Statistics Exam 5: Independent and Dependent Measures

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Radhika316
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Statistics Exam 5: Independent and Dependent Measures
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2014-05-06 18:15:20
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Stats Statistics
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Independent and Dependent Measures: Chapter 10 + 11
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  1. "The Between Groups T-Statistics"
    -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 T-Test (T-observed) with t-table entered with df (n1+n2-2)

    -Reject the Null if T-Observed is GREATER than T-Critical; meaning t-critical should be smaller (means it is special)

    -Fail to reject the null: if T-critical is greater than the T-Observed. Concludes the treatment didn't work.

    -Two tails and .05 alpha level by default.
  2. Independent T-Statistics INTERPRETATION:
    An Independent T-Statistics was performed and revealed a significant difference between Herd 1 (M= "x") and Herd 2 (M= "y"); t(df)=t-observed, p<.05.
  3. **Steps of an Independent T-Test:
    1. N1 & N2

    2. Sum X

    3. Sum X^2

    4. Sample means (Numerator)

    5 SS1 & SS2

    6. df: n1+n2-2

    7. Plug 5&6 into denominator and calculate.

    8. Evaluated T Observed vs. T critical.
  4. **T Observed Vs. T-Critical:
    -Reject the Null if
    -
    Fail to reject the null:
    -Reject the Null if T-Observed is GREATER than T-Critical; meaning t-critical should be smaller (means it is special)

    -Fail to reject the null: if T-critical is greater than the T-Observed. Concludes the treatment didn't work.

    -T Critical gets smaller as you move to the left; increasing the alpha level makes the t-critical smaller also (so that you're less likely to reject the null--speciallness)

    -Two tails and .05 alpha level by default.
  5. Independent--Reading 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
  6. "Estimated Standard Error":
    • measures amount of error expected when you use "sample mean difference" to represent a population mean.
    • -Ch 10/Independent
  7. **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
  8. **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 t-value (farther from 0)-more likely to reject the null (special)
  9. 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.
  10. Degrees of Freedom (Dependent)
    n-1;

    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.
  11. **The T value observed is significant forever; the within (correlated) t-statistics 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
  12. **The within (correlated) t-statistic 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
  13. **Dependent T-Test 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/n-1 (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 T-Critical and Evaluate.
  14. Interpretation: Dependent /Within Subjects
    A dependent T-Test was performed and revealed a significant difference between Treatment 1 (M="x") and Treatment 2 (M="y"), t(df)=T observed, p<.05

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