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"The Between Groups TStatistics"
assume the usual, real world assumptions (normal distribution)
Sample vs. Sample; gives difference between one mean and another.
Only adjustment: T calculation of the standard error of the mean of the sampling distribution of the difference between two means. (aka denominator).
=> Evaluation: Evaluate the TTest (Tobserved) with ttable entered with df (n1+n22)
Reject the Null if TObserved is GREATER than TCritical; meaning tcritical should be smaller (means it is special)
Fail to reject the null: if Tcritical is greater than the TObserved. Concludes the treatment didn't work.
Two tails and .05 alpha level by default.

Independent TStatistics INTERPRETATION:
An Independent TStatistics was performed and revealed a significant difference between Herd 1 (M= "x") and Herd 2 (M= "y"); t(df)=tobserved, p<.05.

**Steps of an Independent TTest:
1. N1 & N2
2. Sum X
3. Sum X^2
4. Sample means (Numerator)
5 SS1 & SS2
6. df: n1+n22
7. Plug 5&6 into denominator and calculate.
8. Evaluated T Observed vs. T critical.

**T Observed Vs. TCritical:
Reject the Null if
Fail to reject the null:
Reject the Null if TObserved is GREATER than TCritical; meaning tcritical should be smaller (means it is special)
Fail to reject the null: if Tcritical is greater than the TObserved. Concludes the treatment didn't work.
T Critical gets smaller as you move to the left; increasing the alpha level makes the tcritical smaller also (so that you're less likely to reject the nullspeciallness)
Two tails and .05 alpha level by default.

IndependentReading Notes:
two sets of data come from two completely separate groups of participants; it is a research design that uses two separate samples to represent the two different populations (or two diff treatments)
Hypothesis test used for two different data samples to evaluate the MEAN DIFFERENCE between the two populations or treatment conditions.
Goal: Evaluate mean difference between two population

"Estimated Standard Error":
 measures amount of error expected when you use "sample mean difference" to represent a population mean.
 Ch 10/Independent

**One Tailed Vs. Two Tailed Tests.
One tailed: Relatively small mean differences can cause rejected null when compared to the magnitude required by a two tailed test; therefore one tailed test should only be used when clearly justified. So assume always two tails

**Factors that influence the outcome of hypothesis test for Independent T Scores:
1. The size of difference between the 2 sample means; large difference means more likely to reject null and increases measures of effect size.
2. Variability of scores: larger variance means larger error
3. Size of Samples: larger tvalue (farther from 0)more likely to reject the null (special)

Within Subjects Design/ "Dependent"
Major source of variance in psychological research results from individual differences; can contribute to systematic error in poor designs
The concept: To establish a "handicap" to account for the individual differences.
Estimate each individual's behavioral abilities; relative to behavioral measure and to other individuals in the sample; and adjust each individuals data by "correcting" it. Either Reducing his/her score if the individual is superior or Increasing the score if the individual is inferior
Each individual score is adjusted with respect to their mean performance and the mean performance of all individuals in the sample.
This is so we can see if actual treatment had the effect and no variance was due to individual differences.

Degrees of Freedom (Dependent)
n1;
remember than n is the number of individual subjects, the number of PAIRS of scores, not the number of individual observations.
Important Note: correct is with regard to "total sample", not the independent variable to see if the independent variable truly worked.

**The T value observed is significant forever; the within (correlated) tstatistics is appropriate when:
Independent variable is within subjects (quantitative or qualitative; has only two levels)
Dependent Variable is Quantitative, measured on an interval scale or better

**The within (correlated) tstatistic assumes
Distribution of scores within groups are normal
Independence of treatments, i.e. no carry over effects
The sample is randomly selected from the population

**Dependent TTest Steps:
 1. Sum X
 2. Find n
 3. Mean averages
 4. Find D: Differences
 5. Sum D's.
 6. Average D.
 7. D^2.
 1. SS:
 2. S^2: SS/n1 (variance)
 3. S (Standard Deviation)
 4. Standard Error of the Mean (S.E): S/Radical N
 5. T score: Avg D/S.E
 6. Find TCritical and Evaluate.

Interpretation: Dependent /Within Subjects
A dependent TTest was performed and revealed a significant difference between Treatment 1 (M="x") and Treatment 2 (M="y"), t(df)=T observed, p<.05

