Stats Exam 6: Ch 12&13

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.

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".

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: n-1

6. Find T-Critical: If 90 % then .10 alpha. If 95% means .05 alpha level, two tails, with df.

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.

"Analysis of Variance"=>compares three or more samples

-uses the F-ratio: Mean Squared _Treatment (BG) over MS_Error (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.

• Formula: Take each group's (EX)² and divide by n, add them and the subtract (EX_TOTAL)²_/n_T
• => df? K-1
• K is the # of groups.

=> Finding the MS: SS_BG/df_BG

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: MS_W/df_W

• 1. SS_T= SS_BG+SS_w
• 2. df_T=df_BG+df_w

3. MS_Total= MS_BG+MS_W

=> F Ratio: MS_BG/MSw

• => F Critical: Rej null if Fobt> F crit
• TOP: df_BG  
• SIDE: df_W  .

• Top number: (.05)-light face.
• Bottom number: (.01)-Bold Face

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 (df_bg,df_w)=T_Obtained, P<.05

• 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.

Treatment groups are normally distributed, homogeneity of within group variance

Subjects are randomly and independently selected from population and Randomly assigned to treatment groups

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

• Fisher’s LSD Test (Least Significant Difference)
• Tukey's HSD (Honest Significant Difference)

Other Post –Hocs comparisions

• Scheffe
• Newman-Keuls
• Duncan
• Bonferroni

 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