Hi I second Scott's advice about indicating reversed items somehow. I too have had times when some items were inadvertently doubly reversed, on occasion causing considerable work on computed scores to have to be redone.
Take care Jim James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax j.cl...@uwinnipeg.ca >>> "Lilienfeld, Scott O" <slil...@emory.edu> 04-Mar-12 4:14 PM >>> Jim Clark is correct: mathematically, there is nothing preventing a Cronbach's alpha or KR-20 (which is equivalent to alpha for dichotomous items) from being negative if the item intercorrelations are negative. I've occasionally seen this in my own questionnaire data for just the reason Jim posits - when we had inadvertently forgotten to flip the coding of reverse-scored items (or more often, flipped them and then inadverently unflipped them - a good reason, incidentally, to recode reverse-scored variables into new variables with little Rs after their labels). ...Scott ________________________________________ From: Jim Clark [j.cl...@uwinnipeg.ca] Sent: Sunday, March 04, 2012 5:04 PM To: Teaching in the Psychological Sciences (TIPS) Subject: Re: [tips] statistical oddity: please help Hi As shown below, the data in its original form has a negative average intercorrelation of items, hence a negative alpha (and KR20). Is it possible that some of the items on your measure need to be reversed (i.e., they were negatively worded)? The summary statistics show possible candidates for reversing. Another possibility (less likely) is that rows and columns are reversed. When I FLIPped the file (i.e., switched rows and columns), the intercorrelation (and alpha) become positive. This could again reflect failure to reverse items (i.e., subjects responded similar to one another to pos and neg items). You may need to convert following to fixed font (e.g., courier) to view properly. Take care Jim data list free / Examinee A B C D E F G H I J. begin data 1 1 1 0 1 1 0 1 0 1 0 2 1 0 0 0 0 1 0 0 0 1 3 1 1 1 1 1 0 1 0 0 0 4 1 1 1 0 0 1 0 1 0 0 5 1 0 1 1 0 0 0 0 0 0 6 1 1 1 0 1 1 1 0 0 0 7 1 0 1 1 0 0 1 1 0 1 8 1 1 1 0 1 1 0 0 1 0 9 1 1 0 1 1 1 0 1 0 0 10 1 1 1 1 1 0 0 0 1 0 end data. reliab /vari = a to j / summ = all. Reliability Warnings No SCALE subcommand was found. Scaling will be done on all specified variables. Each of the following component variables has zero variance and is removed from the scale: A The determinant of the covariance matrix is zero or approximately zero. Statistics based on its inverse matrix cannot be computed and they are displayed as system missing values. Scale: ALL VARIABLES Case Processing Summary N % Cases Valid 10 100.0 Excluded(a) 0 .0 Total 10 100.0 a Listwise deletion based on all variables in the procedure. Reliability Statistics Cronbach's Cronbach's N of Items Alpha(a) Alpha Based on Standardized Items(a) -.447 -.544 9 a The value is negative due to a negative average covariance among items. This violates reliability model assumptions. You may want to check item codings. Summary Item Statistics Mean Minimum Maximum Range Maximum / Variance N of Items Minimum Item Means .478 .200 .700 .500 3.500 .034 9 Item Variances .243 .178 .278 .100 1.563 .001 9 Inter-Item -.009 -.222 .200 .422 -.900 .006 9 Covariances Inter-Item -.041 -.816 .802 1.618 -.982 .107 9 Correlations Item-Total Statistics Scale Mean if Scale Variance Corrected Squared Cronbach's Item Deleted if Item Deleted Item-Total Multiple Alpha if Item Correlation Correlation Deleted B 3.600000 .933 .429 . -1.252(a) C 3.600000 1.600 -.218 . -.254(a) D 3.700000 1.567 -.206 . -.259(a) E 3.700000 .900 .408 . -1.298(a) F 3.800000 1.956 -.452 . .026 G 3.900000 1.211 .078 . -.671(a) H 4.000000 1.556 -.184 . -.294(a) I 4.000000 1.333 .000 . -.533(a) J 4.100000 2.100 -.582 . .048 a The value is negative due to a negative average covariance among items. This violates reliability model assumptions. You may want to check item codings. flip /newnames = examinee. FLIP performed on 10 cases and 11 variables, creating 10 cases and 11 variables. The working file has been replaced. Variable examinee has been used to name the new variables. It has not been transformed into a case. A new variable has been created called CASE_LBL. Its contents are the old variable names. New variable names: CASE_LBL K_1.0000 K_2.0000 K_3.0000 K_4.0000 K_5.0000 K_6.0000 K_7.0000 K_8.0000 K_9.0000 K_10.000 list. K_1.00 K_2.00 K_3.00 K_4.00 K_5.00 K_6.00 K_7.00 K_8.00 K_9.00 CASE_LBL 00 00 00 00 00 00 00 00 00 K_10.000 A 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 B 1.0000 .0000 1.0000 1.0000 .0000 1.0000 .0000 1.0000 1.0000 1.0000 C .0000 .0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 .0000 1.0000 D 1.0000 .0000 1.0000 .0000 1.0000 .0000 1.0000 .0000 1.0000 1.0000 E 1.0000 .0000 1.0000 .0000 .0000 1.0000 .0000 1.0000 1.0000 1.0000 F .0000 1.0000 .0000 1.0000 .0000 1.0000 .0000 1.0000 1.0000 .0000 G 1.0000 .0000 1.0000 .0000 .0000 1.0000 1.0000 .0000 .0000 .0000 H .0000 .0000 .0000 1.0000 .0000 .0000 1.0000 .0000 1.0000 .0000 I 1.0000 .0000 .0000 .0000 .0000 .0000 .0000 1.0000 .0000 1.0000 J .0000 1.0000 .0000 .0000 .0000 .0000 1.0000 .0000 .0000 .0000 Number of cases read: 10 Number of cases listed: 10 reliab /vari = K_1.0000 to K_10.000 / summ = all. Warnings No SCALE subcommand was found. Scaling will be done on all specified variables. The determinant of the covariance matrix is zero or approximately zero. Statistics based on its inverse matrix cannot be computed and they are displayed as system missing values. Scale: ALL VARIABLES Case Processing Summary N % Cases Valid 10 100.0 Excluded(a) 0 .0 Total 10 100.0 a Listwise deletion based on all variables in the procedure. Reliability Statistics Cronbach's Cronbach's N of Items Alpha Alpha Based on Standardized Items .610 .608 10 Summary Item Statistics Mean Minimum Maximum Range Maximum / Variance N of Items Minimum Item Means .530 .300 .600 .300 2.000 .016 10 Item Variances .261 .233 .278 .044 1.190 .000 10 Inter-Item .035 -.178 .156 .333 -.875 .007 10 Covariances Inter-Item .134 -.667 .583 1.250 -.875 .096 10 Correlations Item-Total Statistics Scale Mean if Scale Variance Corrected Squared Cronbach's Item Deleted if Item Deleted Item-Total Multiple Alpha if Item Correlation Correlation Deleted K_1.0000 4.700000 5.122 .171 . .610 K_2.0000 5.000000 5.778 -.096 . .662 K_3.0000 4.700000 4.233 .607 . .502 K_4.0000 4.800000 4.844 .287 . .583 K_5.0000 5.000000 4.444 .546 . .523 K_6.0000 4.700000 4.456 .489 . .533 K_7.0000 4.700000 6.011 -.193 . .686 K_8.0000 4.700000 4.678 .378 . .561 K_9.0000 4.700000 4.900 .272 . .587 K_10.000 4.700000 4.456 .489 . .533 James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax j.cl...@uwinnipeg.ca >>> Julie Osland <osla...@wju.edu> 04-Mar-12 2:36 PM >>> Hi all-- In my tests and measurements course, we just covered reliability, including different ways to compute reliability (test-retest, Cronbach's, KR-20, etc). Part of their homework assignment was compute the KR-20 for a given set of data. After giving the assignment, I performed all of the assigned reliability. In so doing, I arrived at a negative KR-20 value, which all of my T & M books say should *not* happen. I have double and triple checked the math both by hand and via MS Exel and I get the same result. When I collected the assignment, my students obtained the same outcome. Prior to the assignment, we worked two problems in class and nothing 'strange' happened. I've attached as an excel file the KR 20 computational problem data, in hopes someone would be willing to verify what we (my class and I) obtained. If a negative value is possible for reliability, what does it mean or communicate about the data? I'm having difficulty wrapping my mind around this right now. Any help and/or insight would be greatly appreciated. Feel free to e-mail me off list. Thank you, Julie Dr. Julie A. Osland, M.A., Ph.D. Assistant Professor of Psychology Wheeling Jesuit University 316 Washington Avenue Wheeling, WV 26003 Office: (304) 243-2329 e-mail: osla...@wju.edu --- You are currently subscribed to tips as: j.cl...@uwinnipeg.ca. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13251.645f86b5cec4da0a56ffea7a891720c9&n=T&l=tips&o=16431 or send a blank email to leave-16431-13251.645f86b5cec4da0a56ffea7a89172...@fsulist.frostburg.edu --- You are currently subscribed to tips as: slil...@emory.edu. 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