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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(S_{M}) AND CI= M  t(S_{M})
=>SM: Estimated Standard Error of the mean (S/ _{})
==> STEPS:
1. SS
2.
 3. S
 4. S_{M}=()
5. Find the Mean, df: n1
6. Find TCritical: 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 tstats, the values used for estimation is the difference b/w two population samples.

Between Groups ANOVA
design?
FRatio:
"Analysis of Variance"=>compares three or more samples
uses the Fratio: Mean Squared _{Treatment} (BG) over MS_{Error} (W)
Many alternative hypotheses and always non directional (twotails)
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 (EX_{TOTAL})^{2}_{/}n_{T}
 => df? K1
 K is the # of groups.
=> Finding the MS: SS _{BG}/df _{BG
}

SS_{W} Formula (Error)
=> df?
=> Finding the MS:
FORMULA: Sum up all the x ^{2 }and subtract Squared Ex's/n for each group.
 => df? NK
 N= Total # of individuals
 K=Total # of groups.
=> Finding the MS: MS _{W}/df _{W}

SS Totals (ANOVA)
 1. SS_{T}= SS_{BG}+SS_{w}
 2. df_{T}=df_{BG}+df_{w}
3. MS _{Total}= MS _{BG}+MS _{W}

Evaluating the FObtained:
=> F Ratio:
=> loooking up Fcritical
Rej Null when?
=> F Ratio: MS_{BG}/MS_{w
=> F Critical: Rej null if Fobt> F critTOP: dfBG SIDE: dfW .
Top number: (.05)light face.Bottom number: (.01)Bold Face
}


ANOVA INTERPRETATION:
A oneway ANOVA was performed and revealed a significant difference among Treatment 1 (m=4.75), Treatment 2 (m=blahh) and treatment 3 (M=teehee), F (df_{bg},df_{w})=T_{Obtained}, 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 FStatistics 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 ttests to compare treatment effects
Multiple ttests 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
 NewmanKeuls
 Duncan
 Bonferroni

Tukey's HSD (Honest Significant Difference)
CD:
q: look up how?
df: ? NK
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

