1 / 14

Examining Confidence Intervals Masson & Loftus

This text explores the application of confidence intervals (CIs) and Bayesian methods in hypothesis testing and data analysis, particularly in the social sciences. It highlights the limitations of traditional null hypothesis significance testing (NHST) and advocates for graphical techniques that simplify data interpretation. The document emphasizes the robustness of CIs over point estimates, providing clear methods for calculating CIs in both between-subjects and within-subjects designs, while also discussing the advantages of using CIs as an alternative to NHST.

edythe
Télécharger la présentation

Examining Confidence Intervals Masson & Loftus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related