This course, classroom can be divided into describe (classroom) and inference statistics.
wiki
Completed in 2017/08/07
Orientation!
Welcome
Intro
Quiz: MnMs
Quiz: Definitely blue
Problem Sets
Quiz: Forums
Quiz: Instructor Notes
My Drive
Quiz: Practice with Spreadsheets
Quiz: Calculate sums
Course Wiki
You can get to the course wiki by clicking “Materials” or following this link.
Intro to Research Methods
Lauren's Intro Video
Quiz: Believe Results
Quiz: Measure Memory
Define Constructs
BBC Memory Test
Memory Test Description
Here is a brief description of how the test worked, to help you follow the rest of the lesson. The test consisted of three parts:
Users were shown 12 photos in the first part.
Users were shown another 12 photos in the second part.
Users were shown 48 photos in the third part and asked if they saw each photo
in the first part, the second part, or neither.
After the test, users were given two scores:
A “Recognition score”, calculated as the percentage of times they correctly identified whether they saw the face at all, regardless of which part the face was from.
A “Temporal memory score”, calculated as the percentage of recognized faces that were identified with the correct part (part 1 or part 2).
Users were advised to take a 5 minute break between each part of the test.
BBC Scores
Google Account
Quiz: BBC Measurement
Operational Definition
Quiz: Constructs
Quiz: Operational Definitions
Data
Quiz: Sleep and Memory
Quiz: Influence Memory
Quiz: Control for Time of Day
lurking variables
extraneous factor
Quiz: Same Scores
Population parameters (such as mu, or μ) are values that describe the entire population. Sample statistics (such as X-bar, or $\bar{x}$ ) are values that describe our sample; we use statistics to estimate the population parameters. Estimates are our best guesses for the population parameters. So, for example, we would use X-bar to estimate mu.
Quiz: Sample Average
Quiz: Better Sample
Randomness
Quiz: Visualize Relationship
Quiz: True or Not?
Golden Arches Theory
McDonald's
Quiz: World Peace
Causal Inference
Quiz: Benefits of Surveys
Quiz: Downsides of Surveys
Quiz: Placebo
Quiz: Blind
Quiz: Double Blind
Quiz: Controlled Factors
Random Assignment
Quiz: Control for What?
Quiz: Katie's Hand
Click this link to access the data: Height and hand length
Copy and paste the data into your own spreadsheet to create the scatterplot. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Quiz: Draw Conclusions
Problem Set 1: Intro to statistical research methods
Quiz: 1. All California Residents
Quiz: 2. Sleepy College Students
Quiz: 3. Not Enough Sleep…?
Quiz: 4. Characteristic of a Sample
Quiz: 5. Freshman 15
Quiz: 6. Characteristic of a Population
Quiz: 7. Sample Approximates Population
Quiz: 8. SAT Scores
Quiz: 9. Survey to Friends
Quiz: 10. Which Are Constructs?
Quiz: 11. Which Are Not Constructs?
Quiz: 12. Define Operational Definition
Quiz: 13. Research Studies
Quiz: 14. Variables
Quiz: 15. Variable Relationships
Quiz: 16. Which Are Hypotheses?
Quiz: 17. Lurking Around
Quiz: 18. Symbols = Fun Fun Fun!
Quiz: 19. n
Quiz: 20. Which Are True?
Quiz: 21. Random Sample
Quiz: 22. Convenience Samples
Quiz: 23. Sample vs. Population
Quiz: 24. Classical Music
Quiz: 25. Caffeine
Quiz: 26. Video Games
Quiz: 27. English Teaching
Quiz: 28. Reading Score
Quiz: 29. Extreme Temperature
Quiz: 30. Teaching Method
Quiz: 31. Reading Scores
Quiz: 32. Which Is Better?
Quiz: 33. All Kinds of Variables
Quiz: 34. Landmines
Quiz: 35. Landmines
Quiz: 36. Student Satisfaction
Quiz: 37. Insomnia
Quiz: 38. Insomnia
Quiz: 39. SAD
Quiz: 40. Random Assignment
Quiz: 41. Placebo Control Condition
Quiz: 42. Why Placebo?
Quiz: 43. Measuring Constructs
Quiz: 44. Participants
Quiz: 45. What Proportion?
Quiz: 46. Blind Studies
Quiz: 47. Causality?
Quiz: 48. Depression
Quiz: 49. Depression
Quiz: 50. Depression
Conclusion
construct
opertaional definition
independent variable
dependent variable
extraneous or lurking variable
experimental study - casual conclusion
observational study
Visualizing Data
Quiz: Where Students Are From
Quiz: Frequency
Quiz: US, China, Pakistan
Quiz: Relative Frequency
Quiz: Range of Proportions
Quiz: Sum Relative Frequencies
Quiz: Proportion from Countries
Quiz: Convert to Percentage
Quiz: Range Percentages
Quiz: Continents
Quiz: Number of Rows
interval = bin = bucket
Quiz: Bin Size
Visualizing Data
Quiz: Histogram
Different Bin Sizes
Click this link to play around with the histogram applet! (You may need to install the Java plug-in.) Interactivate Histogram Applet
Udacity Student Ages Data: Make sure you have one number per line for the applet.
Quiz: Smaller Bin
Quiz: Find Bin Size
Quiz: Most Frequent Age
Quiz: Proportion over 60
Quiz: Percentage Under 60
Quiz: Younger than 20
Quiz: Continent Graph
Quiz: Difference Between Graphs
histogram: bin x-axis: numerical/quantitative
bar: x-axis: categorical/qualitative
Quiz: Biased Graphs
Changing Bin Size
Quiz: Interpret Histogram
Quiz: Skewed Distribution
Problem Set 2: Visualizing data
Quiz: 1. Blood Types
The Σ symbol means the total sum. It is the Greek letter capital sigma. f stands for frequency (count), p stands for proportion.
The Σ symbol means the total sum. It is the Greek letter capital sigma. f stands for frequency (count), p stands for proportion.
Enter each answer as a number without any special characters, including % signs. Enter proportions as decimals.
The Σ symbol means the total sum. It is the Greek letter capital sigma.
Quiz: 2. Rare Blood
Quiz: 3. Common Blood
Quiz: 4. Type A
Quiz: 5. Guesstimate
Quiz: 6. Analyze Stuff
Quiz: 7. Ode to n
Quiz: 8. Calculate Percentages
Quiz: 9. Common Decade
Quiz: 10. How Old?
Quiz: 11. Really Old!
Quiz: 12. Birth Year Histogram
Quiz: 13. Most Common Bin
Quiz: 14. When Most Were Born
Quiz: 15. Type of Data
Quiz: 16. Heights of Bars
Quiz: 17. Which Region?
Quiz: 18. Calculate Bin Size
Quiz: 19. How to Find n
Quiz: 20. How to Analyze Shape
Quiz: 21. Commute Time
Quiz: 22. Commute an Hour
Quiz: 23. Find Bin Width
Quiz: 24. Analyze Histogram
Quiz: 25. Frequency and Bin Size
Quiz: 26. Positively Skewed
Quiz: 27. Distribution of What?
Quiz: 28. Thinking About Distributions
Quiz: 29. Frequency Axis
Quiz: 30. X-Axis Represent!
Quiz: 31. Skewness
positively skewed
Quiz: 32. Negatively Skewed
Quiz: 33. Normal Distribution
Quiz: 34. Table vs. Histogram
Google Spreadsheet Tutorial
Tutorial
Link to Udacians’ Facebook Friends
Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
You will work with this data in Lesson 3.
Central tendency
Quiz: Which Major?
One Number to Describe Data
Quiz: Which Number to Choose?
Quiz: Mode of Dataset
mode: most frequency
Quiz: Mode of Distribution
Quiz: Mode - Negatively Skewed Distribution
Quiz: Mode - Uniform Distribution
Quiz: More than One Mode?
Quiz: Mode of Categorical Data
Quiz: More o' Mode!
Quiz: Find the Mean
Quiz: Procedure for Finding Mean
Quiz: Iterative Procedure
Helpful Symbols
Quiz: Properties of the Mean
Quiz: Mean with Outlier
Quiz: What Can You Expect?
UNC
Quiz: Requirement for Median
Quiz: Find the Median
Quiz: Median with Outlier
Quiz: Find Median with Outlier
Measures of Center
mean median mode
Quiz: Order Measures of Center 1
Quiz: Order Measures of Center 2
Use Measures of Center to Compare
Quiz: Udacians' Facebook Friends - Mean
Quiz: Udacians' Facebook Friends - Median
Quiz: Formula for Location of Median
Quiz: Wrap Up - Measures of Center
Good Job!
Problem Set 3: Central tendency
Quiz: 1. BBC Memory Scores
Link to spreadsheet with sample memory scores: BBC Sample Scores
Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Quiz: 2. BBC Memory Scores
Quiz: 3. BBC Memory Scores
Quiz: 4. What Distribution?
Quiz: 5. What Distribution?
Quiz: 6. Normal Distribution
Quiz: 7. Positively Skewed
Quiz: 8. Mean
Quiz: 9. Median
Quiz: 10. Mode
Quiz: 11. Deal or No Deal? (Median)
Quiz: 12. Deal or No Deal? (Mode)
Quiz: 13. Deal or No Deal? (Number)
Quiz: 14. Deal or No Deal? (Mean vs. Median)
Quiz: 15. Deal or No Deal? (Mean)
Quiz: 16. Deal or No Deal? (Proportion)
Quiz: 17. Deal or No Deal? (Frequency)
Quiz: 18. Deal or No Deal? (Distribution)
Quiz: 19. Deal or No Deal? (Center)
Quiz: 20. NHL (Mean)
Round to the nearest hundredth (xx.xx)
Quiz: 21. NHL (Mode)
Quiz: 22. NHL (Median)
Quiz: 23. Which Distributions?
Quiz: 24. Median Given Histogram
Variability
Quiz: Social Networkers' Salaries
Quiz: Should You Get an Account?
Quiz: What's the Difference?
Quiz: Quantify Spread
Quiz: Does Range Change?
Quiz: Mark Z the Outlier
Chop Off the Tails
Quiz: Where Is Q1?
quartile
Quiz: Q3 - Q1
Quiz: IQR
IQR=Q3-Q1
Quiz: What Is an Outlier?
Quiz: Define Outlier
< Q1 - 1.5 IQR
> Q3 + 1.5 IQR
Quiz: Match Boxplots
Quiz: Mean Within IQR?
Problem with IQR
Quiz: Measure Variability
Quiz: Calculate Mean
Quiz: Deviation from Mean
Quiz: Average Deviation
Quiz: Equation for Average Deviation
Quiz: Be Happy and Get Rid of Negatives
Quiz: Absolute Deviations
Quiz: Average Absolute Deviation
Quiz: Formula for Avg. Abs. Dev.
Quiz: Squared Deviations
Quiz: Sum of Squares
Quiz: Average Squared Deviation
variance
Quiz: Avg. Squared Dev. in Words
Quiz: One Dimension
Standard Deviation
square root of variance
Quiz: Calculate SD
Quiz: SD Social Networkers
Quiz: SD in Words
Quiz: Spreadsheet SD
Click here to access the data: Sample Social Networkers’ Salary
Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Click here to access the data: Sample Social Networkers’ Salary Enter your answer as a number without any special characters, including $ or commas.
Link to Sample Social Networkers’ Salary Copy and paste this data into your own spreadsheet to calculate the standard deviation.
Point of SD
Quiz: Find Values
Quiz: Sample SD
Quiz: Bessel's Correction
Standard Deviation of sample is smaller than Standard Deviation of population, so we use n-1 to estimate the Standard Deviation of population(sample Standard Deviation)
Sample Standard deviation(Standard deviation of population):
$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$$
Variance:
$$\frac{\sum (x_i - \bar{x})^2}{n -1}$$
Standard deviation of sample
$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}}$$
Clarifying Sample SD
Jelly Beans
Problem Set 4: Variability
Quiz: 1. Udacians' Facebook Friends (Mean)
Click here for the link to the data: Udacians’ Facebook Friends
Quiz: 2. Udacians' Facebook Friends (Avg. Dev)
Quiz: 3. Udacians' Facebook Friends (SS)
Quiz: 4. Udacians' Facebook Friends (Variance)
Quiz: 5. Udacians' Facebook Friends (Std Dev)
Quiz: 6. Udacians' Facebook Friends (mean +/- std dev)
Quiz: 7. Udacians' Facebook Friends (proportion)
Quiz: 8. Udacians' Facebook Friends (sample sd)
Quiz: 9. Class Exam
Quiz: 10. Where's Your Score? (sd = 5)
Quiz: 11. Where's Your Score? (sd = 2.5)
Quiz: 12. Where's Your Score? (sd = 10)
Quiz: 13. BBC Sample Scores (Std. Dev.)
Link to BBC Sample Scores
Quiz: 14. BBC Sample Scores (Variability)
Lessons 1-4 Review/Assessment
Quiz: I
Quiz: II
Quiz: III
Quiz: IV
Quiz: V
Quiz: VI
Quiz: VII
Quiz: VIII
Quiz: IX
Quiz: X
Quiz: XI
Quiz: XII
Quiz: XIII
Quiz: XIV
Quiz: XV
Quiz: XVI
Quiz: XVII
Quiz: XVIII
Quiz: XIX
Quiz: XX
Quiz: XXI
Quiz: XXII
Quiz: XXIII
Quiz: XXIV
Quiz: XXV
Quiz: XXVI
Quiz: XXVII
Quiz: XXVIII
Quiz: XXIX
Quiz: XXX
Quiz: XXXI
Standardizing
Quiz: Chess
USCF Distribution
Quiz: Absolute or Relative
Quiz: Relative Frequency Histogram
Quiz: Proportion Between 170 and 210
Quiz: Proportion Between 180 and 200
Quiz: More Detail
Infinitely Small
Quiz: Continuous Distribution
Theoretical Normal Distribution
Z
number of standard deviations away from the mean
Unpopular
Quiz: Katie - SDs Below
Quiz: Andy - SDs Below
Quiz: Who's More Unpopular?
Quiz: Formula for Number of SDs
Z-Score
Link to poll: How many Facebook friends do you have?
$z = \frac{x-\mu}{\sigma}$
Quiz: Negative Z-Score
Quiz: Mean of Standardized Distribution
Quiz: SD of Standardized Distribution
Standard Normal Distribution
Quiz: Popular Chris
Quiz: Convert to Z-Score
Quiz: Convert to Popularity Score
Problem Set 5: Standardizing
Quiz: 1. Which Distribution Is Which?
Quiz: 2. Z-Scores
Quiz: 3. OkCupid
Quiz: 4. Social Media
Quiz: 5. Z-Scores of Usage
Quiz: 6. Where on the Distribution?
Quiz: 7. Mean and SD
Quiz: 8. IQ 125
Quiz: 9. IQ 150
Quiz: 10. Scores
Quiz: 11. Grade on a Curve
Quiz: 12. Extreme
Quiz: 13. SD
Quiz: 14. SJSU Football
Quiz: 15. Exams
Quiz: 16. Which SD?
Quiz: 17. Closest to Mean
Quiz: 18. Farthest from Mean
Quiz: 19. True or False?
Quiz: 20. BBC - Sleep
Quiz: 21. BBC - Recognition
Quiz: 22. BBC - Temporal
Quiz: 23. BBC - What Score?
Normal Distribution
Intro to the PDF
probability density function
Quiz: Probability
Get to Know the PDF
Quiz: Probability Greater
Quiz: Probability Less
Quiz: 2 SDs Below or Above
Quiz: Proportion of Facebook Friends
Quiz: More than 262
Quiz: Between 118 and 226
Quiz: Less than 240
Z-Table
Here is a link to the z-table shown in the video:
z-table
Quiz: Using the Z-Table
Karma
Udacity forums no longer use the karma system Katie describes. However, you can still access the dataset Katie created by clicking here: Average Karma points per post.
Quiz: Average Karma Points per Post
Quiz: SD of Karma Points per Post
Quiz: Integer SDs
Quiz: Less than 5
Quiz: More than 20
Quiz: Between 10 and 16
Quiz: Top 5%
Great Job!
Link to visualize the area under the curve
Problem Set 6: Normal Distribution
Quiz: 1. Heights
Quiz: CHALLENGE 2. Heights
Quiz: 3. Houses
Quiz: 4. Houses
Quiz: 5. Houses
Quiz: 6. Houses
Quiz: 7. Greater than 108
Quiz: 8. Less than 76
Quiz: 9. Between 65 and 90
Quiz: 10. Between 80 and 95
Quiz: 11. Top 30%
Quiz: 12. Greater than 1.64
Quiz: 13. Less than -2.33
Quiz: 14. Top 40%
Quiz: 15. Meanings
Quiz: 16. 64th Percentile
Sampling Distributions
Quiz: Compare Sample Means
Quiz: Gambling in Vegas
A tetrahedral die will result in a 1, 2, 3, or 4 on each roll. If you’re curious about how this works, you can read this thread. Write your answer as a proportion.
Quiz: Tetrahedral Die
Quiz: Total Number of Samples
Quiz: Mean of Each Sample
Quiz: Mean of Sample Means
Quiz: Sampling Distribution
distribution of sample means = Sampling Distribution
Mean of each sample:
1, 1.5, 2, 2.5, 1.5, 2, 2.5, 3, 2, 2.5, 3, 3.5, 2.5, 3, 3.5, 4
Copy and paste the sample means into WolframAlpha and hit enter. Pay particular attention to the histogram showing the frequency of each mean.
Quiz: Probability Mean > or = 3
Quiz: What We Need to Compare the Means
Quiz: Calculate SDs
SE: standard deviation of all our sample means
Quiz: Relationship Between SDs
Quiz: Ratio of SDs
$$SE = \frac{ \sigma }{ \sqrt{n} }$$
$\sigma$: population standard deviation
SE: standard deviation of distribution of sample means(sampling distribution)
Quiz: SD of Sampling Distribution
The Central Limit Theorem
SE: standard error
Quiz: Roll 1 Die
NOTE: Unfortunately, the rolling die simulation we used to link to here is no longer valid. Don’t worry! You have enough information now to answer this question without it. Give it your best shot, and you’ll see how the applet works in the solution video.
An alternative simulation can be found here.
Quiz: Roll 2 Dice
Quiz: Find Standard Error
The “standard deviation of the sampling distribution” is also known as the standard error.
The mean is solved for by adding up the different outcomes (1, 2, 3, 4, 5, 6) and dividing by the number of outcomes (6), yielding a result of 3.5
Quiz: Roll 5 Dice
Quiz: Standard Error for Avg of 5 Dice
Quiz: Standard Error When n Increases
Quiz: Shape of Distribution When n Increases
Simulation Applet
Link to awesome simulation applet
M&Ms
Quiz: M&M CLT
Using Sampling Distribution
Klout
What is Klout and how does it work?
Quiz: Klout Parameters
Link to Klout data Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.” Your calculations should automatically save in Google Drive.
Quiz: Klout Sampling Distribution (Mean)
Quiz: Klout Sampling Distribution (SD)
Quiz: Sampling Distribution Shape
What Do You Get with a Good Klout Score?
Quiz: Location of Mean on Distribution
Quiz: Probability of Obtaining Mean
Quiz: Does Low Probability = Causation?
Quiz: Increase Sample Size
Quiz: Location of Mean
Quiz: Probability of Mean
Quiz: Something Fun
Problem Set 7: Sampling Distributions
Quiz: 1. Central Limit Theorem
Quiz: 2. Location of Sample Mean
Quiz: 3. Average Difference
Quiz: 4. Increase Sample Size
Quiz: 5. Standard Error
Quiz: 6. n and σ
Quiz: 7. n and x-bar
Quiz: 8. Mean of Sample Means
Quiz: 9. Standard Error
Quiz: 10. Z-Score
Quiz: 11. Probability
Quiz: 12. Mean n = 25
Quiz: 13. Standard Error
Quiz: 14. Probability
Quiz: 15. Probability Decreased
Quiz: 16. Population Distribution Shape
Quiz: 17. Sampling Distribution Shape
Quiz: 18. Mean of Sampling Distribution
Quiz: 19. SD of Sampling Distribution
Quiz: 20. Which Distribution?
Quiz: 21. Greater or Less?
Quiz: CHALLENGE 22. What Sample Size?
Final project
Estimation
Summary
Quiz: Mean of Treated Population
point estimate
Quiz: Population Mean vs. Sample Mean
Quiz: Percent of Sample Means
Approximate Margin of Error
margin of error: $\frac{2\sigma}{\sqrt{n}}$
Interval Estimate for Population Mean
Quiz: Confidence Interval Bounds
Quiz: Exact Z-Scores
Sampling Distribution
Quiz: 95% CI with Exact Z-Scores
Quiz: Generalize Point Estimate
Quiz: Generalize CI
Quiz: CI Range for Larger Sample Size
Quiz: CI When n = 250
Bigger Sample, Smaller CI
Quiz: Z for 98% CI
Quiz: Find 98% CI
Critical Values of Z
-1.96 and 1.96 are the critical values of z for 95% confidence
Quiz: Engagement Ratio
Link to Engagement Ratio data Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.” Enter your answer as a number without any special characters, including commas.
Hypothesis Testing Song
Quiz: Point Estimate Engagement Ratio
Quiz: Standard Error
Quiz: CI Bounds
Quiz: Generalize CI
Margin of Error
The margin of error is half the width of the confidence interval.
Quiz: Rate Engagement and Learning
Link to rate your engagement and learning in this class
Results from Sample
Quiz: What Statistics?
Quiz: Sampling Distributions
Quiz: Z-Scores of Sample Means
Quiz: Probability Sample Mean Is at Least…
Quiz: What Does This Mean?
Wrap-Up
Problem Set 8: Estimation
Quiz: 2. Larger Range
Quiz: 3. Increase Sample Size
Quiz: 4. Increase Population SD
Quiz: 5. 95% CI
Quiz: 6. Critical Values 95% CI
Quiz: 7. Standard Error
Quiz: 8. Probability
Write the probability as a proportion.
Hint: Theoretically, z-scores can be anything from -infinity to +infinity. What does it say about the probability if you get really high or really low z-scores?
Quiz: 9. Margin of Error
Quiz: 10. 95% CI
Quiz: 11. Interpret CI
Quiz: 12. Critical Values 99% CI
Quiz: 13. Standard Error
Quiz: 14. Probability
Quiz: 15. Margin of Error
Quiz: 16. 99% CI
Quiz: 17. Interpret CI
Hypothesis testing
Quiz: Likely or unlikely
Quiz: Likely or Unlikely
Quiz: Alpha Levels
0.05 5%
0.01 1%
0.001 0.1%
Quiz: Z-Critical Value 0.05
critical region
z-critical value
Quiz: Critical Values 0.01
Quiz: Critical Values 0.001
Critical Regions
Note that when it comes to constructing a hypothesis test, it is best to choose a significant level before you perform the test. You can report the results as significant at a certain critical level after obtaining your result, but it is important that you are not ‘fishing’ for results before you see the results in your sample. This article has some additional information about understanding significance levels and p-values in hypothesis testing.
Quiz: Significance
| $\alpha$ level | z-critical value |
|---|---|
| 0.05 | 1.65 |
| 0.01 | 2.32 |
| 0.001 | 3.08 |
| z-score | significant at |
|---|---|
| 3.14 | p<0.001 |
Darts
Quiz: Z-Score
Quiz: Two-Tailed Critical Values 0.05
Quiz: Two-Tailed Test
Quiz: Two-Tailed Probability
Quiz: Two-Tailed Critical Values 0.01
Quiz: Two-Tailed Critical Values 0.001
Hypotheses
Quiz: Fail to Reject the Null
Quiz: Evidence to Reject the Null
Quiz: Mean and SD
Link to Learning and Engagement Data (use this data for quiz)
Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Link to Full Learning and Engagement Results (optional)
Quiz: Null Hypothesis
Quiz: Alternative Hypothesis
One tailed or two tailed
Quiz: Conduct Hypothesis Test
what does it mean to reject the null?
- our sample mean falls within the critical region
- the z-score of our sample mean is greater than the z-critical value
- the probability of obtaining the sample mean is less than the alpha level
Quiz: Critical Values 0.05
Quiz: Z-Score of Sample Mean
Quiz: Results of Hypothesis Test
Quiz: Increase Sample Size
Quiz: Reject or Fail to Reject
Quiz: Probability of Obtaining Mean
Quiz: Decision Errors
Type 1 error: reject true H0
Type 2 error: retain false H0
Quiz: Hot Beverage
Quiz: Raining
Quiz: What Happened?
Quiz: What Happened?
Prone to Misinterpretations
To Finish This Lesson…
Hypothesis Testing
Quiz: Increase Engagement?
Problem Set 9: Hypothesis testing
Quiz: 1. True or False?
Quiz: 2. Null Hypothesis
Quiz: 3. Alternative Hypothesis
Quiz: 4. Standard Error
Quiz: 5. Z-Score
Quiz: 6. Z-Critical Value
Quiz: 7. Statistical Decision
Quiz: 8. Conclusion
Quiz: 9. Type I Error
Quiz: 10. Hypotheses
Quiz: 11. Standard Error
Quiz: 12. Z-Score
Quiz: 13. Valentine's Day
Lessons 5-9 Review/Assessment
Quiz: 1. Find z-score
Quiz: 2. Probability
Quiz: 3. Z-score furthest from mean
Quiz: 4. Find x given z-score
Quiz: 5. Proportion
Quiz: 6. Probability
Quiz: 7. Compare using distributions
Quiz: 8. Standard Normal Distribution
Quiz: 9. Probability
Quiz: 10. Z-score
Quiz: 11. Percentile
Quiz: 12. Distribution of means
Quiz: 13. Standard Error
Quiz: 14. Z-score of mean
Quiz: 15. Probability of sample mean
Quiz: 16. Unlikely
Quiz: 17. Proportion of samples
Quiz: 18. Proportion of samples
Quiz: 19. Increase n
Quiz: 20. Point estimate
Quiz: 21. 95% CI
Quiz: 22. Hypotheses
Quiz: 23. Decision
Quiz: 24. Probability of Type I error
Quiz: 25. Find sigma
t-Tests
Quiz: t-Distribution
$t = \frac{mean difference}{S}$
S: population standard deviation estimated by standard deviation of sample means
Guinness
Quiz: Degrees of Freedom
Quiz: DF - Choose n Numbers
Quiz: DF - Add to 10
Quiz: DF - Marginal Totals
DF - Sample SD
n-1 in sample standard deviation can be denoted as effctive sample size
t-Table
Quiz: One-Tailed t-Test
Quiz: Two-Tailed t-Test
Quiz: Bounds of Area
t-statistic: t critical value
Quiz: Affect t-Statistic
One-Sample t-Test
$t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}$
Quiz: Increase t
Quiz: Finches
Quiz: Finches - n and DF
Quiz: Finches - Mean and s
Quiz: Finches - Find t-Statistic
Quiz: Finches - Decision
p-value: probability of getting this t-statistic
Quiz: P-Value
reject the null when the p-value is less than the $\alpha$ level
Quiz: Visualize P-Value
Quiz: Find P-Value
Link to GraphPad Remember, our sample has 8 values, and our t-statistic is 0.977.
Quiz: Rent - t-Critical Values
Quiz: Rent - t-Statistic
Quiz: Rent - Decision
Quiz: Rent - Cohen's d
standardized mean difference
Cohen’s d =
$$\frac{\bar{x} - \mu_0}{s}$$
Quiz: Rent - CI
Quiz: Rent - Find CI
Quiz: Rent - Margin of Error
Quiz: Rent - Increase n
Dependent Samples
Dependent t-test for paired samples
within-subject designs
- two conditions
- pre-test, post-test
- growth over time(longitudinal study)
Quiz: Keyboards
Quiz: Keyboards: Point Estimate for Difference
point estimate is based on samples
Quiz: Keyboards - SD of Differences
Quiz: Keyboards - t-Statistic
Quiz: Keyboards - t-Critical Values
Quiz: Keyboards - Decision
Quiz: Keyboards - Cohen's d
Cohen’s d = difference of means / sample standard deviation estimated by samples
Quiz: Keyboards - CI for Dependent Samples
Notation for Difference
Types of Designs
repeated measures design
Effect Size
effect size=mean difference
Quiz: Everyday Meaning
Types of Effect-Size Measures
- difference measures
- mean difference
- standarized difference
Cohen’s d
- Correlation measures
$r^2$
Statistical Significance
Cohen's d
$d=\frac{\bar{x}-\mu}{s}$
s: standard deviation of sample means
r^2
coefficieng of determination
0-1
$$r^2 = \frac{t^2}{t^2 + df}$$
t: not the t-critical
df: degrees of freedom
0: the variables are not at all related
Quiz: Compute r^2
Report Results
APA style
t(df) = x.xx, p=.xx, direction
t(24) = -2.50, p<.05, one-tailed
Report CI Results
Report CI Results 2
APA style-CIs
confidence interval on the mean difference; 95%CI = (4,6)
Report Results Effect Size
Cohen’s d, $r^2$
d = x.xx
$r^2$ = .xx
One-Sample t-Test
formulas:
df = n-1
$SEM = \frac{s}{\sqrt{n}}$
s: sample standard deviation
$t = \frac{\bar{x} - \mu}{SEM}$
$\bar{x}$: sample mean
$\mu$: population mean
CI = $\bar{x}\pm$ margin of error
margin of error = t-critical * SEM
Cohen’s d = $\frac{\bar{x}-\mu}{s}$
$r^2 = \frac{t^2}{t^2 + df}$
t: not the t-critical
Mu
Quiz: Dependent Variable
Quiz: Treatment
Quiz: Null Hypothesis
Quiz: Alternative Hypothesis
Hypotheses
Quiz: Which-Tailed Test?
Quiz: Degrees of Freedom
Quiz: t-Critical
can be found directly via t-table
Quiz: SEM
standard error of mean
sample standard deviation / sqrt(n)
Quiz: Mean Difference
sample mean and population mean
Quiz: t-Statistic
Quiz: Critical Region
Quiz: P-Value
Quiz: Statistically Significant
Quiz: Meaningful Results
Quiz: Cohen's d
Quiz: r^2
Quiz: Margin of Error
Quiz: Compute CI
Problem Set 10: t-Tests
Quiz: 1. Normal vs. t-Distribution
Quiz: 2. Z vs. t
Quiz: 3. Vocabularies - Type of Study
Quiz: 4. Vocabularies - Independent Variable
Quiz: 5. Vocabularies - Dependent Variable
Quiz: 6. Vocabularies - Null Hypothesis
Quiz: 7. Vocabularies - Alternative Hypothesis
Quiz: 8. Vocabularies - One- or Two-Tailed?
Quiz: 9. Vocabularies - t-Critical Value
Quiz: 10. Vocabularies - Mean and SD
Quiz: 11. Vocabularies - t-Statistic
Quiz: 12. Cell Phone Law: Type of Study
Quiz: 13. Cell Phone Law: Dependent Variable
Quiz: 14. Cell Phone Law: Independent Variable
Quiz: 15. Cell Phone Law: Null Hypothesis
Quiz: 16. Cell Phone Law: Alt. Hypothesis
Quiz: 17. Cell Phone Law: t-Test
Quiz: 18. Cell Phone Law: Difference Scores
Quiz: 19. Cell Phone Law: t-Critical Value
Quiz: 20. Cell Phone Law: Standard Error
Quiz: 21. Cell Phone Law: t-Statistic
Quiz: 22. Cell Phone Law: Decision
Quiz: 23. Cell Phone Law: Cohen's d
Quiz: 24. Cell Phone Law: CI
Make sure you use the t-critical value for a two-tailed test, even if you are doing a one-tailed test. This is because you center the confidence interval around your point estimate, rather than letting one bound go to positive or negative infinity depending on the direction of your test.
t-Tests continued
Independent Samples
independent samples
- experimental
- observational
Standard Error
standard error =
$$\frac{s}{\sqrt{n}} = \frac{\sqrt{s^2_1 + s^2_2}}{\sqrt{n}} = \sqrt{\frac{s^2_1 + s^2_2}{n}} = \sqrt{\frac{s^2_1}{n_1} + \frac{s^2_2}{n_2}}$$
$$df = n_1 + n_2 -2$$
t-statistic = $\frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{SE}$
Quiz: Meal Prices
Click here to access the data: Meal prices in Gettysburg and Wilma
If you would like to perform any calculations, copy and paste the data into your own spreadsheet. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Quiz: Average Meal Price
Quiz: SD for Meal Price
Quiz: Meal Price SEM
Quiz: Meal Price t-Statistic
Quiz: Calculate t-Statistic
Quiz: t-Critical Values
Quiz: Gettysburg or Wilma?
Acne Medication
Quiz: Acne Medication t-Statistic
Quiz: Acne Medication - t-Critical Values
Quiz: Acne Medication - Decision
Who Has More Shoes?
Quiz: Mean Number of Shoes
Click here to access the data: Pairs of shoes owned by males and females
Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Quiz: Shoes - Standard Error
Quiz: Shoes - t-Statistic
Quiz: Shoes - Decision
Quiz: Shoes - 95% CI
Quiz: Shoes - Calculate CI
Quiz: Gender and Shoes
Quiz: Pooled Variance Sum of Squares
Assumes samples are approximately the same size
$$SS^2_p = \frac{SS_1 + SS_2}{df_1 +df_2}$$
SS: sum of squares
$SS^2_p$: pooled variance
Quiz: Calculate Pooled Variance
Quiz: Corrected Standard Error
standard error :
$$\sqrt{\frac{S^2_1}{n_1} + \frac{S^2_2}{n_2}}$$
corrected Standard Error:
$$\sqrt{\frac{S^2_p}{n_1} + \frac{S^2_p}{n_2}}$$
Quiz: t-Statistic
Quiz: t-Critical and Decision
Assumptions
standard error:
$$\sqrt{\frac{S^2_1}{n_1} + \frac{S^2_2}{n_2}}$$
corrected Standard Error:
$$\sqrt{\frac{S^2_p}{n_1} + \frac{S^2_p}{n_2}}$$
T-test assumption
- X and Y should be random samples from two different independent populations
- Populations are approximately normal
- Sample data can extimate population variances
- Population variances are roughly equal
Problem Set 11: t-Tests continued
Quiz: 1. t-Test
Quiz: 2. t-Test
Quiz: 3. t-Test
Quiz: 4. t-Critical Value
Quiz: 5. P-Value
Quiz: 6. P-Value
Quiz: 7. t-Statistic
Quiz: 8. True or False?
Quiz: 9. Sum of Squares
Quiz: 10. Pooled Variance
Quiz: 11. Standard Error
Quiz: 12. t-Statistic
Quiz: 13. Decision
Quiz: 14. Independent Variable
Quiz: 15. Dependent Variable
Quiz: 16. Null Hypothesis
Quiz: 17. Degrees of Freedom
Quiz: 18. t-Critical Values
Quiz: 19. t-Statistic
Quiz: 20. Decision
Quiz: 21. Cohen's d
Quiz: 22. Percent of Variability
One-way ANOVA
Quiz: Intuition
Quiz: Number of t-Tests
Quiz: Extended t-Test Numerator
grand mean
Quiz: Grand Mean
grand mean sometimes equal to mean of sample means
Quiz: Between-Group Variability
Quiz: Significantly Different Means
Quiz: Sample Variability and Significance
within-group variability: the variability of indivisual samples
ANOVA
ANOVA: analysis of variance
one-way ANOVA: one independent vaiable
Quiz: Hypotheses
Quiz: Within-Group Variability
Within-Group Variability greater, test statistics smalller
Quiz: Between-Group Variability
Between-Group Variability greater, test statistics greater
Quiz: F-Ratio
F-Ratio = Between-Group Variability / Within-Group Variability
Quiz: Visualize Statistical Outcome
Quiz: Formalize Within-Group Variability
Formula for F-Ratio
$$F = \frac{Between-Group Variability}{Within-Group Variability} = \frac{n\sum(\bar{x}_k - \bar{x}_G)^2/(k-1)}{\sum(\bar{x}_i - \bar{x}_k)^2/(N-k)} = \frac{SS_{between}/df_{between}}{SS_{within}/df_{within}} = \frac{MS_{between}}{MS_{within}}$$
Quiz: Degrees of Freedom
$$df_{total} = N-1$$
$$df_{between} + df_{within} = (k-1) + (N-k) =N-1$$
Total Variation
$$SS_{between} + SS_{within} = SS_{total} = \sum(\bar{x}_i - \bar{x}_G)^2$$
Quiz: F-Distribution
F-Distribution Shape
Quiz: Table for F-Critical
Click here if you’d like to check out the F-table!
Quiz: Sample Means and Grand Mean
Quiz: SS Between
Quiz: SS Within
Quiz: Degrees of Freedom
Quiz: Mean Squares
Quiz: F-Statistic
Quiz: F-Critical
Quiz: Decision
Problem Set 12: One-way ANOVA
Quiz: 1. Within-Group Variability
Quiz: 2. Between-Group Variability and F-Ratio
Quiz: 3. Source of Variation
Quiz: 4. Between-Group Variability
Quiz: 5. True or False?
Quiz: 6. Large F-Statistic
Quiz: 7. Degrees of Freedom
Quiz: 8. Decision
Quiz: 9. Degrees of Freedom
Quiz: 10. Decision
Quiz: 11. Null Hypothesis
Quiz: 12. Alternative Hypothesis
Quiz: 13. SS Between
Quiz: 14. SS Within
Quiz: 15. Degrees of Freedom
Quiz: 16. MS
Quiz: 17. F-Statistic
Quiz: 18. F-Critical Value
3.8853
Quiz: 19. Decision
Quiz: 20. DF Total
26
Quiz: 21. Null Hypothesis
Quiz: 22. N
28=3+24+1
Quiz: 23. Decision
Quiz: 24. SS Between
150=200-50
Quiz: 25. True or False?
True
ANOVA continued
Quiz: Cows and food
Quiz: Grand mean
Quiz: Group means
Quiz: SS between
Quiz: SS within
Quiz: Degrees of Freedom
Quiz: Mean squares
Quiz: F statistic
Quiz: F critical and decision
Quiz: Deviation from grand mean
Quiz: SS total
Quiz: Conclusion
Multiple Comparison Tests
compare all of the means with each other
Quiz: Tukeys HSD
Tukey’s Honostly Significant Difference(HSD) =
$$q^{\star} \sqrt{\frac{MS_{within}}{n}} = q^{\star} \frac{S_p}{\sqrt{n}}$$
q: Studentized Range Statistic
n: sample size
Link to Studentized Range Statistic (q) Table for alpha = 0.05
df is the degrees of freedom for within-group variability; k is the number of groups/samples in your study
Quiz: Which differences are significant
if difference between sample means greater than Tukey’s HSD, we can conclude that two sample is Honostly Significant Difference
Quiz: Cohens d for multiple comparisons
$$d = \frac{\bar{x_1} - \bar{x_2}}{S_p} = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{MS_{within}}}$$
Quiz: Eta squared
propotion of total variation that is due to between-group differences(explained variation)
$$\eta^2 = \frac{SS_{between}}{SS_{total}}$$
Quiz: Calculate eta squared
Quiz: Range of eta squared
Quiz: Software output
Quiz: Missing mean differences
Quiz: Different sample sizes
Quiz: Grand mean
Quiz: SS between
$$SS_{between} = \sum n_k (\bar{x_k} - \bar{x_G})^2$$
sample mean minus grand mean
Quiz: SS within
Quiz: Degrees of freedom
Quiz: MS and F
Quiz: Proportion due to drug type
$$\eta^2 = \frac{SS_{between}}{SS_{total}}$$
$\eta^2$ propotion of the difference between tumor reduction can be explained by the different treatments
Quiz: Power
type II error: failing to reject the null when we should have
- larger samples result in higher power
- lower within-group variability leads to higher power
- choosing treatments with strong effect sizes will increase power
ANOVA Assumptions and Wrap Up
$$F = \frac{Between-Group Variability}{Within-Group Variability} = \frac{n\sum(\bar{x}_k - \bar{x}_G)^2/(k-1)}{\sum(\bar{x}_i - \bar{x}_k)^2/(N-k)} = \frac{SS_{between}/df_{between}}{SS_{within}/df_{within}} = \frac{MS_{between}}{MS_{within}}$$
$$q^{\star} \sqrt{\frac{MS_{within}}{n}} = q^{\star} \frac{S_p}{\sqrt{n}}$$
$$\eta^2 = \frac{SS_{between}}{SS_{total}}$$
Problem Set 13: ANOVA continued
Quiz: 1. Decision
3.3158
retain
Quiz: 2. Decision
3.2874
reject
Quiz: 3. SS Within
SStotal - SSbetween
Quiz: 4. Symbolize SS Within
SS{within} is also called SS{error} because this is the variation that can’t be explained by the independent variable.
Quiz: 5. Degrees of Freedom
k-1
N-k
Quiz: 6. Hypotheses
Quiz: 7. Post-hoc Tests
We conduct post-hoc tests in order to determine which pair(s) of groups were significantly different, since ANOVA only tells us that at least one pair is significantly different.
Quiz: 8. Tukey's HSD
smaller than HSD, retain
Quiz: 9. Tukey's HSD
Quiz: 10. η^2
Quiz: 11. η^2 Meaning
Quiz: 12. Decision
0.05 F(1,30)-critical = 4.1709
Quiz: 13. Decision
Quiz: 14. SS Between
Quiz: 15. Normality Assumption
Quiz: 16. Homogeneity of Variance
Quiz: 17. Grand Mean
Quiz: 18. SS Between
Quiz: 19. Degrees of Freedom
Quiz: 20. MS Between
Quiz: 21. Decision
Quiz: 22. Conclusion
Quiz: 23. η^2
Quiz: 24. η^2 Meaning
Quiz: 25. Explained Proportion
Quiz: 26. Tukey's HSD
Correlation
Relationships
Quiz: The Variables x and y
Quiz: Show Relationship
Quiz: Scatterplot
Quiz: Stronger Relationship
Quiz: As x Increases
Quiz: Strength and Direction
Correlation Coefficient
Correlation Coefficient r: Pearson’s r
$$r = \frac{cov(x,y)}{S_x \cdot S_y} = \frac{cov_{x,y}}{S_x \cdot S_y}$$
$r^2$ = % of the variation in Y explained by the variation in X.
$r^2$: coefficient of determination
Quiz: Match with r
Quiz: Age in Months and Years
Quiz: Hours Asleep vs. Awake
Quiz: Create Scatterplot
Data from poll Copy and paste the data into your own spreadsheet to perform the calculations. From Google Drive (at the top of the page once you’re signed in to your Google account), click the button on the left that says “CREATE” and click “Spreadsheet.”
Quiz: Calculate r
Google Spreadsheets function to calculate r:
=PEARSON(start cell for variable x:end cell for variable x, start cell for variable y:end cell for variable y)
Quiz: Stronger
Quiz: Hypothesis Testing for ρ$\rho$: true correlation for population.
correlation between variable and population
Quiz: Testing for Significance
Quiz: CI for ρ
Quiz: Find p
Quiz: Add Outlier
Add the outlier (20, 8) to the data for age and number of pets (i.e., age = 20, number of pets = 8). Calculate the new correlation coefficient.
Correlation vs. Causation
Here is a link to the original comic
Fallacies
ambigous temporal precedence
third variable problem
post hoc fallacy
Problem Set 14: Correlation
Quiz: 1. Positive Directions
Quiz: 2. Order Correlation Coefficients
Quiz: 3. Interpret Results
Quiz: 4. Unlikely Value of ρ
Quiz: 5. ρ CI
Quiz: 6. Decision Based on t-Statistic
Quiz: 7. Writing Down Dreams
0.95
Dream Data
Quiz: 8. Relationships
Quiz: 9. No Correlation
Quiz: 10. Direction of Relationship
Quiz: 11. Approximate Correlation
Quiz: 12. Approximate Correlation
Quiz: 13. Increase Sample Size
When we were doing t-tests, as the sample size increased, we could reach significance with a smaller difference between the means. That’s because increasing the sample size makes it harder to get a large difference by chance. What’s the analogous idea here?
Quiz: 14. Direction of Relationship
Quiz: 15. Estimate r
0.58
Quiz: 16. Compute r
Quiz: 17. Coefficient of Determination
Quiz: 18. Calculate p
Quiz: 19. Decision
Quiz: 20. Conclusion
Quiz: 21. Decision Based on p
Regression
Intro to Linear Regression
Airplane Flights
Quiz: Symbolize Regression Equation
Try not to get confused with the typical way that the equation for the regression line is often presented: y = mx + b. There are a variety of standard ways for symbolizing the slope and y-intercept, and in this class we’ll use a to represent the y-intercept and b to represent the slope. In general, try not to memorize equations or formulas, because this will hinder your ability to understand the same formulas when different symbols are used to symbolize the same coefficients. Instead, it’s far better to understand the format of an equation or formula so you can recognize what each symbol means.
Quiz: Guess Best Fit Line
Minimize Sum of Squares
$$b = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2} = r(\frac{S_y}{S_x})$$
r: Pearson’s r
We have decided to symbolize the regression line by y = bx + a, where b represents the slope and a represents the y-intercept.
Since b = r(standard deviation of y-values)/(standard deviation of x-values), we can also symbolize the regression line like this:
y = r(standard deviation of y-values)/(standard deviation of x-values)x + a
Quiz: Calculate r
Quiz: Calculate Standard Deviations
Quiz: Calculate Slope
Quiz: Find y-Intercept
Quiz: What Point Does the Line Go Through?
Quiz: Calculate Means
Quiz: Calculate y-Intercept
Quiz: Travel 4000 Miles
Quiz: Additional Cost per Mile
Quiz: Cost to Travel 0 Miles
Quiz: Travel on a Budget
Quiz: Which Has More Error?
Standard Error of Estimate
Standard Error Of Estimate =
$$\frac{\sum(y - \hat{y})^2}{N - 2}$$
N: number of points
Confidence Intervals
Quiz: Hypothesis Testing for Slope
Quiz: t-Test for Slope
df = N -2
N: number of x points
R Output
Factors Affecting Linear Regression
Summary of Linear Regression
Intro to Multiple Regression
R: multiple correlation coefficient
$R^2$: propotion of variability in Y explained by out set of predictors
Quiz: Alcohol, Religiosity, & Self-Esteem
Quiz: Make Predictions
Quiz: Relationship
Quiz: Causation
Applets
Problem Set 15: Regression
Quiz: 1. Stem Cells & Vision - Slope
Quiz: 2. Stem Cells & Vision - r^2
Quiz: 3. Stem Cells & Vision - y-Intercept
Quiz: 4. Stem Cells & Vision - Regression Eqn
Quiz: 5. Stem Cells & Vision - # of Stem Cells
Quiz: 6. Stem Cells & Vision - Photoreceptors
Quiz: 7. Estimate Slope
Quiz: 8. Indicate Slope
Quiz: 9. CI for Slope
Quiz: 10. Symbols
Quiz: 11. Make Predictions
Quiz: 12. Standard Error
Quiz: 13. r^2
Quiz: 14. Definition of Slope
Quiz: 15. Definition of y-Intercept
Quiz: 16. Definition of y-Hat
Quiz: 17. Definition of Std Error of Estimate
Quiz: 18. Describe Relationship
Quiz: 19. Describe Relationship
Quiz: 20. Describe Relationship
Chi-Squared tests
Quiz: Scales of Measurement
Ratio data
Ordinal data
Interval data
If you would like some additional discussion on the scales of measurement, then take a look at this very nice little tutorial.
As you watch the tutorial, think about what properties must a measurement have for us to consider it a nominal scale or an ordinal scale, etc.
Quiz: Choose Type of Data
Non-Parametric Tests
Quiz: Mount Shasta
Quiz: Expected Frequencies
Quiz: Observed Frequency
Quiz: Hypotheses Percent
Quiz: Hypotheses Frequency
Quiz: Expected Frequencies
χ^2 Goodness-of-Fit Test
Quiz: χ^2 Statistic
| successful | unsuccessful | |
|---|---|---|
| expected frequency | 33 | 67 |
| observed frequency | 41 | 59 |
$$\chi^2 = \sum \frac{(f_o - f_e)^2}{f_e}$$
$f_o$: observed frequency
$f_e$: expected frequency
Quiz: Observed Equals Expected
Quiz: χ^2 Values
Quiz: Degrees of Freedom
Quiz: Which Has More df?
the more categories we have, the more degree of freedoms we have and the larger $\chi^2$ statistics will be. We need higher critical value to reject the null hpyothesis.
Quiz: Calculate χ^2 Statistic
Quiz: Find df
df = 1 = Number of categories - 1
Quiz: Calculate p
P value equals 0.0891
Not significant at either level
The instructor should have said, “Calculate the one-tailed p-value.” GraphPad’s Chi-Square calculator reports the p-value as two-sided, but should be taken as the one-sided p-value we desire.
χ^2 Test for Independence
Quiz: Remember Details
Elizabeth Loftus: Eyewitness Testimony
Source: Loftus, E.F. & Palmer, J.C. (1974). Reconstruction of automobile destruction: An example of the interaction between language and memory. Journal of Verbal Learning and Verbal Behavior. 13, 585-589.
Quiz: Broken Glass
| Hit | Smashed | Control | Total | |
|---|---|---|---|---|
| Yes | 7 | 16 | 6 | 29 |
| No | 43 | 34 | 44 | 121 |
| Total | 50 | 50 | 50 | 150 |
Null Hypothesis: Student’s response for whether or not they saw broken glass is independent of the wording used in question
Expected frequencies:
For (Yes, Hit) is (29/150) * 50
For (No, Hit) is (121/150) * 50
Quiz: Expected Frequencies
Quiz: Calculate χ^2 Statistic
Quiz: Degrees of Freedom
df = 2 = (number of rows - 1)(number of columns - 1)
Quiz: Decision
GraphPad QuickCalcs
Chi-Square Table
Quiz: Effect Size
Chi-square Test for Independence
$$Cramer’s V (\phi_c) = \sqrt{\frac{\chi^2}{n(k - 1)}}$$
k: smaller of number of rows or columns (2)
n: total number (150)
Quiz: Calculate Cramér's V
Assumptions and Restrictions
Avoid dependent observations
Avoid small expected frequencies (large n)
Summary
Congrats
Problem Set 16: Chi-Squared tests
Quiz: 1. Dependent Variable
Ranking
Quiz: 2. Scale of Measurement
Ordinal
Quiz: 3. Dependent Variable
help
Quiz: 4. Scale of Measurement
Nominal
Quiz: 5. Dependent Variable
time
Quiz: 6. Scale of Measurement
ratio
Quiz: 7. Dependent Variable
error
Quiz: 8. Scale of Measurement
ratio
Quiz: 9. Specify Level of Measurement
Quiz: 10. Select χ^2 Test
Quiz: 11. Null Hypothesis
not
Quiz: 12. Which χ^2 Test?
| outcome | frequencies | expected frequencies |
|---|---|---|
| 1 | 8 | 4 |
| 2 | 4 | 4 |
| 3 | 1 | 4 |
| 4 | 8 | 4 |
| 5 | 3 | 4 |
| 6 | 0 | 4 |
good nominal
Quiz: 13. Degrees of Freedom
5
Quiz: 14. χ^2 Critical Value
Quiz: 15. Calculate χ^2 Statistic
Quiz: 16. Decision
Quiz: 17. Conclusion
Quiz: 18. Null Hypothesis
| Cabin | Steerage | Total | |
|---|---|---|---|
| Yes | 299 | 186 | 485 |
| No | 280 | 526 | 806 |
| Total | 579 | 712 | 1291 |
independent
Quiz: 19. Which χ^2 Test?
Indenpence nominal
Quiz: 20. Degrees of Freedom
1
Quiz: 21. χ^2 Critical Value
Quiz: 22. Calculate χ^2
Quiz: 23. Decision
Quiz: 24. Conclusion
Lessons 10-16 Review/Assessment
Quiz: 1
Quiz: 2
Quiz: 3
Quiz: 4
Quiz: 5
Quiz: 6
Quiz: 7
0.3/15
Quiz: 8
120*0.02+5.24
Quiz: 9
Quiz: 10
Quiz: 11
Quiz: 12
Quiz: 13
Quiz: 14
Quiz: 15
Quiz: 16
Quiz: 17
Quiz: 18
Quiz: 19
Quiz: 20
Quiz: 21
Quiz: 22
Quiz: 23
Quiz: 24
Quiz: 25
Quiz: 26
Quiz: 27
Quiz: 28
Quiz: 29
Quiz: 30
Final Project
Final project details can be found [here](https://www.udacity.com/wiki/ud201/final_project.
Here are helpful tips and suggestions as you work on your final project!