Stats Exam 6: Ch 12&13

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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/Image Upload 1)

    ==> STEPS:

    1. SS

    2. Image Upload 2 

    • 3. S 
    • 4. SM=(Image Upload 3)

    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. 

    • -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
    "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:
    Image Upload 4
    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)

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

    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
Card Set
Stats Exam 6: Ch 12&13
Chapter 12 & 13 Confidence Interval ANOVA & F Obtained vs F Crit. Post Hoc Comparisons
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