WEEK 2 REFLECTION

 Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically:

• What did you find that was really useful, or that challenged your thinking?
• What are you still mulling over?
• Was there anything that you may take back to your classroom?
• Is there anything you would like to have clarified?

ANSWER THE ABOVE QUESTIONS BASED ON THE DOCUMENTS BELOW

Introduction & Goals

• DOW #2: How Long Is A Minute?

  In week 1, we gathered data for this week’s DoW, addressing the question: “How long is a minute to an adult?”

  This week we'll:

  • In investigations 1 & 2, you will analyze the data with dot plots, frequency tables, stemplots, and histograms.
    
    
  • In Exercise B2, you will post your initial analysis and interpretation to the discussion board by Wednesday, 10 PM EST and create at least three follow-up posts by Friday, 10 PM EST.
    
    
  • In Exercise D2 & E2, you will post your best histogram to the discussion board by Friday, 10 PM EST. Compare the histograms and choose the one you think best represents the distribution by Sunday, 10 PM EST
   

• Investigation 1: Seeing the Distribution

  As we emphasized in Week 1, data varies. This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics: variability. Statistical Analysis is really a study of the patterns we find within this variation in the data. The pattern(s) in the variation is called the distribution of the variable. Much of statistics focuses on ways to represent and describe the distribution of a variable.

  Activities A & B in this investigation focus on representing and describing the distribution.

  Activity C introduces Excel as a tool for looking at a distribution. 

   

• Inv 1, Activity A: Patterns in the Variation

  As we emphasized in Week 1, data varies. This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics: variability. Statistical Analysis is really a study of the patterns we find within this variation in the data. The pattern(s) in the variation is called the distribution of the variable. Much of statistics focuses on ways to represent and describe the distribution of a variable.

  Whether a variable is categorical or quantitative, two good tools for looking at the distribution are a frequency table and a dot plot (also called a line plot). This activity introduces and explores these two tools.

  You should self-pace your work according to your familiarity with these topics.

  Exercise A1: Annenberg Investigations, Session 2

  Complete the following investigations about line plots and frequency tables in your journal.

  • Line Plot Investigation (approx. 40 min) (Line Plots and Dot Plots are the same things. Different sources use different names)
  • Frequency Tables Investigation (approx. 40 min)
  • Bar Graphs and Relative Frequency Tables (approx. 30 min)

  Exercise A2: Analyze DoW #2

  In your journal create a frequency table of the variable Time, a relative frequency table and a dot plot BY HAND. Briefly describe patterns you see in the distribution for Time.

   

• Inv 1, Activity B: Picturing a Distribution

  There are key features about a distribution that you need to be on the lookout for as you make and interpret graphical displays. Five important features are:

  1. The center of the distribution
  
  Center refers to the representative value for the data – a “typical” or “expected” value. This can be estimated from a dot plot or histogram; it can also be calculated numerically. There are three different measures of center: mean, median, and mode. We will look at these in more detail in Investigation 2.

  2. The spread of the distribution

  Spread refers to how variable the distribution is – how spread out or compact. A dot plot or histogram can provide a good overall view of spread; boxplots provide another view. There are many different numerical measures of spread. The simplest is the range, the difference between the maximum and minimum values. We will study many other measures of spread in the next two weeks.

  3. The shape of the distribution

  There are countless shapes, but three that occur often are symmetric, skewed right (the tail extends to the right of the peak), and skewed left (the tail extends to the left of the peak). Another common shape is uniform (roughly the same height throughout).

  4. Peaks or clusters

  Peaks are values where the frequency is the highest. Numerically, this corresponds with the mode (the value(s) that occur most often). Graphically, there are often one or more clear areas where the frequency is highest. Clusters are subgroups in the data; on a graph, they will be separated, and often have their own peaks.

  5. Outliers

  Outliers are individual points that are significantly above or below the “majority” of the data. On a dot plot, we can visually inspect for possible outliers. There are methods for numerically identifying outliers as well. We will look at those in the next two weeks.

  Exercise B1: Watch the video Picturing Distributions in the Against All Odds video series at this link:

  If you have problems with the video link above please try this entry point. 

  This 30-minute video describes the common features of a distribution, how to look for them in different displays, and the significance of each one. Take notes in your journal on the five key features (listed above) as you watch the video. Pay particular attention to how you interpret each feature (or differences in features).

  Exercise B2: Interpret DOW #2

  Look at the dot plot you made in Exercise A2. In your journal, describe the key features that you see in the plot. (Some features may not be present.) Make at least two summary statements for distribution of Time.

  Post these summary statements to the discussion board for DoW #2 by Wednesday, 10 PM EST. Review the posts.

  Post at least three follow-up comments on the analysis and interpretation of DoW #2 by Friday, 10 PM EST.

  Consider the following as you continue your interpretation of the data:

  • What do you see as the key features of the distribution of the variable Time?
  • Do you think we'd see different features/patterns if we looked at the trials separately?
  • Do you agree on the key features?
   

• Inv 1, Activity C: Exploring Technology

  Data analysis can be done by hand, and there is particular value to by-hand analysis for our students who are learning such tools for the first time. You may reflect on your own experience in Exercise A1, creating dot plots and frequency tables by hand. However, technology greatly enhances our ability to represent data in meaningful ways and understand the patterns in the variation of the data. Technology allows us shift the focus from making the graphs to interpreting the data. For these reasons, we will be using technology in addition to by-hand analysis for this course. Depending on your security settings for Java, this may be a useful applet. Note: Information on Java settings is available.

  Exercise C1: Analyzing DoW #2

  Use the data from DoW #2. Create a dot plot for the variable Time in DoW #2. You should make a picture of the dot plot so you can post if necessary.

  A few technical hints:

  • Please Use unlined white paper
  • Use a ruler
  • Make sure to create a good scale and labels
  • Be sure the dot plot is dark enough so others will be able to read it online
  • You can Paste into Word or another application for sharing. This is useful for Weekly Reflections, Discussion Posts, and if you are keeping an electronic journal.

  Exercise C2: Frequency Tables in Excel

  The investigation is written to be used with Excel, but other spreadsheets work similarly. Depending on your prior experiences, this investigation may range from being entirely unnecessary to being not nearly enough. This is a time when you can benefit greatly from the help of your peers. The exercise is guided, but it is a chance to explore the menus and options as you work, so you become familiar with what the spreadsheet can do. Be an active learner in this investigation.

   

• Discussion: Research Plan Draft

  You will work with your assigned group for your Comparative Study. This group serves a valuable purpose as a peer-review. You are encouraged to embrace the group, take on each individual's study as your own, and help each other make the best choices possible. Statistical studies are difficult to conduct - many professionals have a hard time employing methods that avoid bias and gather meaningful data. Data is difficult to analyze - there are many choices about the best way to analyze the data in a meaningful way. This group serves as a sounding board for each of you - the more you put into it, the more you can get out of it!

  Your first task is to brainstorm with your group about the Comparative Study Project. In 250 words or less, share your thoughts, ideas, and questions about the final project. Some things you might consider as you write (do not limit yourself to these prompts or feel the need to address any/all of them):

  • What makes a good study?
  • How might you use your students to gather data?
  • Do you want to try to use a sampling strategy?
  • What topics interest you for this project?
  • What questions do you have about study design and your work in Investigation 2?
  • What questions do you have about the final project?

  Post your brainstorm to your Group Discussion Board by Wednesday 10 PM EST.

  Make at least two follow-up posts that meaningfully add to the discussion by Sunday, 10 PM EST.

  You will be posting a draft of your project proposal to your Group Discussion Board in Week 3 by Wednesday at 10 PM EST.

   

• Investigation 2: Stemplots & Histograms

  Visual representations of a distribution, when properly constructed, help you see the patterns in the variation. They become even more valuable as we work with larger data sets. Dot plots, like the ones used in Module 2, work well for small data sets or as a quick “view” of the data. Dot plots do not provide a “big picture” view of the distribution. Often, the details seen in the dot plots can distract you from seeing the key features that define the distribution.

  In order to better see the “big picture” of a distribution, we group the data. This investigation looks at ways to group data to better identify the key features of the distribution (shape, center, spread, clusters, outliers).

  In Activities D & E, we look at stem plots and histograms for this purpose.

   

• Inv 2, Activity D: Stem Plots and Histograms

  Stemplots and Histograms are visual displays of the distribution. Much like a dot plot, they display the frequency of each outcome vertically (through height). Unlike a dot plot, stem plots and histograms group data (by 5’s, 10’s or other meaningful grouping) in order to provide a big picture of the shape, center, and spread of the data. The following exercises introduce and explore stem plots and histograms.

  Exercise D1: Complete the following two activities from the Annenburg series in your journal. They introduce you to stemplots and histograms, with an emphasis on how to construct each one and the ways in which they are meaningful.

  • Stemplots (55 min)
  • Histograms (30 min)

  Exercise D2: Analyze DoW #2 By Hand

  Make a stem plot for the variable Time. In your group, each member should select and post a different interval width he or she will use in making the histogram. Using your interval width, create a histogram for the variable Time.

  Post the histogram to the DB thread for Exercise D2/E2 by Friday, 10 PM EST.

   

• Inv 2, Activity E: Histograms with Technology

  In Activity D, you saw some examples of how changing the width of the intervals in a histogram can affect the patterns you see in the distribution. This fact about histograms means that the analyst making the histogram must use his/her judgment to create a histogram that represents the distribution well.

  • When the width of the intervals is too small, the histogram will look just like a dot plot. It will show all the variations in the data, and it does not highlight significant patterns in the distribution.
    
    
  • When the width of the intervals is too large, all variation is lost in one or two bars. Key features of the distribution are no longer visible.

  Somewhere in between is an optimal interval width, one which smoothes over the less significant variations in the data, while highlighting the more significant features of the distribution. For instance, if there are two distinct clusters in a distribution, the interval width should not be so large as to make the histogram one continuous bar graph (with no breaks). Likewise, the interval would should be large enough to smooth over less significant variations that detract from the break in the two clusters.

  Because histograms depend on the judgment of the analyst, they are also subject to manipulation. Choosing an inappropriate interval width can smooth over features that might be less desirable. It is our responsibility (and challenge) in making a histogram to try to capture all its key features, while smoothing over less significant variations.

  In this activity, we will use Excel to adjust the interval width of the hsitograms for DoW #2. The goal of the activity is to create a histogram that you believe best represents the key features of this data.

  Exercise E1: Explore the Illuminations Histogram Plotter. Use the data on the website and try creating some data of your own.

  Exercise E2: Create the histogram that you think best represents the distribution of the variable Time in DoW #2. You can copy the data from Word, etc., into the data box in the Applet. If you use Word for your data, be sure to include commas.

  Post this histogram, with a brief justification of why you think it is best, to the DB for DoW #2 by Friday, 10 PM EST.

  Review the histograms. Compare them and choose which histogram(s) best represent the key features of distribution.

  Post at least two follow-up responses by Sunday, 10 PM EST.

  As you discuss, you might:

  • look back to your discussion of the key features (from Activity B)
  • consider whether any of the histograms might be misleading
  • compare the histograms to the stemplots from Activity D.
   

• Gather Data for DoW #3

  In Week 1, your group developed a tool for gathering data on the question: Does the number of raisins in a ½ oz box of raisins differ for a generic (store-brand) box of raisins and a name-brand box of raisins?

  Implement your tool and collect the data.

  Post the data to the google docs spreadsheet (accessible via the course menu) by Sunday, 10 PM EST.

   
•  
  Week 2 B2:DOW #2Post:RE: Week 2 B2:DOW #2Author:Access the profile card for user: Nerlande Monfort Nerlande Monfort

  Posted Date:

  July 10, 2014 12:13 PM

  Status:

  Published

  Time variable is distributed around the ‘expected’ (known) value and the subsequent observation have a reversing behavior towards 60s.

  There would be differences in patterns if the trials were looked at separately. This is because the participant would not have a reference point to act as his error correction basis.

  I agree on the key features. Individuals know that a minute has 60s. That is why every subsequent observation is reverting towards the known value.

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  Thread:

  Week 3 Research Draft

  Post:

  RE: Week 3 Research Draft

  Author:

  Access the profile card for user: Nerlande Monfort Nerlande Monfort

  Posted Date:

  July 8, 2014 10:13 PM

  Status:

  Published

    I think what makes a good study is something that gives meaningful results. That is where I am having the biggest problem. I have three ideas that I will share but I am not sure how meaningful they are, just interesting. 

   

  My first idea was to see if there is a difference between whether more men or more women hold the door for the person behind them. I also thought about maybe an adult/teenager twist to it. I thought I would sit at the mall at the food court entrance, which has the biggest amount of traffic, and collect my data. I am not sure how long I should collect for yet or to be honest whether this is a study worth doing. What can I extract from this study that would be useful?

   My second idea was to study whether or not boys show a significant height difference from girls in a specific grade level. I could also choose two grade levels to collect data on and compare if there is a difference. This could prove interesting because my guess is that I would see a difference if I chose a 1^st grade class and a 6^th grade class.

  Waiting for your reply,