Statistics from the Students Voices Monica Dabos & Dustin Silva College of the Canyons

How not to be ignorant about the world F-Uygdg&start=10

How did deaths per year from natural disasters change in the last century? A.More than doubled B.Remained about the same C.Decreased to less than half

Women aged 30 spent how many years in school? (Man of the same age spent 8 years) A.7 years B.5 years C.3 years

In the last 20 years the percent of people living in extreme poverty has…? A.Almost doubled B.Remained about the same C.Almost halved

We Need Statistics!!!

Shape Center & Spread

1 3 2 Distribution Shape Center and Spread Shape Spread Center

Shape, Center and Spread Math 140 Center = Mean, Median, Mode or bulk of the data Shape = Unimodal, Skewed, Symetric IN CONTEXT Spread= Range, IQR SD 1234

Got it ?

Lets See

I know everyone LOVES grading on a Saturday…. Please grade the student description of a histogram Grade on a scale of 0-10, with 10 being the maximum point value On a Post It put your grade and any pros and cons about your student’s description Compare your responses with your group

If you have not seen the graph and/or have no idea of the topic being described, which of the following descriptions would be the best to understand the data (topic).

Student 1

Student 2

Student 3

Student 4

Student 5

The Graph

How would you describe a distribution? CONCLUSION

Learn from Students Voices LESSON ONE: Don’t let students follow a script Students will mimic us, if we let them. Coach students to be independent and take risks Guide students to success beyond the classroom Move away from recipes What is our students’ greatest competition in the workforce?

LESSON 2: Make students understand why histograms are important Why Students struggle with histograms? What do we want them students to learn? Why histograms are important? Learn from Students Voices

LESSON 3: Why do students have difficulties with histograms? Students… – …. Don’t understand aggregated data – ….Don’t understand what the x and y axis represent – ….Don’t emphasize context – …. Focus on statistics lingo rather than understanding what it tells us about the data – …. Don’t connect histograms to other statistics topics Learn from Students Voices

WHY HISTOGRAMS?

Why are histograms so important? They are the most widely used type of graph in media They are widely misused Three types of Lies:

Histograms are a Multipurpose tool. Need to be understood

Levels of Understanding (according to Monica Dabos) – Level one ~ understand ~ x-axis and y-axis – Level two ~ extract info from Histogram ~ find the median or other percentages – Level three ~ Describe in context ~ unveiling information from our data – Level four ~ Understand variability in data – Level five ~ Which Standard deviation is larger or smaller – Level six ~ Informal Inference – Level seven ~ sampling distribution

Proportion of hits

Figure 1 From Meletiou-Mavrotheris and Lee (2006) p. 5

Comparing Standard Deviation A has larger standard deviation than B B has larger standard deviation than A Both have equal standard deviation Both have the same range Relative few deviations of -2 or 2 in Graph A Majority of the deviation are -2 or 2 in Graph B What Makes the SD Larger or Smaller?

Comparing Standard deviation A has larger standard deviation than B B has larger standard deviation than A Both have equal standard deviation One graph mirrors the other Frequencies of each mean deviation the same Therefore, average deviation is the same.

Comparing Standard deviation A has larger standard deviation than B B has larger standard deviation than A Both have equal standard deviation All deviations in Graph B are -2.5 or 2.5 1/3 deviations in Graph A are -2.5 or 2.5 Therefore, average deviation is larger for Graph B.

Connection with Formal Inference

Null Hypothesis: Average salary for females equals average salary for males Alternative Hypothesis: Average salary for females is not equal to average salary for males 1) Given the following graphs describe if there is a difference between male and female beginning salary. Make sure you use shape, center and spread in context to compare and contrast the beginning salaries. 2) By considering shape center and spread, do you think there is a significant difference between the beginning salaries for the two groups? Can you predict if the p-value will small or large? T-Value = P-Value=0.000 Gender N Mean StDev SE Mean f m

Two-sample T for Beginning Salary Gender N Mean StDev SE Mean f m Difference = mu (f) - mu (m) Estimate for difference: % CI for difference: (-8340, -5986) T-Test of difference = 0 (vs not =): T-Value = P-Value = DF=321

Who would like to Tango? Mentors Mentees Hub coordinators TANGO STAT ED Training a New Generation of Statistics Educators

CSI CSI is a collection of yearlong activities for high school and community college faculty that will help deepen understanding of the teaching and learning of statistics. This first weekend will focus on statistical inference and will include topics such as conceptual understanding, informal inference vs. formal inference, utilizing technology, choosing the proper test, and p-value. Keynote Speaker Friday/Saturday: Roxy Peck Mark your calendar! Date: Saturday, October 24, :45am to 4:00pm with an optional reception and talk at 6pm on Friday, October 23 rd. Location: University Center 258 College of the Canyons Rockwell Canyon Road Santa Clarita, CA Please register at:

Thank You Statistics Dr. Monica Dabos & Dustin Silva