Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.
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Transcript of Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.
![Page 1: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/1.jpg)
Chapter 7
Introduction to the t Test
Part 1: One-sample t test
Sept. 25, 2014
![Page 2: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/2.jpg)
t Test for a Single Sample• Z test requires that you know from pop• Use a t-test when you don’t know the
population standard deviation.• One sample t-test:– Compare a sample mean to a population with a
known mean but an unknown variance
![Page 3: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/3.jpg)
Hypothesis testing procedure for t-test• Same general procedure:– Assume null hypothesis is true, relative to an alternate
(research hypothesis)– Compute observed t statistic from sample data based
on sampling distribution of the mean– Determine cutoff point (now a critical t) in comparison
distribution based on – Reject the null hypothesis if your observed t value falls
in critical region • |t observed| > |t critical|
![Page 4: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/4.jpg)
One–sample t Test• Must estimate the population variance from the
sample scores
– Unbiased estimate of the population variance (S2)
11
)( 22
N
SS
N
MXS
Sum of squareddeviations
Use N-1 to makeS2 bigger than sample
![Page 5: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/5.jpg)
t Test for a Single Sample
• Degrees of freedom– Number of scores that are
“free to vary”– Formula for S2 using degrees of freedom
1Ndf
df
SS
df
MXS
2
2 )(
Note: S2 indicates we estimated this from a sample ( always indicates population info)
![Page 6: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/6.jpg)
t Test for a Single Sample• Also need to find standard deviation of
distribution of means (SM)• The variance of the distribution of means
• The standard deviation of the distribution of means
22
N
SSM
2MM SS
![Page 7: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/7.jpg)
t Test for a Single Sample
• For t-tests, relevant comparison distribution is t distribution (not the normal curve used before in z test)
• The t distribution
![Page 8: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/8.jpg)
One-sample t Test• State null & research hypotheses• Assuming null is true, compute observed t
statistic for your sample mean
• Find correct critical t value based on your df• When do we reject the null?
MS
Mt
![Page 9: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/9.jpg)
Note on t-table• When > 30 df, critical values only given for 35, 40,
45 df, etc.• If your df are in between these groups, be more
conservative and use the lower df
• Do example in class…
![Page 10: Chapter 7 Introduction to the t Test Part 1: One-sample t test Sept. 25, 2014.](https://reader036.fdocuments.us/reader036/viewer/2022082405/5697bf871a28abf838c88c1e/html5/thumbnails/10.jpg)
One Sample t-test in SPSS• Use menus for:
Analyze Compare Means One sample tGives pop-up menu…need 2 things:– select variable to be tested/compared to
population mean (use “self-esteem”)– Notice “test value” window at bottom. Enter the
population/comparison mean here (use x.xx from past semester)
– Hit OK, get output and find sample mean, observed t, df, significance value (if < .05, reject null)