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Power, Effect Sizes, Confidence Intervals, & Academic Integrity

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Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic …

Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic integrity.

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  • 7126/6667 Survey Research & Design in Psychology
    Semester 1, 2014, University of Canberra, ACT, Australia
    James T. Neill
    Home page: http://en.wikiversity.org/wiki/Survey_research_and_design_in_psychology
    Lecture page: http://en.wikiversity.org/wiki/Survey_research_and_design_in_psychology/Lectures/Power_%26_effect_sizes
    Image name: Nuvola filesystems socket
    Image source: http://commons.wikimedia.org/wiki/File:Nuvola_filesystems_socket.png
    Image author: David Vignoni, http://en.wikipedia.org/wiki/David_Vignoni
    License: GNU LGPL, http://en.wikipedia.org/wiki/GNU_Lesser_General_Public_License
    Description:
    Explains use of statistical power, inferential decision making, effect sizes, confidence intervals in applied social science research, and addresses the issue of publication bias and academic integrity.
  • Image source: http://commons.wikimedia.org/wiki/File:Information_icon4.svg
    License: Public domain
  • Image source: http://commons.wikimedia.org/wiki/File:Information_icon4.svg
    License: Public domain
  • If I flipped a coin multiple times and called out the result each time, how many flips would it take if I was flipping straight heads, before you would suspect that I wasn’t telling the truth or using a bias coin?
    This is the logic of ST: How different does a sampling distribution need to be in order for us to conclude that it is different to our expectations?
    See: A Coin-Flipping Exercise to Introduce the P-Value: http://www.amstat.org/publications/jse/v2n1/maxwell.html
    Image: http://www.codefun.com/Genetic_Info1.htm
  • ST evolved and became a 20th century science phenomenon.
    Karl Pearson laid the foundation for ST as early as 1901 (Glaser, 1999)
    Sir Ronald Fisher 1920’s-1930’s (1925) developed ST for agricultural data to help determine agricultural effectiveness e.g., whether plants grew better using fertilizer A vs. B.
    Image source: https://commons.wikimedia.org/wiki/File:R._A._Fischer.jpg
    Image license: Released under the GNU Free Documentation License; PD-OLD-7
    Image author: USDA Natural Resources Conservation Service, http://photogallery.nrcs.usda.gov/res/sites/photogallery/
    Image source: http://commons.wikimedia.org/wiki/File:NRCSCA06195_-_California_(1257)(NRCS_Photo_Gallery).jpg
    Image license: Public domain
  • These designs couldn’t be fully experimental e.g., because variables (such as weather, soil quality, etc.) could not be controlled. Therefore they needn’t to determine whether plant growth differences were due to chance or due to agricultural methods.
  • For more info: http://www.aacn.org/AACN/jrnlajcc.nsf/GetArticle/ArticleThree85?OpenDocument
  • Cohen (1980’s-1990’s) critiqued ST: Inherent problems and weaknesses with ST tended to be ignored, even though since Cohen (1980’s), formal critiques and alternatives to ST had been available.
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    Whether a result is significant or not is a function of:
    Effect size (ES)
    N
    Critical alpha () level
    Sig. can be manipulated by tweaking any of the three
    as each of them increase, so does the likelihood of a significant result
  • <number>
    Kirk, R. E. (1996). Practical significance: A concept whose time has come. Educational and Psychological Measurement, 56(5), 746-759.
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    Image source: http://commons.wikimedia.org/wiki/File:Crystal_Clear_action_apply.png
    Image license: GFDL 2.1 http://en.wikipedia.org/wiki/GNU_Lesser_General_Public_License
  • <number>
    Image source: http://commons.wikimedia.org/wiki/File:Crystal_Clear_action_button_cancel.png
    Image license: GFDL 2.1 http://en.wikipedia.org/wiki/GNU_Lesser_General_Public_License
  • <number>
    Power = “The probability of detecting a given effect size in a population from a sample of size N, using significance criterion ”
  • <number>
  • <number>
    = 1 - likelihood that an inferential test won’t return a sig. result when there is a real difference (1 – β)
    An inferential test is more ‘powerful’ (i.e. more likely to get a significant result) when any of these 3 increase:
    ES (i.e., strength of relationship or effect)
    Sample size (N)
    Critical alpha
  • <number>
  • <number>
    Image screen shot from: http://www.danielsoper.com/statcalc3/calc.aspx?id=9
  • d is a standardised difference between two means, commonly refered to as Cohen’s d.
    Eta-squared is the proportion of total variance in a DV that can be attributed to an IV(s).
    r can be converted to d, d can be converted to r.
    Eta-squared can be converted to R, R can be converted to eta-squared.
  • d is a standardised difference between two means, commonly refered to as Cohen’s d.
    Eta-squared is the proportion of total variance in a DV that can be attributed to an IV(s).
    r can be converted to d, d can be converted to r.
    Eta-squared can be converted to R, R can be converted to eta-squared.
  • <number>
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    From slide 9: elderlab.yorku.ca/.../lectures/05%20Power%20and%20Effect%20Size/05%20Power%20and%20Effect%20Size.ppt
  • <number>
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    “Cohen’s (1977) caveat that it is better to obtain comparison standards from the professional literature than to use arbitrary guidelines of small, medium, and large effect sizes.”
    - Cason & Gills (1994, p.44)
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  • Memory and attention for schizophrenics and normals.
    Image: http://www.cognitivedrugresearch.com/newcdr/imageuploads/medium-untitled.jpg
  • Oral cancer screen leaflets were given to patients in dental waiting rooms, followed by a measure of their oral cancer knowledge and attitudes and intention towards screening tests.
    The immediate effect on knowledge, attitudes and intentions in primary care attenders of a patient information leaflet: a randomized control trial replication and extension
    Image: http://www.nature.com/bdj/journal/v194/n12/fig_tab/4810283t3.html
    Article Abstract: http://www.nature.com/bdj/journal/v194/n12/abs/4810283a.html
  • <number>
  • <number>
  • <number>
    Ward, R. M. (2002). Highly significant findings in psychology: A power and effect size survey. http://digitalcommons.uri.edu/dissertations/AAI3053127/
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    If the CI around a M does not include 0, then we can conclude that there is a significant difference between the means
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    Image source: This document
    Image author: James Neill, 2014
    Image license: Public domain
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    Answer: B
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    Answer: A
  • <number>
    Scargle, J. D. (2000). Publication Bias: The "File-Drawer Problem" in Scientific Inference. Journal of Scientific Exploration, 14 (2) 94-106.
    http://www.scientificexploration.org/jse/abstracts/v14n1a6.php
    http://en.wikipedia.org/wiki/Publication_bias
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    Image source: http://commons.wikimedia.org/wiki/File:Edge-drawer.png
    Image license: GFDL 2 http://en.wikipedia.org/wiki/GNU_General_Public_License
    See also:
    http://skepdic.com/filedrawer.html
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    Power (on average) is moderate, ~.6, resulting in the published literature under-reporting of real results due to insufficient power
    On the other hand, as if to ‘compensate’, journal editors and reviewers seem to favour publication of studies which report significant results
  • <number>
    Funnel Plot slides are from: ssrc.tums.ac.ir/SystematicReview/Assets/publicationbias.ppt
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    Note that the funnel plots’ X-axis in this example represents a bias towards not publishing large effects (more commonly the bias is towards is towards not publishing insignificance results)
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    Also see: Hubbard, Raymond and Armstrong, J. Scott (1992) Are Null Results Becoming an Endangered Species in Marketing?. Marketing Letters 3(2):pp. 127-136.
  • <number>
    Marsden, H., Carroll, M., & Neill, J. (2005). Who cheats at university? A self-report study of dishonest academic behaviours in a sample of Australian university students.  Australian Journal of Psychology, 57(1), 1-10.
  • <number>
    Marsden, H., Carroll, M., & Neill, J. (2005). Who cheats at university? A self-report study of dishonest academic behaviours in a sample of Australian university students.  Australian Journal of Psychology, 57(1), 1-10.
  • <number>
    Marsden, H., Carroll, M., & Neill, J. (2005). Who cheats at university? A self-report study of dishonest academic behaviours in a sample of Australian university students.  Australian Journal of Psychology, 57(1), 1-10.
  • <number>
  • Transcript

    • 1. Lecture 9 Survey Research & Design in Psychology James Neill, 2014 Creative Commons Attribution 4.0 Power, Effect Sizes, Confidence Intervals, & Academic Integrity
    • 2. 2 Overview 1. Significance testing 2. Inferential decision making 3. Statistical power 4. Effect size 5. Confidence intervals 6. Publication bias 7. Academic integrity 8. Statistical method guidelines
    • 3. 3 Readings 1. Ch 34: The size of effects in statistical analysis: Do my findings matter? 2. Ch 35: Meta-analysis: Combining and exploring statistical findings from previous research 3. Ch 37: Confidence intervals 4. Ch 39: Statistical power 5. Wilkinson, L., & APA Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604.
    • 4. 4 Significance Testing
    • 5. 5 Significance Testing: Overview • Logic • History • Criticisms • Decisions • Practical significance
    • 6. Logic of significance testing How many heads in a row would I need to throw before you'd protest that something “wasn't right”?
    • 7. Logic of significance testing Based on the distributional properties of a sample dataset, we can extrapolate (guessestimate) about the probability of the observed differences or relationships existing in a population. In so doing, we are assuming that the sample data is representative and that data meets the assumptions associated with the inferential test.
    • 8. 8 • Null hypothesis (H0) usually reflects an expected effect in the population (or no effect) • Obtain p-value from sample data to determine the likelihood of H0 being true • Researcher tolerates some false positives (critical α) to make a probability-based decision about H0 Logic of significance testing
    • 9. 9 History of significance testing • Developed by Ronald Fisher (1920’s-1930’s) • To determine which agricultural methods yielded greater output • Were variations in output between two plots attributable to chance or not?
    • 10. 10 • Agricultural research designs couldn’t be fully experimental because variables such as weather and soil quality couldn't be fully controlled, therefore it was needed to determine whether variations in the DV were due to chance or the IV(s). History of significance testing
    • 11. 11 • ST spread to other fields, including social sciences. • Spread aided by the development of computers and training. • In the latter decades of the 20th century, widespread use of ST attracted critique for its over-use and mis-use. History of significance testing
    • 12. 12 • Critiqued as early as 1930. • Cohen's (1980’s-1990’s) critique helped a critical mass of awareness to develop. • Lead to changes in publication guidelines and teaching about over-reliance on ST and alternative and adjunct techniques. Criticisms of significance testing
    • 13. 13 • The null hypothesis is rarely true. • ST only provides a binary decision (yes or no) and the direction of the effect. • But mostly we are interested in the size of the effect – i.e., how much of an effect? • Statistical vs. practical significance • Sig. is a function of ES, N and α Criticisms of significance testing
    • 14. 14 Statistical significance • Statistical significance means that the observed mean differences are not likely to be due to sampling error –Can get statistical significance, even with very small population differences, if N, ES and/or critical alpha are large enough
    • 15. 15 Practical significance • Practical significance is about whether the difference is large enough to be of value in a practical sense –Is it an effect worth being concerned about – are these noticeable or worthwhile effects? –e.g., a 5% increase in well-being probably has practical value
    • 16. Criticisms of significance testing Ziliak, S. T. & McCloskey, D. N. (2008). The cult of statistical significance: How the standard error cost us jobs, justice, and lives. Ann Arbor: University of Michigan Press.
    • 17. Criticisms of significance testing Kirk, R. E. (2001). Promoting good statistical practices: Some Suggestions. Educational and Psychological Measurement, 61, 213-218. doi: 10.1177/00131640121971185
    • 18. Criticisms of significance testing Meehl, P. E. (1978). Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of Consulting and Clinical Psychology, 46, 806-834.
    • 19. Criticisms of Significance Testing 999). The insignificance of null hypothesis significance testing. Political Research Quarterly, 52(3), 647-674.
    • 20. 20 APA Style Guide recommendations about effect sizes, CIs and power • APA 5th edition (2001) recommended reporting of ESs, power, etc. • APA 6th edition (2009) further strengthened the requirements to use NHST as a starting point and to also include ESs, CIs and power.
    • 21. 21 NHST and alternatives “Historically, researchers in psychology have relied heavily on null hypothesis significance testing (NHST) as a starting point for many (but not all) of its analytic approaches. APA stresses that NHST is but a starting point and that additional reporting such as effect sizes, confidence intervals, and extensive description are needed to convey the most complete meaning of the results... complete reporting of all tested hypotheses and estimates of appropriate ESs and CIs are the minimum expectations for all APA journals.” (APA Publication Manual (6th ed., 2009, p. 33)
    • 22. 22 Recommendations • Use traditional Fisherian logic methodology (inferential testing) • Also use alternative and complementary techniques (ESs and CIs) • Emphasise practical significance • Recognise merits and shortcomings of each approach
    • 23. 23 • Logic: –Examine sample data to determine p that it represents a population with no effect or some effect. It's a “bet” - At what point do you reject H0 ? • History: –Developed by Fisher for agricultural experiments in early 20th century –During the 1980's and 1990's, ST was increasingly criticised for over-use and mis-application. Significance testing: Summary
    • 24. 24 • Criticisms: –Binary, Depends on N, ES, and critical alpha, Need practical significance • Recommendations: –Wherever you report a significance test (p-level), also report an ES –Also consider power and CIs Significance testing: Summary
    • 25. Inferential Decision Making
    • 26. 26 Hypotheses in inferential testing Null Hypothesis (H0): No differences / No relationship Alternative Hypothesis (H1): Differences / Relationship
    • 27. 27 Inferential decisions Upon testing a hypothesis we draw a conclusion based on the sample data; either we: Do not reject H0 p is not sig. (i.e. not below the critical α) Reject H0 p is sig. (i.e., below the critical α)
    • 28. 28 Inferential Decisions: Correct Decisions We are hoping to make a correct inference from the sample; either: Do not reject H0 : Correctly retain H0 when there is no real difference/effect in the population Reject H0 (Power): Correctly reject H0 when there is a real difference/effect in the population
    • 29. 29 Inferential Decisions: Type I & II Errors However, when we fail to reject or reject H0 , we risk making errors: Type I error: Incorrectly reject H0 (i.e., there is no difference/effect in the population) Type II error: Incorrectly fail to reject H0 (i.e., there is a difference/effect in the population)
    • 30. Inferential Decision Making Table
    • 31. 31 • Correct acceptance of H0 • Power (correct rejection of H0) = 1- β • Type I error (false rejection of H0) = α • Type II error (false acceptance of H0) = β • Traditional emphasis has been too much on limiting Type I errors and not enough on Type II error – a balance is needed. Inferential decision making: Summary
    • 32. Statistical Power
    • 33. 33 Statistical power Statistical power is the probability of • correctly rejecting a false H0 • Getting a sig. result when there is a real difference in the population
    • 34. Statistical power
    • 35. 35 Statistical power • Desirable power > .80 • Typical power (in the social sciences) ~ .60 • Power becomes higher when any of these increase: –Critical alpha (α) –Sample size (N) –Effect size (Δ)
    • 36. 36 Power analysis • If possible, calculate expected power before conducting a study, based on: –Estimated N, –Critical α, –Expected or minimum ES (e.g., from related research) • Report actual power in the results.
    • 37. 37 Power analysis for MLR • Free, online post-hoc power calculator for MLR • http://www.danielsoper.com/statcalc3/calc.aspx?id=9
    • 38. 38 Summary: Statistical power 1. Power = p (detecting a real effect as statistically significant) 2. Increase by: –↑ N –↑ critical α –↑ ES • Power – >.8 “desirable” – ~.6 is more typical • Can be calculated prospectively and retrospectively
    • 39. Effect Sizes
    • 40. 40 • A measure of the strength of a relationship or effect. • Where p is reported, also present an effect size. –"reporting and interpreting effect sizes in the context of previously reported effects is essential to good research" (Wilkinson & APA Task Force on Statistical Inference, 1999 ,p. 599) What is an effect size?
    • 41. 41 • An inferential test may be statistically significant (i.e., unlikely to have occurred by chance), but this doesn’t necessarily indicate how large the effect is. • There may be non-significant, notable effects esp. in low powered tests. • Unlike significance, effect sizes are not influenced by N. Why use an effect size?
    • 42. 42 Commonly used effect sizes Correlational • r, r2 , sr2 • R, R2 Mean differences • Cohen’s d • η2 , ηp 2
    • 43. 43 Standardised mean difference The difference between two means in standard deviation units. -ve = negative difference/effect 0 = no difference/effect +ve = positive difference/effect
    • 44. 44 Standardised mean difference • A standardised measure of the difference between two Ms –d = M2 – M1 / σ –d = M2 – M1 / pooled SD • e.g., Cohen's d, Hedges' g • Not readily available in SPSS; use a separate calculator e.g., Cohensd.xls
    • 45. 45 Standardised mean difference • Represents a standardised group contrast on an inherently continuous measure • Uses the pooled standard deviation (some situations use control group standard deviation)
    • 46. Example effect sizes -5 0 5 0 0.2 0.4 d=.5 -5 0 5 0 0.2 0.4 d=1 -5 0 5 0 0.2 0.4 d=2 -5 0 5 0 0.2 0.4 d=4 Group 1 Group 2
    • 47. 47 • Cohen (1977): .2 = small .5 = moderate .8 = large • Wolf (1986): .25 = educationally significant .50 = practically significant (therapeutic) Standardised Mean ESs are proportional, e.g., .40 is twice as much change as .20 Rules of thumb for interpreting standardised mean differences
    • 48. 48 Interpreting effect size • No agreed standards for how to interpret an ES • Interpretation is ultimately subjective • Best approach is to compare with other studies
    • 49. 49 • A small ES can be impressive if, e.g., a variable is: –difficult to change (e.g. a personality construct) and/or –very valuable (e.g. an increase in life expectancy). • A large ES doesn’t necessarily mean that there is any practical value e.g., if –it isn’t related to the aims of the investigation (e.g. religious orientation). The meaning of an effect size depends on context
    • 50. Graphing standardised mean effect size - Example
    • 51. Standardised mean effect size table - Example
    • 52. 52 Standardised mean effect size – Exercise • 20 athletes rate their personal playing ability, M = 3.4 (SD = .6) (on a scale of 1 to 5) • After an intensive training program, the players rate their personal playing ability again, M = 3.8 (SD = .6) • What is the ES? How good was the intervention?
    • 53. 53 Standardised mean effect size - Answer Standardised mean effect size • = (M2 - M1 ) / SDpooled • = (3.8 - 3.4) / .6 • = .4 / .6 • = .67 • = a moderate-large change over time For simplicity, this example uses the same SD for both occasions.
    • 54. 54 Power & effect sizes in psychology Ward (2002) examined articles in 3 psych. journals to assess the current status of statistical power and effect size measures. • Journal of Personality and Social Psychology • Journal of Consulting and Clinical Psychology • Journal of Abnormal Psychology
    • 55. 55 Power & effect sizes in psychology • 7% of studies estimate or discuss statistical power. • 30% calculate ES measures. • A medium ES was discovered as the average ES across studies • Current research designs typically do not have sufficient power to detect such an ES.
    • 56. 56 Summary: Effect size 1. Standardised size of difference or strength of relationship 2. Inferential tests should be accompanied by ESs and CIs 3. Common bivariate ESs include Correlation (r) and Standardised mean difference (Cohen’s d) 4. Cohen’s d - not in SPSS – use a separate calculator
    • 57. Confidence Intervals
    • 58. 58 Confidence intervals • Very useful, underutilised • Gives ‘range of certainty’ or ‘area of confidence’ e.g., true M is 95% likely to lie between -1.96 SD and +1.96 of the sample M • Expressed as a: –Lower-limit –Upper-limit
    • 59. 59 Confidence intervals • CIs can be reported for: –B (unstandardised regression coefficient) in MLR –Ms –ESs • CIs can be examined statistically and graphically (e.g., error-bar graphs)
    • 60. CIs & error bar graphs ● CIs can be presented as error bar graphs ● Show the mean and upper and lower CI ● More informative alternatives to bar graphs or line graphs
    • 61. CIs in MLR ● CIs for Bs indicate that we should not reject the possibility that the population Bs are zero, except for Attentiveness (we are 95% sure that the true B for Attentiveness is between .91 and 2.16)
    • 62. 62 Confidence intervals: Review question 1 Question If a MLR predictor has a B = 5, with a 95% CI of .25 to .75, what should be concluded? A. Do not reject H0 (that B = 0) B. Reject H0 (that B = 0)
    • 63. 63 Confidence intervals: Review question 2 Question If a MLR predictor has a B = .2, with a 95% CI of -.2 to .6, what should be concluded? A. Do not reject H0 (that B = 0) B. Reject H0 (that B = 0)
    • 64. 64 Summary: Confidence interval 1. Gives ‘range of certainty’ 2. Based on M, SD, N, critical α 3. CIs e.g., M, M differences, ESs, β 4. Can be examined 1. Statistically (upper and lower limits) 2. Graphically (e.g., error-bar graphs)
    • 65. Publication Bias
    • 66. 66 Publication bias • When publication of results depends on their nature and direction. • Studies that show sig. effects are more likely to be published. • Type I publication errors are underestimated to the extent that they are: “frightening, even calling into question the scientific basis for much published literature.” (Greenwald, 1975, p. 15)
    • 67. 67 File-drawer effect • Tendency for non-sig. results to be ‘filed away’ (hidden) and not published. • # of null studies which would have to ‘filed away’ in order for a body of significant published effects to be considered doubtful.
    • 68. 68 Two counter-acting biases • Low Power: → under-estimation of real effects • Publication Bias or File-drawer effect: → over-estimation of real effects
    • 69. 69 Funnel plots • A scatterplot of treatment effect against study size. • Precision in estimating the true treatment effect ↑s as N ↑s. • Small studies scatter more widely at the bottom of the graph. • In the absence of bias the plot should resemble a symmetrical inverted funnel.
    • 70. Risk ratio (mortality) 0.025 1 40 2 1 0 Standarderror 0.25 4 Funnel plots No evidence of publication bias
    • 71. Publication Bias Missing non-sig. result studies Publication Bias: Asymmetrical appearance of the funnel plot with a gap in a bottom corner of the funnel plot As studies become less precise, results should be more variable, scattered to both sides of the more precise larger studies … unless there is publication bias.
    • 72. 72 Publication bias • If there is publication bias this will cause meta-analysis to overestimate effects. • The more pronounced the funnel plot asymmetry, the more likely it is that the amount of bias will be substantial.
    • 73. Countering the bias
    • 74. 74 Summary: Publication bias 1. Tendency for statistically significant studies to be published over non- significant studies 2. Indicated by gap in funnel plot → file-drawer effect 3. Counteracting biases in scientific publishing; tendency: –towards low-power studies which underestimate effects –to publish sig. effects over non-sig. effects
    • 75. Academic Integrity
    • 76. 76 Academic Integrity: Students (Marsden, Carroll, & Neill, 2005) • N = 954 students enrolled in 12 faculties of 4 Australian universities • Self-reported: –Plagiarism (81%) –Cheating (41%) –Falsification (25%)
    • 77. Academic Integrity: Academic staff - Examplehttp://www.abc.net.au/news/2014-04-17/research-investigations-mounting-for-embattled-professor/5397516
    • 78. Academic Integrity: Academic staff - Examplehttp://www.abc.net.au/news/2014-04-04/uq-research-retraction-barwood-murdoch/5368800
    • 79. 79 Summary: Academic integrity 1. Violations of academic integrity are prevalent for: 1. Students 2. Researchers 3. Commercial sponsors 2. Adopt a balanced, critical approach, striving for objectivity and academic integrity
    • 80. Statistical Methods in Psychology Journals: Guidelines and Explanations (Wilkinson, 1999)
    • 81. Method - Design (Wilkinson, 1999)
    • 82. Method - Population (Wilkinson, 1999)
    • 83. Method - Sample (Wilkinson, 1999)
    • 84. Method – Nonrandom assignment (Wilkinson, 1999)
    • 85. Method – Instruments (Wilkinson, 1999)
    • 86. Method – Variables (Wilkinson, 1999)
    • 87. Method – Procedure (Wilkinson, 1999)
    • 88. Method – Power and sample size (Wilkinson, 1999)
    • 89. Results – Complications (Wilkinson, 1999)
    • 90. Results – Min. sufficient analysis (Wilkinson, 1999)
    • 91. Results – Computer programs (Wilkinson, 1999)
    • 92. Results – Assumptions (Wilkinson, 1999)
    • 93. Results – Hypothesis tests (Wilkinson, 1999)
    • 94. Results – Effect sizes (Wilkinson, 1999)
    • 95. Results – Interval estimates (Wilkinson, 1999)
    • 96. Results – Causality (Wilkinson, 1999)
    • 97. Discussion – Interpretation (Wilkinson, 1999)
    • 98. Discussion – Conclusions (Wilkinson, 1999)
    • 99. 102 Further resources • Statistical significance (Wikiversity) • http://en.wikiversity.org/wiki/Statistical_significance • Effect sizes (Wikiversity): http://en.wikiversity.org/wiki/Effect_size • Statistical power (Wikiversity): http://en.wikiversity.org/wiki/Statistical_power • Confidence interval (Wikiversity) • http://en.wikiversity.org/wiki/Confidence_interval • Academic integrity (Wikiversity) • http://en.wikiversity.org/wiki/Academic_integrity • Publication bias • http://en.wikiversity.org/wiki/Publication_bias
    • 100. 103 1. Marsden, H., Carroll, M., & Neill, J. T. (2005). Who cheats at university? A self-report study of dishonest academic behaviours in a sample of Australian university students. Australian Journal of Psychology, 57, 1-10. http://wilderdom.com/abstracts/MarsdenCarrollNeill2005W 2. Ward, R. M. (2002). Highly significant findings in psychology: A power and effect size survey. http://digitalcommons.uri.edu/dissertations/AAI3053127/ 3. Wilkinson, L., & APA Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604. References
    • 101. 104 Open Office Impress ● This presentation was made using Open Office Impress. ● Free and open source software. ● http://www.openoffice.org/product/impress.html