explicit preference for abled people aligns with its implicit attitude toward abled people as measured by the IAT .

Due to the outliers, the overall range in the Disability-IAT-Score for this group (1.47) could be misleading. So for the group of participants who indicate a strong preference for abled people, the better measure of variability is the IQR. As we can see from the boxplots, the typical range of IAT scores is very small for this group when compared to the other groups, only 0.32 (from 0.64 to 0.95). This indicates that the middle 50% of IAT scores are clustered tightly around the median IAT score of 0.85. Furthermore, there are no negative scores in the typical range from this group. So the group of IAT participants who indicate that they have a strong preference for abled people are consistent in demonstrating that preference implicitly on the IAT test (more positive scores indicate a stronger association between abled and good).

COMPARING GROUPS 1 & 7

The median IAT score for each group represents the typical implicit attitude toward abled/disabled people. Each group’s median score aligns with the group’s stated (explicit) preference for abled or disabled people. However, when we consider the typical range of IAT scores, the group of participants who explicitly indicate a strong preference for abled people are more consistent (smaller IQR) in demonstrating that preference implicitly through the Disability IAT test.

Looking at the boxplots for the two groups, we note that the boxes (Q1 to Q3) do not overlap. So, at least 75% of the group with an explicit preference for disabled people scored lower on the IAT, and at least 75% of the group with an explicit preference for abled people scored higher. This is strong evidence, that on average the group with a stated preference for abled people scores higher on the Disability IAT than the group with a stated preference for disabled people. Comparatively, the Disability IAT’s measurement of implicit attitudes seems to align with each group’s typical range of stated preferences (lower scores on the IAT indicate an implicit association between disabled and good while higher scores indicate an implicit association between abled and good).