Day Four

What standards were addressed yesterday?

MELT wiki: melt-institute-resources.wikispaces.com

Hold My Calls -• According to the National Safety

Council, cell phones are a factor in 1.3 million traffic accidents each year, resulting in thousands of deaths and injuries. Many have conjectured that this is due to decreased reaction time and attentiveness.

• What questions does this prompt you to ask?

Hold My Calls -• A statistics question does not “anticipate a

deterministic answer”, but instead “anticipates an answer based on data that vary” (Franklin, et al., 2007).

• We want a question that is specific enough to define and clarify the problem, but one that is not directed at an issue that can be resolved with a single data point

• Ex: “How tall am I?” can be answered with a single height. “How tall are adult men in the USA?” anticipates variability and is an example of a statistics question.

Hold My Calls -• How could we collect data in order to

answer this question?

• Data collection must acknowledge variability. We want to emphasize one potential source of variability (cell phone usage) while minimizing other potential sources.

Hold My Calls – (I Have a Ruler to Catch)

• Work in groups of three. Members will take turns taking on three roles: The “catcher”, who will be the one having their reaction time measured; the “dropper” who will hold and drop the ruler; the “recorder”, who will record data and be the cell phone distraction.• What issues need addressed here to minimize

sources of potential variability?• Procedures and Norms:

Hold My Calls – (I Have a Ruler to Catch)

• Come up with a list of 10 random words. During a cell phone conversation, Person A will list 10 random words. Person B will then repeat back as many as he or she can. A should keep track of how many B gets correct. Person B will then list 10 random words and Person A will try to repeat them back.

• Input your data into the spreadsheet at the front of the room

Hold My Calls – (I Have a Ruler to Catch)

Another (possibly better) way to get data here is to use the site

http://www.humanbenchmark.com/tests/reactiontime

The process would be similar, just without the ruler dropping.

Hold My Calls – (I Have a Ruler to Catch)

•Now that we’ve collected data, how might we analyze it in order to answer the question?

•What types of graphical displays might be useful?

•In your group, create a graphical display of the data. Be prepared to discuss how it addresses the question at hand.

Hold My Calls – (I Have a Ruler to Catch)

•What calculations can we do to quantify what we’ve seen here?

•Are the means different enough to conclude that the difference is significant? How can we decide this?

Break Time

But before we go, what Math III standards were addressed this morning?

Hold My Calls – (I Have a Ruler to Catch)

•What conclusions do you feel comfortable drawing here?

•How comfortable are you really? Would you:• Change your own behavior?• Use it as evidence to influence the

behavior of others?• Present it to statistically proficient

people?

GAISE Framework1. Formulate Questions – Anticipating

Variability2. Collect Data – Acknowledging

Variability3. Analyze Data – Accounting for

Variability4. Interpret Results – Allowing for

Variability

•Compare this to the more general Mathematical Modeling Cycle from the Common Core State Standards for Mathematics.

Lunch Time

We’re going to meet up in room 103A for a large-group meeting.

GAISE Framework•Modeling Cycle from CCSSM:

Hold My Calls – (I Have a Ruler to Catch)

The null hypothesis for this experiment is that the reaction times are the same – it doesn’t matter if you’re on your cell phone or not.

We can simulate this in the classroom by randomly reordering each pair (if they’re the same, order shouldn’t matter), and computing the differences. We’ll compare these to the actual differences to see how likely it is that we just randomly ended up with this result.

Hold My Calls – (I Have a Ruler to Catch)

1. Compute the mean difference of C-N for the data we collected.

2. For each data point, flip a coin. If it’s heads, compute C-N. If tails, compute N-C. Once finished, compute the mean of your randomized differences.– If there is truly no difference between cell phone

usage and non-cell phone usage, what would we expect to see?

3. Let’s compare our mean randomized differences to the actual mean difference.

Break Time

But before we go, what Math III standards were addressed this afternoon?

Here’s data on reaction time from http://www.humanbenchmark.com/tests/reactiontime/statistics

What do you notice about this data?

This isn’t a perfect normal distribution (which way is it skewed?), but it’s fairly close. The mean is approximately 262 ms and the standard deviation is approximately 42 ms.

If we assume a normal distribution, how likely is it that a randomly chosen person reacted faster than 150 ms?

Wrap-upWhat Math III standards were addressed this

afternoon?

Write down:I have learned …

I wonder …I wish …