# ANOVA Statistical Significance, where does "d" value come from?

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## ANOVA Statistical Significance, where does "d" value come from?

 5 months into learning SPSS / Statistics and need a hopefully quick primer on one statistic from ANOVA. I am duplicating a report from last year, which worked great for this year's data. SPSS ran great and I got the output I expected, but need help in interpreting last year's report. ANOVA output from last year is Fall CALC1  grades                   N Mean        Std. Deviation Class of 2020 125 2.0720 1.01740 Class of 2021 149 2.6644  .96989 Total                274 2.3942 1.03320 Fall CALC1 grades                          SS        df Mean Square F Sig. Between Groups 23.857 1 23.857 24.252 .000 *** Within Groups 267.573 272 .984 Total                291.431 273 *** The footnote on this data says "There is a statistically significant and moderately sized (d = .60) difference in Calculus I grades between 2020 and 2021. " My question is where do you get "d = .60" (because I don't see it anywhere). If I can find that, at least I'll have a reference for the comment, then I'll study ANOVA myself and post questions as needed. (The statistician who did last year's report is nowhere to be found ...) ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: ANOVA Statistical Significance, where does "d" value come from?

 It must be Cohen's d effect size. See Wikipedia. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: ANOVA Statistical Significance, where does "d" value come from?

 In reply to this post by William Peck I would bet that it is Cohen's d... The difference between the means is approximately .59.  The pooled standard deviation is a little less than 1.00, so the ratio is approximately .6 or so.. Bill   William B. Ware, Professor Emeritus Educational Psychology, Measurement, and Evaluation Learning Sciences and Psychological Studies University of North Carolina at Chapel Hill McMichael Term Professor of Education, 2011-2013 Adjunct Professor, School of Social Work Academy of Distinguished Teaching Scholars at UNC-Chapel Hill, Charter Member EMAIL: [hidden email] -----Original Message----- From: SPSSX(r) Discussion <[hidden email]> On Behalf Of William Peck Sent: Wednesday, January 30, 2019 11:01 AM To: [hidden email] Subject: ANOVA Statistical Significance, where does "d" value come from? 5 months into learning SPSS / Statistics and need a hopefully quick primer on one statistic from ANOVA. I am duplicating a report from last year, which worked great for this year's data. SPSS ran great and I got the output I expected, but need help in interpreting last year's report. ANOVA output from last year is Fall CALC1  grades                   N Mean        Std. Deviation Class of 2020 125 2.0720 1.01740 Class of 2021 149 2.6644  .96989 Total                274 2.3942 1.03320 Fall CALC1 grades                          SS        df Mean Square F Sig. Between Groups 23.857 1 23.857 24.252 .000 *** Within Groups 267.573 272 .984 Total                291.431 273 *** The footnote on this data says "There is a statistically significant and moderately sized (d = .60) difference in Calculus I grades between 2020 and 2021. " My question is where do you get "d = .60" (because I don't see it anywhere). If I can find that, at least I'll have a reference for the comment, then I'll study ANOVA myself and post questions as needed. (The statistician who did last year's report is nowhere to be found ...) ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: ANOVA Statistical Significance, where does "d" value come from?

 He probably calculated it by hand. SPSS produces the partial eta squared as the measure of effect size, if the option is checked when preparing the analysis. Brian From: SPSSX(r) Discussion <[hidden email]> on behalf of Ware, William B <[hidden email]> Sent: Wednesday, January 30, 2019 11:12:02 AM To: [hidden email] Subject: Re: ANOVA Statistical Significance, where does "d" value come from?   I would bet that it is Cohen's d... The difference between the means is approximately .59.  The pooled standard deviation is a little less than 1.00, so the ratio is approximately .6 or so.. Bill   William B. Ware, Professor Emeritus Educational Psychology, Measurement, and Evaluation Learning Sciences and Psychological Studies University of North Carolina at Chapel Hill McMichael Term Professor of Education, 2011-2013 Adjunct Professor, School of Social Work Academy of Distinguished Teaching Scholars at UNC-Chapel Hill, Charter Member EMAIL: [hidden email] -----Original Message----- From: SPSSX(r) Discussion <[hidden email]> On Behalf Of William Peck Sent: Wednesday, January 30, 2019 11:01 AM To: [hidden email] Subject: ANOVA Statistical Significance, where does "d" value come from? 5 months into learning SPSS / Statistics and need a hopefully quick primer on one statistic from ANOVA. I am duplicating a report from last year, which worked great for this year's data. SPSS ran great and I got the output I expected, but need help in interpreting last year's report. ANOVA output from last year is Fall CALC1  grades                          N       Mean            Std. Deviation Class of 2020   125     2.0720  1.01740 Class of 2021   149     2.6644    .96989 Total                   274      2.3942  1.03320 Fall CALC1 grades                          SS              df       Mean Square     F       Sig. Between Groups  23.857  1       23.857  24.252  .000 *** Within Groups   267.573 272     .984            Total                   291.431  273                     *** The footnote on this data says "There is a statistically significant and moderately sized (d = .60) difference in Calculus I grades between 2020 and 2021. " My question is where do you get "d = .60" (because I don't see it anywhere). If I can find that, at least I'll have a reference for the comment, then I'll study ANOVA myself and post questions as needed. (The statistician who did last year's report is nowhere to be found ...) ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: ANOVA Statistical Significance, where does "d" value come from?

 In reply to this post by William Peck Note that, in general, there are two types of effect size measures:(1) Percentage of variance accounted for (e.g., eta-square, R-square, etc;historically, SPSS has peovided only this type of effect size measure).and(2) Difference(s) between means (e.g., d, g, f, etc.)Because of the critical role effect size measures play in statistical poweranalysis, one nice reference for effect size measures and power analysisis Jack Cohen's 1992 article "A Power Primer"; see:https://psycnet.apa.org/fulltext/1992-37683-001.htmlNote2:  For a one-way independent groups ANOVA, Cohen recommendsthe effect size measure "f".  However, in your example you only have twogroups (which could have been analyzed by independent groups t-test),though f can be calculated, d is a simpler and more familiar measure.Cohen's Table 1 provides a listing of effect size measures, their formulas,and guidelines for the interpretation of the magnitude of an ES.HTH.-Mike PalijNrw York UniversityOn Wed, Jan 30, 2019 at 11:01 AM William Peck <[hidden email]> wrote:5 months into learning SPSS / Statistics and need a hopefully quick primer on one statistic from ANOVA. I am duplicating a report from last year, which worked great for this year's data. SPSS ran great and I got the output I expected, but need help in interpreting last year's report. ANOVA output from last year is Fall CALC1  grades                         N       Mean            Std. Deviation Class of 2020   125     2.0720  1.01740 Class of 2021   149     2.6644    .96989 Total                   274     2.3942  1.03320 Fall CALC1 grades                          SS             df      Mean Square     F       Sig. Between Groups  23.857  1       23.857  24.252  .000 *** Within Groups   267.573 272     .984            Total                   291.431 273                      *** The footnote on this data says "There is a statistically significant and moderately sized (d = .60) difference in Calculus I grades between 2020 and 2021. " My question is where do you get "d = .60" (because I don't see it anywhere). If I can find that, at least I'll have a reference for the comment, then I'll study ANOVA myself and post questions as needed. (The statistician who did last year's report is nowhere to be found ...) ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: ANOVA Statistical Significance, where does "d" value come from?

 And while the t test output doesn't include d, it is easy to add it to the output using the STATS  TABLE CALC extension command as explained in my chapter (18) in McCormick and Salcedo, SPSS Statistics for Data Analysis and Visualization .  I can send the code to anyone who wants it.On Wed, Jan 30, 2019 at 10:27 AM Michael Palij <[hidden email]> wrote:Note that, in general, there are two types of effect size measures:(1) Percentage of variance accounted for (e.g., eta-square, R-square, etc;historically, SPSS has peovided only this type of effect size measure).and(2) Difference(s) between means (e.g., d, g, f, etc.)Because of the critical role effect size measures play in statistical poweranalysis, one nice reference for effect size measures and power analysisis Jack Cohen's 1992 article "A Power Primer"; see:https://psycnet.apa.org/fulltext/1992-37683-001.htmlNote2:  For a one-way independent groups ANOVA, Cohen recommendsthe effect size measure "f".  However, in your example you only have twogroups (which could have been analyzed by independent groups t-test),though f can be calculated, d is a simpler and more familiar measure.Cohen's Table 1 provides a listing of effect size measures, their formulas,and guidelines for the interpretation of the magnitude of an ES.HTH.-Mike PalijNrw York UniversityOn Wed, Jan 30, 2019 at 11:01 AM William Peck <[hidden email]> wrote:5 months into learning SPSS / Statistics and need a hopefully quick primer on one statistic from ANOVA. I am duplicating a report from last year, which worked great for this year's data. SPSS ran great and I got the output I expected, but need help in interpreting last year's report. ANOVA output from last year is Fall CALC1  grades                         N       Mean            Std. Deviation Class of 2020   125     2.0720  1.01740 Class of 2021   149     2.6644    .96989 Total                   274     2.3942  1.03320 Fall CALC1 grades                          SS             df      Mean Square     F       Sig. Between Groups  23.857  1       23.857  24.252  .000 *** Within Groups   267.573 272     .984            Total                   291.431 273                      *** The footnote on this data says "There is a statistically significant and moderately sized (d = .60) difference in Calculus I grades between 2020 and 2021. " My question is where do you get "d = .60" (because I don't see it anywhere). If I can find that, at least I'll have a reference for the comment, then I'll study ANOVA myself and post questions as needed. (The statistician who did last year's report is nowhere to be found ...) ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD -- Jon K Peck[hidden email] ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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## Re: ANOVA Statistical Significance, where does "d" value come from?

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## Re: ANOVA Statistical Significance, where does "d" value come from?

There's an unlocked copy at http://www.bwgriffin.com/workshop/Sampling%20A%20Cohen%20tables.pdf

Brian Dates

From: SPSSX(r) Discussion <[hidden email]> on behalf of Michael Palij <[hidden email]>
Sent: Wednesday, January 30, 2019 1:55:03 PM
To: [hidden email]
Subject: Re: ANOVA Statistical Significance, where does "d" value come from?

the article (I guess I get it because I come from the nyu.edu domain but
I don't remember acess being so seamless).  The full reference for the
Cohen article is:

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159.
doi:10.1037/0033-2909.112.1.155

A Google search may turn up an unlocked copy (it is a popular
article with over 32K citations according to Google Scholar).

-Mike Palij
New York University

On Wed, Jan 30, 2019 at 1:11 PM Jon Peck <[hidden email]> wrote:
The Cohen article you cite is under lock and key.

On Wed, Jan 30, 2019 at 10:27 AM Michael Palij <[hidden email]> wrote:
Note that, in general, there are two types of effect size measures:
(1) Percentage of variance accounted for (e.g., eta-square, R-square, etc;
historically, SPSS has peovided only this type of effect size measure).
and
(2) Difference(s) between means (e.g., d, g, f, etc.)

Because of the critical role effect size measures play in statistical power
analysis, one nice reference for effect size measures and power analysis
is Jack Cohen's 1992 article "A Power Primer"; see:

Note2:  For a one-way independent groups ANOVA, Cohen recommends
the effect size measure "f".  However, in your example you only have two
groups (which could have been analyzed by independent groups t-test),
though f can be calculated, d is a simpler and more familiar measure.
Cohen's Table 1 provides a listing of effect size measures, their formulas,
and guidelines for the interpretation of the magnitude of an ES.

HTH.

-Mike Palij
Nrw York University

On Wed, Jan 30, 2019 at 11:01 AM William Peck <[hidden email]> wrote:
5 months into learning SPSS / Statistics and need a hopefully quick primer on one statistic from ANOVA.

I am duplicating a report from last year, which worked great for this year's data. SPSS ran great and I got the output I expected, but need help in interpreting last year's report.

ANOVA output from last year is

N       Mean            Std. Deviation
Class of 2020   125     2.0720  1.01740
Class of 2021   149     2.6644    .96989
Total                   274     2.3942  1.03320

SS             df      Mean Square     F       Sig.
Between Groups  23.857  1       23.857  24.252  .000 ***
Within Groups   267.573 272     .984
Total                   291.431 273

*** The footnote on this data says "There is a statistically significant and moderately sized (d = .60) difference in Calculus I grades between 2020 and 2021. "

My question is where do you get "d = .60" (because I don't see it anywhere). If I can find that, at least I'll have a reference for the comment, then I'll study ANOVA myself and post questions as needed.

(The statistician who did last year's report is nowhere to be found ...)

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

--
Jon K Peck
[hidden email]

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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