MAKING DECISIONS IN
THE FACE OF
VARIABILITY
TWSSP Wednesday
Agenda for today
• Larger Sample Size
• Standard Deviation
• Raisins
• Memorizing Words
• Gummy Bears
• GOALS:
• Understand
sampled
• Understand
• Understand
• Know when
• Understand
how a distribution changes when more data points are
how standard deviation appears in a graph
what factors can influence differences in two groups
a difference between two groups is statistically significant
one technique for testing for statistical significance
Larger Sample Size
Standard Deviation
• Measure and record your hand span in mm
• Make a dot plot of the class data and use a wedge (▲) to
mark the mean below the horizontal axis.
• I notice, I wonder
• What are two sources for the variability in the data?
Standard Deviation
• Make a second dot plot where the data points are the
differences (deviations) between each hand span
measurement and the mean
• Use a wedge to mark the mean of the deviations
• I notice, I wonder
• Could you get from the first plot to the second without any
computations?
• How would you describe the ‘typical’ deviation from the
hand span mean?
Standard Deviation
Calculate the deviations from the
mean
Draw horizontal lines off of the
mean to show the deviations
Standard Deviation
• Draw a line the length of which is the average of the
deviations from the mean. Don’t worry about whether the
deviation is positive or negative. Estimate the length of
the line.
• This length is a good estimate for the standard deviation,
a measure of the extent to which data varies from the
mean, without consideration for whether a data point is
above the mean or below.
Estimate the standard deviation
• Mean is 2.5
Standard Deviation
• For each of the pairs of graphs on your handout, decide
which has the greater standard deviation, and why.
Raisins
• How do you know when the store brand is a
better buy than the name brand?
• Price is one factor to consider, but quantity is
important, too!
Raisins
• Plot the data for the quantity of raisins in small
boxes of both generic and name-brand in a way
that enables you to draw conclusions about the
relative quantities of each.
• I notice, I wonder
• What features of the plot should you consider in
your decision of which raisins to buy?
Raisins
• These data are for small boxes of raisins. What
would you predict about quantities in large boxes
of raisins? Why?
Memorizing Words
• You will receive a list of 20 words. You have 1
minute to memorize as many words as possible.
• Swap with a partner and count number correct.
• Analyze the data, considering both the numerical
representation and a graphical representation.
Memorizing Words
• Research study
• When researchers conducted this study, they found that
the difference between the mean of the meaningful
words memorized and the mean of the nonsense words
memorized was 4.27
• What might have caused this result?
Memorizing Words
• Assume treatment has no effect. Is it still
possible that the difference in the means could
occur?
• Is it probable that the difference in means could
occur in the absence of a treatment effect?
• How might we determine if the difference in
means is more likely a result of the treatment or a
result of variability?
Memorizing Words
• Simulation
• Write the following data set on index cards so one data point
is on each card
• 12, 15, 12, 12, 10, 3, 7, 11, 9, 14, 9, 10, 9, 5, 13
• 4, 6, 6, 5, 7, 5, 4, 7, 9, 10, 4, 8, 7, 3, 2
• Shuffle the cards well and deal them into two groups
of 15.
• One is Set A, the other is Set B
• Find the mean score for each group, and calculate
the difference in means (mean A – mean B)
• Repeat the simulation 20 times
Memorizing Words
• Based on the results of the simulations, what
conclusion would you be more likely to draw and
why?
• There is no real difference between the treatments, and the
researchers were unlucky in the random assignment to have found
the difference of 4.27
• I am now convince that there is a genuine effect from memorizing
meaningful words instead of nonsense words
• If the mean for the meaningful group were only 2 words
larger than that for the nonsense group, what would you
conclude? Why?
Memorizing Words
• There are two types of variability to which we
must attend in this task. What are they?
• When it can be determined that it is more likely
for an effect to be the result of a treatment than
the result of randomness, the results are
considered to be statistically significant.
Memorizing Words
• You have the graphs for 3 other classes to
compare with the original data.
• For each case, do the results provide more
convincing evidence or less that the meaningful
words list was easier to memorize? Explain.
• Make up 15 hypothetical results for the
meaningful words group and 15 for the
nonsensical words group that would help you to
be very convinced that the meaningful words list
made a difference. What factors are you
considering in making your lists?
Gummy Bears
• Will gummy bears travel farther if they are launched
from a steeper height or a lower height?
• 3 sets of 10 launches, find the mean of each set of 10
• Create a representation of your data to show in a
gallery walk.
• After the gallery walk, do you think height of launch
pad matters?
• Organize the mean data
• I notice, I wonder
Gummy Bears
• Comparing the data
• How can you summarize the difference in
distances between the two conditions?
• Is there variability in the measurements for one
condition? How do you see that variability?
What do you think causes it?
• Is there variability between the two conditions?
How do we see it and what causes it?
• What, if anything, could you do to minimize the
variability?
Gummy Bears
• Based on these data, are you willing to say that
the height from which a gummy bear is launched
causes it to travel farther?
• What are important parts of an experiment which
are necessary to show causation?
Gummy Bears - Analysis
• Determine if the difference in travel distance
means is statistically significant
• Is it caused by the launch height, or is it random?
• Devise and implement a plan to test for statistical
significance.
• Consider what is feasible to do in the next 30 minutes
• Consider what is necessary to test for significance
• Prepare to report the results of your tests.
Exit Ticket (sort of…)
• What would you expect to happen to variability when
a sample size is increased?
• In your own words, explain what standard deviation
measures and what it tells you about a set of data.
• When you are comparing two data sets, what
features of their graphs should you consider? How
does each feature help you to compare the data
sets?
• What are the possible sources of variability between
two data sets? Why do we need to consider the
different sources?