1. StatCrunch Workshop
Hector Facundo

2. Resources Math Lab Website
Small Group Math Tutoring
Math-Tutorial-Hours.aspx

3. Basic Summary Stats
Calculates Mean, Median, Mode, Q1, Q3, Standard Deviation, Variance, etc.
Stat -> Summary Stats -> Column
Calculates statistics from Column Variable
Lets Play Around with the “Test Scores” Column
Compute:
Mean
Min, Q1, Median, Q3, Max
Standard Deviation and Unadjusted Standard Deviation
Note: The difference between the two is Standard Deviation is for sample data and Unadjusted Standard Deviation is for Population data.

4. Simple Graphs
Lets create a histogram of the “Test Scores” data with starting value 50 and class width of 10.
Graph -> Histogram Frequency Histogram: Relative Frequency Histogram

5. Simple Graphs
Lets do a split bar plot of the “Education” data with the salaries for men and women.
Graph -> Chart -> Column

6. Data is Your Friend! Manipulate values, columns, rows, etc.
Data -> Arrange -> Stack
Allows you to stack observations from multiple columns into one column.
Let’s Stack the “Height” Data for Men and Women into one column.

7. Data is Your Friend! Data -> Compute -> Expression
Allows you to do arithmetic operations (+, -, *, /)
Allows you to do operations with more than one column.
Has built in functions for better “equation” building.
Some built in functions:
Mean -> mean()
Sum -> sum()
Cumulative Sum -> cumsum() “Good for cumulative frequencies”
Standard Deviation -> std()
Unadjusted Standard Deviation -> ustd()

8. Data is Your Friend! Some simple computations:
Add 2 to every score in “Test Scores”
Subtract the Height of Men and the Height of women
(i.e. Height (Men) – Height (Women))
Subtract the mean of “Test Scores” from all the values in “Test Scores”

9. Graph Revisited
Create a cumulative frequency bar graph for the “Frequency” column
Step 1: Get cumulative frequency counts from “Frequency” column using Data -> Compute -> Expression
Step 2: Graph the cumulative frequencies
Graph -> Chart -> Column

10. Probability with Stat X (Outcome) P(x) “Probability” 0.1 1 0.15 2 0.3
0.1 1
0.15 2
0.3 3
0.25 4
0.2
Probability with Stat
Discrete Random Variable Example: 𝑀𝑒𝑎𝑛= 𝜇 𝑋 = 𝑖=1 𝑛 𝑋 𝑖 ∗𝑃( 𝑋 𝑖 ) = 0∗ ∗ ∗ ∗ ∗0.2 =2.3 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒= 𝜎 𝑋 2 = 𝑖=1 𝑛 𝑋 𝑖 − 𝜇 𝑋 2 ∗𝑃( 𝑋 𝑖 ) = 0−2.3 2 ∗0.1 +…+ 4−2.3 2 ∗0.2 =1.51 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛= 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 1.51 ≈ Stat -> Calculators -> Custom

11. Probability with Stat Normal Distribution
Stat -> Calculators -> Normal
Say X come from a normal distribution with a mean of 0 and standard deviation of 1 (Standard Normal). How would we find the following probabilities:
P(X ≥ 0.5)
P(X ≤ -1)
P(-3 ≤ X ≤ -2) Hint: Use “Between”
P(X ≥ 0.5) =
P(X ≤ -1) =
P(-3 ≤ X ≤ -2) =

12. Probability with Stat Normal Distribution
Stat -> Calculators -> Normal
On the contrary, what if X has a normal distribution of mean 1 and standard deviation of 0 and we wanted to find the value(s) that gave us the upper 5%?
Lower 1%? Middle 90%
P(X ≥ ?) = 0.05
P(X ≤ ?) = 0.01
P(? ≤ X ≤ ?) = 0.90
P(X ≥ 1.645) = 0.05
P(X ≤ ) = 0.01
P( ≤ X ≤ 1.645) = 0.90
This will be very helpful when finding
“critical values”

13. Confidence Intervals 100(1 - α)% Confidence intervals for μ (Mean)
Say we want a 95% Confidence Interval for the mean of “Test Scores”
Note: I’m assuming we are using t – distribution for this problem.
𝑋 + 𝑡 ∝ 2 ,𝑛−1 𝑠 𝑛
Stat -> T-Stats -> One Sample -> With Data
Lots of Work!

14. Confidence Intervals 100(1 - α)% Confidence intervals for μ (Mean)
Say we want a 90% Confidence Interval for the mean and we are given the following data:
Sample Mean = 34.5, Sample Standard Deviation = 2.3, Sample Size = 20
Note: I’m still assuming we are using t – distribution for this problem.
Stat -> T-Stats -> One Sample -> With Summary

15. Confidence Intervals
100(1 - α)% Confidence intervals for p (Proportion)
We have Political “Party” data where we have the political affiliation of 50 people (Rep, Dem, Ind). We want a 92% Confidence Interval of the true proportion of people who are republican.
Note: I’m using Normal distribution for this problem.
𝑝 ± 𝑍 1− ∝ 𝑝 (1− 𝑝 ) 𝑛
Stat -> Proportion Stats -> One Sample -> With Data
More Work!

16. Confidence Intervals
100(1 - α)% Confidence intervals for p (Proportion)
Say we did a survey in which we sampled 2500 people if they eat tofu and 768 people respond with yes. We want a 98% Confidence Interval of the true proportion of people who eat tofu.
“Successes” = 768, Observations = 2500
Stat -> Proportion Stats -> One Sample -> With Summary

17. Hypothesis Testing
Say we believe that the average for all test scores in math classes that took a particular test is 80. However others believe it is not 80. We set up a hypothesis test to test this claim at the α = 0.05 level using the “Test Scores” column as our random sample. Note: I’m Assuming a t-distribution for this problem 𝐻 0 :𝜇=80 𝐻 𝐴 :𝜇≠80 Stat -> T-Stats -> One Sample -> With Data

18. Hypothesis Testing Tips
𝐻 0 :𝜇=80 𝐻 𝐴 :𝜇≠80 Hints to set up the Alternative Hypothesis: Conclusions Guide:
 This is referred to as the alternative hypothesis
<
> ≠
“Less Than”
“Smaller”
“Lower”
“Greater Than”
“More”
“Higher”
“Different”
“Difference”
“Change”
“If they are the same”
P-Value > ∝
P-Value < ∝
Fail to Reject Null Hypothesis
Reject Null Hypothesis

19. Thank You For Coming!
If you have any suggestions on how we can improve the workshop, send an to
Don’t forget, you can get extra math help in the Math Lab in the Learning Resource Center.