1. What’s a researcher to do with it all?????
Data! Data! Data!
What’s a researcher to do with it all?????

2. Organize , Summarize and Analyze
But first………………………………

3. Run a CREDIBLE experiment!
Minimize bias
Use a large enough sample size
Collect “good” data
Decide ahead of time how you will analyze the “good” data

4. So, what is “good” data??? Repeatable Accurate
Valid (it measures what you need measured)
Collected using an appropriate measuring tool
Unbiased
Data was not systematically over or under measured (inaccurate scale)
Subjects did not have biases

5. Back to organizing, summarizing, & analyzing
Charts & Graphs – Pictures Worth a 1000 Words !!!!!

6. Analyzing: So Many Choices!!!!
Mean
Standard deviation (from the mean)
Median
Percentiles ≠ percentages
5 number rule
Interquartile range (not range)
P value
Statistical significance
Frequency counts
Relative frequency (frequency count + %)
Correlation (r) vs cause / effect
Box plots
Line graphs
Confidence Intervals
Hypothesis tests
Correlation and regressions analysis
Measure of Error (MOE)

7. Analyzing: Do’s and Don’ts
Don’t use a technique if you can’t answer this question clearly!
“Why did you choose to do “X” and how did it help you to make sense of your data?”. DO
Use ONLY techniques you understand!
Double / triple check the math
Make sure %’s add up to 100

8. Before choosing a chart or graph consider the following:
What kind of data do you have?
What do you want to communicate about the data?

9. Graph Guidelines – Less is More Examples: Histogram; Bar Graph; Box Plot; Scatter Plot
Use large, bold plotting symbols
Don’t let lines obscure data points
Connect the points with lines IF there is a natural order as a time sequence
The axes DO NOT need to include zero
Eliminate unnecessary “clutter”

10. Chart Guidelines – Less is More Examples: Two-Way Table ; Pie Charts; Time Sequence
Font size – 24 point (avoid using ALL CAPITALS)
Highlight using larger font size, bolding, or italicizing
List items to be compared in vertical columns
Group related items together
Use lines only to relate and divide data
Include units in column headings
Align numbers along the decimal point
Note standard conditions

11. Two-Way Tables (aka Cross Tabs)
Used to summarize a large data set when you are examining two categorical variables
Especially useful with survey results
When organizing a two-way table always include:
Marginal totals (summarize each variable SEPARATELY)
Grand Total (sample size)

12. Two Way (Cross Tab) Table
These tables examine the relationships between two categorical variables.
Use them to analyze survey results

13. Pie Charts Be sure the percentages add up to 100%
Slices of the pie labeled “other” should be very small.
Include what the total number of “units” was before being divided up into % slices
Avoid 3-dimensional charts - they don’t show the “slices” in their proper proportion

14. Resource: https://www.mathsisfun.com/data/pie-charts.html

15. Side by Side Pie Charts
Same coding
Same order of slices

16. Histogram vs Bar Graph
Both organize and display numerical data in picture form
A bar graph is a way to represent any numerical data in a graphical form. A histogram is a concrete use of a bar graph to represent the frequency of each element in a group of elements.

17. Bar Graphs vs Histograms

18. Need Help????? Khan Academy Statistics for Dummies Dummies.com
Includes instruction and practice problems
Statistics for Dummies
Isbn
Dummies.com
Videos, step-by-step examples, how-to articles

19. Percentile ≠ Percentage
Percent - determines part of a whole
To calculate percentage
Part ÷ Whole X 100 = %
Percentile – determines relative standing
To interpret percentiles
5 number summary
Interquartile range

20. Five Number Summary More Bang for The Buck!!!!!!!
Descriptive statistics highlighting center, variation and relative standing all at the same time.
Set of 5 descriptive statistics that divide the data set into 4 EQUAL sections
The minimum (smallest number) in the data set
The 25th percentile (Q1)
The 50th percentile (median)
The 75th percentile (Q3)
The maximum (largest) number in the data set

21. Interquartile Range (IQR)
gives you a good measure of the variation within the data (as opposed to the min/max range)
IQR does not take the outliers into account
Finding IQR
Subtracting Q3 – Q1 gives you the range taken up by the inner most 50% of the data
Examples and practice problems:

22. Where’s the center of the numerical data?
Mean (aka the average)
Add up all the numbers in the data set
Divide by the number of numbers in the data set, n.
Median (split the data down the middle)
Order the numbers from smallest to largest
If the data set has an odd number of numbers, the median is the number exactly in the middle.
If the data set has an even number of numbers, take the two numbers in the middle and average them to find the median.
Best Practice
Find both the mean and the median. If they are not close then you have more work (analyses) to do with data.

23. How much does the data vary? Standard Deviation (s)
Standard Deviation measures how concentrated the data are around the mean. (ie The Standard Deviation is a measure of how spread out numbers are.
Find the average of the data set (x)
Take EACH number in the data set and subtract the mean from it.
Square EACH difference
Add up ALL the results from step 3 (sum of the squares)
Divide the sum of squares by the number of numbers in the data set minus 1 (n-1)
Take the square root to get the sample standard deviation
The units for s are the same as the units for the original data
Examples:

24. Properties of Standard Deviation
It’s never a negative number (because it is measuring a distance)
The smallest possible value is 0 (this happens only when every single number in a data set is the same)
It’s affected by outliers
It has the same units as the original data

25. P-value (between 0 &1) measures the strength of the evidence
A small p-value ≤ 0.05 indicates strong evidence against the null hypothesis, so the null hypothesis is rejected
A large p-value > 0.05 indicates weak evidence against the null hypothesis, so the null hypothesis is not rejected (accepted)
P-values very close to the cut off of 0.05 are considered marginal and so could go either way

26. When is something statistically significant (p-value)
A statistically significant result is a result with a very small probability of happening just by chance.
Be careful! You may find your experiment to have statistically significant results but what’s more important is evidence built up over time from well designed studies (Continue your projects!!)

27. Measure of Error (MOE)±
Accounts for sampling errors (i.e measures accuracy) (researchers can’t ask everyone!)
The MOE measures the maximum amount by which a sample are expected to differ from the actual population
To Approximate the MOE :
1 ÷ square root of n (n= sample total)
For an accurate MOE use z-values

28. Accurate MOE’s require
Confidence Levels – Z values

29. FINDING HELP Look for “tutors” to help students analyze their data.
Students who might be looking for service hours
Math teachers in your building (maybe the principal could ask them to be available in exchange for an assigned duty?)
Local college students
Student teachers in the school
Retired teachers: the district knows who they are! 
Parents (Have the PTO send out a request for volunteers)
Math (statistics) textbooks currently not being used