slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Chapter 12: Comparing Independent Means PowerPoint Presentation
Download Presentation
Chapter 12: Comparing Independent Means

Loading in 2 Seconds...

play fullscreen
1 / 22

Chapter 12: Comparing Independent Means - PowerPoint PPT Presentation


  • 154 Views
  • Uploaded on

Chapter 12: Comparing Independent Means. In Chapter 12:. 12.1 Paired and Independent Samples 12.2 Exploratory and Descriptive Statistics 12.3 Inference About the Mean Difference 12.4 Equal Variance t Procedure (Optional) 12.5 Conditions for Inference 12.6 Sample Size and Power.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Chapter 12: Comparing Independent Means' - amory


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
in chapter 12

In Chapter 12:

12.1 Paired and Independent Samples

12.2 Exploratory and Descriptive Statistics

12.3 Inference About the Mean Difference

12.4 Equal Variance t Procedure (Optional)

12.5 Conditions for Inference

12.6 Sample Size and Power

types of samples
Types of Samples
  • Single sample. One group; no concurrent control group
  • Paired samples. Two samples; data points uniquely matched
  • Two independent samples. Two samples, separate (unrelated) groups.
what type of sample
What Type of Sample?
  • Measure vitamin content in loaves of bread and see if the average meets national standards
  • Compare vitamin content of loaves immediately after baking versus content in same loaves 3 days later
  • Compare vitamin content of bread immediately after baking versus loaves that have been on shelf for 3 days

Answers:

1 = single sample

2 = paired samples

3 = independent samples

experimental vs observational groups
Experimental vs. Observational Groups

Independent samples can

  • Experimental –an intervention or treatment is assigned as part of the study protocol
  • Non-experimental (observational) – groups defined by a innate characteristics or self-selected exposure

“Two Groups” by Pieter Bruegel the Elder (c. 1525 – 1569)

illustrative data
Illustrative Data*

* Data set WCGS.sav (p. 49)

Type A personality men (n = 20)233, 291, 312, 250, 246, 197, 268, 224, 239, 239, 254, 276, 234, 181, 248, 252, 202, 218, 212, 325

Type B personality men (n = 20)344, 185, 263, 246, 224, 212, 188, 250, 148, 169, 226, 175, 242, 252, 153, 183, 137, 202, 194, 213

Do means from these populations differ? If so, by how much?

illustrative data cholesterol levels mg dl
Illustrative DataCholesterol levels (mg / dL)

Type A men in the sample have higher average cholesterol by 35 mg/dL

standard error
Standard Error

To address this question, calculate the standard error of the mean difference:

degrees of freedom
Degrees of Freedom
  • Two ways to estimate degrees of freedom:
  • dfWelch[complex formula on p. 244 of text]
  • dfconserv. = the smaller of (n1 – 1) or (n2 – 1)

For the illustrative data:

dfWelch = 35.4 (via SPSS)

dfWelch = 35.4 (via SPSS)

dfconserv. = smaller of (n1–1) or (n2 – 1)

= 20 – 1 = 19

dfconserv. = smaller of (n1–1) or (n2 – 1)

= 20 – 1 = 19

1 100 ci for 1 2
(1 – α)100% CI for µ1–µ2

Note:

(point estimate) ± (t)(SE)

margin of error

interpretation
Interpretation

The CI interval aims for µ1− µ2 with (1– α)100% confidence

hypothesis test
HypothesisTest
  • Test claim of “no difference in populations”
  • Note: widely different sample means can arise just by chance
  • Null hypothesis: H0: μ1 – μ2 = 0 (equivalently H0: μ1 = μ2)
  • Alternative hypothesis Ha: μ1 – μ2 ≠ 0 (two-sided) OR Ha: μ1 – μ2 > 0 (“right-sided”) ORHa: μ1 – μ2 < 0 (“left-sided”)
test statistic
Test Statistic

dfWelch= 35.4 (via SPSS)

dfconserv. = 19

p value via table c
P-value via Table C

tstat = 2.56 with 19 df

  • One-tailed P between .01 and .005
  • Two-tailed P between .02 and .01 (i.e., less than .02)
  • .01 < P < .02 provides good evidence against H0  observed difference is statistically significant
slide18
SPSS

Response variable (chol) in one column

Explanatory variable (group) in a different column

summary of independent t test
Summary of independent t test
  • H0: μ1 –μ2 = 0

C. P-value from Table C or computer(Interpret in usual fashion)

hypothesis test with the ci
Hypothesis Test with the CI
  • H0: μ1 – μ2 = 0 can be tested at α-level of significance with the (1 – α)100% CI
  • Example: 95% CI for μ1 – μ2 = (6.4 to 63.1)  excludes μ1 – μ2 = 0

 Significant difference at α = .05

hypothesis test with the ci1
Hypothesis Test with the CI
  • H0: μ1 – μ2 = 0
  • 99% CI for μ1 – μ2 is (-2.2 to 71.7), which includes μ1 – μ2 = 0

 Not Significant at α = .01