The flashcards below were created by user
Radhika316
on FreezingBlue Flashcards.
-
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.
-
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".
-
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.
-
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.
-
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.
-
SS BG Formula:
=> df?
=> Finding the MS:
- Formula: Take each group's (EX)2 and divide by n, add them and the subtract (EXTOTAL)2/nT
- => df? K-1
- K is the # of groups.
=> Finding the MS: SS BG/df BG
-
SSW Formula (Error)
=> df?
=> Finding the MS:
FORMULA: Sum up all the x 2 and subtract Squared Ex's/n for each group.
N-K - N= Total # of individuals
- K=Total # of groups.
=> Finding the MS: MSW/dfW
-
SS Totals (ANOVA)
- 1. SST= SSBG+SSw
- 2. dfT=dfBG+dfw
3. MS Total= MS BG+MS W
-
Evaluating the F-Obtained:
=> F Ratio:
=> loooking up F-critical
-Rej Null when?
=> F Ratio: MS BG/MS w
=> F Critical: Rej null if Fobt> F crit- TOP: dfBG
- SIDE: dfW .
- Top number: (.05)-light face.
- Bottom number: (.01)-Bold Face
-
-
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
-
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.
-
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
-
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
-
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
-
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
|
|