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Examining Confidence Intervals Masson & Loftus

Examining Confidence Intervals Masson & Loftus. b y Gordon Peyton. Bayes Theorem. Bayes Theorem P(S & Pos) = P( Pos|S )P(S) (Positive result) P(S|POS) = P(S & Pos)/P(Pos) (Neg. Result) Goal: Estimate if a hypothesis is true and/or define data distribution

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Examining Confidence Intervals Masson & Loftus

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  1. Examining Confidence IntervalsMasson & Loftus by Gordon Peyton

  2. Bayes Theorem • Bayes Theorem • P(S & Pos) = P(Pos|S)P(S) (Positive result) • P(S|POS) = P(S & Pos)/P(Pos) (Neg. Result) • Goal: Estimate if a hypothesis is true and/or define data distribution • Uses probability as the main tool

  3. Null Hypothesis and Significance Testing (NHST) • Data evaluation as an inductive inference • Significance testing under the assumption that one hypothesis is valid • H(0) - statement that a parameter takes a particular effect i.e. H(0): p= 1/3 • H(a) - statement that the parameter takes an alternative value i.e. H(A): p > 1/3

  4. Competing Hypothesis • Instead of a null hypothesis, two competing hypothesis are examined • H(a): p ≥ 3.5 • H(b): P < 3.5 • Hypothesis testing is ill-suited for the complex and multidimensional nature of most social science data sets?

  5. Graphical Procedures • The primary goal in the social sciences has been confirmation? • Graphical techniques generally accepted equivalent to other statistical in confirmation • Accepted tool for exploratory data analysis • What are the advantages of graphical in comparison to non-graphical analysis techniques? • Single glance rudimentary information gathering • Allows to compare multiple statistics within one graph • More convincing to a novice in data analysis • Where & when would a researcher gain an advantage using these techniques? • Preliminary Data Analysis to see if further analysis is necessary • Procure Grant money from a novice in statistics

  6. Confidence Interval (CI) • What kind of estimate is a confidence interval? • Interval estimate that is usually centered around a point the point estimate (mean) • Called a CI; for interval estimates are presumed to contain the parameter with a certain degree of confidence • In regards to violation of assumptions, (i.e. the normal distribution of data) how valid are CIs in comparison to point estimates? • CIs are considered robust in comparison, as it is more likely for a parameter to fall within a range of points than a single point. • CI with 95% confidence level • CI(95%) = (se) • /n

  7. CI continued • Is Hypothesis testing primarily designed to indirectly examine a restricted, convoluted, and usually uninteresting question? • Are CI s in contrast designed to address a more general and simpler question? • Easy determination of statistical power? • Best estimate of pattern of underlying population means • Power of underlying pattern

  8. CIs in Between-Subjects Design • Please explain these graphs… • (A) No CIs, (B) & (C) • No Interaction A & B, interaction (C) • Assuming the same data sets are used; how does one explain the difference of the CIs between Figure (B) and (C)? • Difference in confidence level(i.e. 95% vs. 99%) • How would this be helpful for Data analysis? • Easy to read and understand • Easy to see interactions

  9. Calculating a Between-Groups CI • Given the formula (1) on the left; how would one calculate a CI for condition M1? • CI(95%) = 11±) • CI = ± 3.85 • df = 27 • CI with 95% confidence level • CI(95%) = SEM

  10. Within Group CI • Formula for within subjects design • CI = Mj ± (tcritical) • CI = 801.2 ±(2.145), df = 14 • CI = ± 24.80

  11. Within Subjects CI • Between and Within subjects CI function the same way • Advantage of within subjects design taking out the between subject error probability, leading to greater power • Great for pattern analysis

  12. More options using CIs

  13. More Options to use CIs for • What other designs do Loftus and Masson address in regard to CIs? • Multifactorial Design s • Mixed Designs • Are these graphical techniques useful? How? • When would these techniques lose their “easy-to-read/examine property”?

  14. Conclusions? • Are CIs good supplement to the NHST? • Great visual indicator for Effects • Without graphical data analysis can be as easy shown by showing the range • Are CIs good alternatives to NHST? • More precise results can be is more easily reported through traditional statistical methods (t-test/ANOVA) • Given this uniqueness, it is almost self evident that no one set of algorithmic rules can appropriately coves all possible situations. (Loftus & Masson, 1994)

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