# Stats Exam 6: Ch 12&13

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 Author: Radhika316 ID: 275039 Filename: Stats Exam 6: Ch 12&13 Updated: 2014-05-22 02:54:39 Tags: Stats Folders: Description: Chapter 12 & 13 Confidence Interval ANOVA & F Obtained vs F Crit. Post Hoc Comparisons Show Answers:

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1. Confidence Interval of the Mean:
A statement concerning a RANGE of values which is likely to include the population mean based upon SAMPLE means from the population

=> sample mean is an unbiased estimate of population mean, so you can determine, with some degree of certainty, a range which contains the mean.
2. Confidence Interval INTERPRETATION:
Based upon this sample from the population, I am 95% certain that the mean of the population falls within a range of values between "x" and "y".
3. Confidence Interval (CI) Calculation:
==> STEPS:
CI= M+t(SM) AND  CI= M - t(SM

=>SM: Estimated Standard Error of the mean (S/)

==> STEPS:

1. SS

2.

• 3. S
• 4. SM=()

5. Find the Mean, df: n-1

6. Find T-Critical: If 90 % then .10 alpha. If 95% means .05 alpha level, two tails, with df.
4. Goals of the Interval estimate vs. Confidence Interval
When an interval estimate is attached to a "specific level of confidence" or probability, it's called a confidence interval

The general goal of estimation is to determine how much effect a treatment has; and if it works.

• BUT THE GOAL of a CONFIDENCE INTERVAL:
• -to use a sample mean or mean difference to estimate the corresponding population mean or mean difference.
• -also for independent/between measures t-stats, the values used for estimation is the difference b/w two population samples.
5. Between Groups ANOVA
-design?
-F-Ratio:
"Analysis of Variance"=>compares three or more samples

-uses the F-ratio: Mean Squared Treatment (BG) over MSError (W)

-Many alternative hypotheses and always non directional (two-tails)

-Design: Partition the total variance of sample into two separate sources hence the name "Analysis of Variance"

-"Total Variance" The variance associated with treatments AND Error, and variance associated with JUST error.
6. SS BG Formula:
=> df?
=> Finding the MS:
• Formula: Take each group's (EX)and divide by n, add them and the subtract (EXTOTAL)2/nT
• => df? K-1
• K is the # of groups.

=> Finding the MS: SSBG/dfBG

7. SSW Formula (Error)
=> df?
=> Finding the MS:
FORMULA:  Sum up all the x2 and subtract Squared Ex's/n for each group.

• => df? N-K
• N= Total # of individuals
• K=Total # of groups.

=> Finding the MS: MSW/dfW
8. SS Totals (ANOVA)
• 1. SST= SSBG+SSw
• 2. dfT=dfBG+dfw

3. MSTotal= MSBG+MSW
9. Evaluating the F-Obtained:
=> F Ratio:
=> loooking up F-critical
-Rej Null when?
=> F Ratio: MSBG/MSw

• => F Critical: Rej null if Fobt> F crit
• TOP: dfBG
• SIDE: dfW  .

• Top number: (.05)-light face.
• Bottom number: (.01)-Bold Face
10. F Ratio:
11. ANOVA INTERPRETATION:
A one-way ANOVA was performed and revealed a significant difference among Treatment 1 (m=4.75), Treatment 2 (m=blahh) and treatment 3 (M=teehee), F (dfbg,dfw)=TObtained, P<.05
12. Formal Properties: Between Groups ANOVA
• Between groups F statistics is appropriate when:
• -Independent measures is between subjects; and design includes three or more treatment groups.
• -Dependent Measures is quantitative, scale of measurement is interval or better.
13. Between Groups F-Statistics assumes:
Treatment groups are normally distributed, homogeneity of within group variance

Subjects are randomly and independently selected from population and Randomly assigned to treatment groups
14. Comparing Treatments: Between Groups ANOVA
Problem with multiple t-tests to compare treatment effects

Multiple t-tests would yield some significant decisions by chance

Can correct by making comparisons with a statistic that accounts for, "corrects for" multiple comparisons
15. Number of different tests: Other Post –Hocs comparisions
• Fisher’s LSD Test (Least Significant Difference)
• Tukey's HSD (Honest Significant Difference)

Other Post –Hocs comparisions

• Scheffe
• Newman-Keuls
• Duncan
• Bonferroni
16. Tukey's HSD (Honest Significant Difference)

CD:
q: look up how?
df: ? N-K
Where:

CD = Absolute critical difference

• q = Studentized range value obtain from table entered with
• k groups signifying appropriate column
• df for within treatments MS signifying row

n = number of individuals/observations per group

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