# contrast (orthogonal) coding with unequal cell frequencies

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## contrast (orthogonal) coding with unequal cell frequencies

 Hi Friends,  I made a post on this forum a few days back relating to use of categorical variables in multiple regression analysis. I was suggested to create contrast groups to overcome the issue I was facing. I have created two contrast variables for a categorical variable with three levels. Variable levels/categories are: 1-single,  2-married/widowed/divorced- with children,  3-married/widowed/divorced- without children  I created following two contrast variables(as I was suggested) category levels      single       mwd-having children          mwd-without children Contrast 1              -2                +1                              +1 Contrast 2               0                +1                               -1   Now the issue is while I was brushing up on my knowledge of contrast coding, I read that categories/levels with unequal size (n) should be adjusted by multiplying each code with the number of observations for the corresponding cell. But  I'm not really sure how to do it exactly and even after I have done it, how to make sure that I did it rightly.  I searched for a query similar to mine posted here and I found the one  given below but unfortunately the question has not been answered by anyone. The frequencies for each cell are as follows: single= 65, Married/widowed/divorced-having children= 50, Married/widowed/divorced-without children= 19 I need your suggestions. http://spssx-discussion.1045642.n5.nabble.com/orthogonal-coding-with-unequal-n-tp1076217.html
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 I re-read the contrast coding section in Cohen (1983) who has a detailed work-through of different coding schemes. He says that with equal cell Ns, the correlations among the contrast variables will be 0.0 but will not be 0.0 if cell Ns are unequal. However, the B (unstandardized coefficient) values are adjusted for the correlations between the contrast variables. The B values (and its standard error) are what you need to know for the significance of the contrast terms. The answer is No, do not multiply the contrast coefficient values by the corresponding cell N. Gene Maguin -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Sidra Sent: Tuesday, October 18, 2016 11:11 PM To: [hidden email] Subject: contrast (orthogonal) coding with unequal cell frequencies Hi Friends,  I made a post on this forum a few days back relating to use of categorical variables in multiple regression analysis. I was suggested to create contrast groups to overcome the issue I was facing. I have created two contrast variables for a categorical variable with three levels. Variable levels/categories are: 1-single,  2-married/widowed/divorced- with children, 3-married/widowed/divorced- without children  I created following two contrast variables(as I was suggested) category levels      single       mwd-having children          mwd-without children Contrast 1              -2                +1                              +1 Contrast 2               0                +1                               -1   Now the issue is while I was brushing up on my knowledge of contrast coding, I read that categories/levels with unequal size (n) should be adjusted by multiplying each code with the number of observations for the corresponding cell. But  I'm not really sure how to do it exactly and even after I have done it, how to make sure that I did it rightly.  I searched for a query similar to mine posted here and I found the one  given below but unfortunately the question has not been answered by anyone. The frequencies for each cell are as follows: single= 65, Married/widowed/divorced-having children= 50, Married/widowed/divorced-without children= 19 I need your suggestions. http://spssx-discussion.1045642.n5.nabble.com/orthogonal-coding-with-unequal-n-tp1076217.html   -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/contrast-orthogonal-coding-with-unequal-cell-frequencies-tp5733307.htmlSent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 OK. Thanks Eugene but Just to be sure, do I need to run the multiple regression with coding scheme you specified before? This is what you are implying, right?
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 Yes. That coding scheme represents the contrasts I understood you to be interested in. Gene Maguin -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Sidra Sent: Wednesday, October 19, 2016 9:46 AM To: [hidden email] Subject: Re: contrast (orthogonal) coding with unequal cell frequencies OK. Thanks Eugene but Just to be sure, do I need to run the multiple regression with coding scheme you specified before? This is what you are implying, right? -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/contrast-orthogonal-coding-with-unequal-cell-frequencies-tp5733307p5733310.htmlSent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 Thanks Gene. you have been a great help indeed.
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 In reply to this post by Maguin, Eugene First. Let me say that I do not remember ever using the exact, adjusted coefficients to account for Ns. Second. The resulting coefficients will be different, at least slightly, when the contrasts correlate, compared to when the correlation is zero -- what you get from exact weights. When two terms are uncorrelated, the presence of absence of the second one does not affect the size of the so-called "partial coefficients" of the other.  When they are /nearly/ uncorrelated -- which is what you usually get with the simple coefficients from Gene -- the sizes are not affected, much.  This is almost always "good enough".  But if your Ns are grossly different (yours are, "I don't know"), you should look at the regression with each predictor without the other, to confirm that they aren't affecting each other by much. -- Rich Ulrich From: SPSSX(r) Discussion <[hidden email]> on behalf of Maguin, Eugene <[hidden email]> Sent: Wednesday, October 19, 2016 9:38 AM To: [hidden email] Subject: Re: contrast (orthogonal) coding with unequal cell frequencies   I re-read the contrast coding section in Cohen (1983) who has a detailed work-through of different coding schemes. He says that with equal cell Ns, the correlations among the contrast variables will be 0.0 but will not be 0.0 if cell Ns are unequal. However, the B (unstandardized coefficient) values are adjusted for the correlations between the contrast variables. The B values (and its standard error) are what you need to know for the significance of the contrast terms. The answer is No, do not multiply the contrast coefficient values by the corresponding cell N. Gene Maguin ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 I have another query. As I'm working through my analysis using contrast variables, I am presented with this new problem. I want to control for the confounding effect of potential confounders using 10% rule to see the adjusted effect of main predictor on outcome. The two contrast categories that were created using "contrast orthogonal coding"  were supposed to represent two variables; marital status and childbearing status. I want to see whether the aforementioned two variables are confounders. Now I'm not sure whether I have to enter both contrast variables simultaneously with main predictor in the model to see the confounding effect of marital status and childbearing status  or I can enter them separately into the model (what I was supposed to do , had I worked with original variables) to see how much change each individual variable brings in the coefficient of main predictor. Kindly help me on this.
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 Note: To be more precise, what I want ask is whether I can treat new contrast coded variables as individual variables (to represent marital status and childbearing status)? or I have to treat them essentialiy as a pair for any analysis?
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 The big virtue of /orthogonal/ coding, using the Ns, is that the two contrasts are created as uncorrelated: which makes them "unconfounded".  If you use that version, then the coefficients are exactly the same whether you look at one contrast or both; the t-test will vary only to the extent that taking into account another variable will reduce the (denominator) error term. As I just posted, with unequal Ns, you can check to see if the simple contrasts (not using Ns) do give essentially the same outcome. If not, then you either look at them together or discuss the mutual impact or switch to the other contrasts. -- Rich Ulrich From: SPSSX(r) Discussion <[hidden email]> on behalf of Sidra <[hidden email]> Sent: Wednesday, October 19, 2016 10:29 PM To: [hidden email] Subject: Re: contrast (orthogonal) coding with unequal cell frequencies   Note: To be more precise, what I want ask is whether I can treat new contrast coded variables as individual variables (to represent marital status and childbearing status)? or I have to treat them essentialiy as a pair for any analysis? ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 Rich, I need some education about what you’re saying in your reply. That first sentence and the phrase “using the Ns”. How does using the Ns change the construction of the contrast coefficients? To be specific suppose cell Ns of 75, 40, 15 and the two contrasts being (-2, 1, 1) and (0, -1, 1). Thanks, Gene Maguin             From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Rich Ulrich Sent: Thursday, October 20, 2016 1:24 AM To: [hidden email] Subject: Re: contrast (orthogonal) coding with unequal cell frequencies   The big virtue of /orthogonal/ coding, using the Ns, is that the two contrasts are created as uncorrelated: which makes them "unconfounded".  If you use that version, then the coefficients are exactly the same whether you look at one contrast or both; the t-test will vary only to the extent that taking into account another variable will reduce the (denominator) error term.   As I just posted, with unequal Ns, you can check to see if the simple contrasts (not using Ns) do give essentially the same outcome. If not, then you either look at them together or discuss the mutual impact or switch to the other contrasts.   -- Rich Ulrich   From: SPSSX(r) Discussion <[hidden email]> on behalf of Sidra <[hidden email]> Sent: Wednesday, October 19, 2016 10:29 PM To: [hidden email] Subject: Re: contrast (orthogonal) coding with unequal cell frequencies   Note: To be more precise, what I want ask is whether I can treat new contrast coded variables as individual variables (to represent marital status and childbearing status)? or I have to treat them essentialiy as a pair for any analysis? ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 In reply to this post by Sidra Sidra, what is the 10% rule?  Gene Maguin -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Sidra Sent: Wednesday, October 19, 2016 9:59 PM To: [hidden email] Subject: Re: contrast (orthogonal) coding with unequal cell frequencies I have another query. As I'm working through my analysis using contrast variables, I am presented with this new problem. I want to control for the confounding effect of potential confounders using 10% rule to see the adjusted effect of main predictor on outcome. The two contrast categories that were created using "contrast orthogonal coding"  were supposed to represent two variables; marital status and childbearing status. I want to see whether the aforementioned two variables are confounders. Now I'm not sure whether I have to enter both contrast variables simultaneously with main predictor in the model to see the confounding effect of marital status and childbearing status  or I can enter them separately into the model (what I was supposed to do , had I worked with original variables) to see how much change each individual variable brings in the coefficient of main predictor. Kindly help me on this. -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/contrast-orthogonal-coding-with-unequal-cell-frequencies-tp5733307p5733323.htmlSent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

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## Re: contrast (orthogonal) coding with unequal cell frequencies

 This post was updated on . I'm sorry fellows, I do not have a background of statistics ..that's why I'm having a hard time understanding your suggestions here. Perhaps I need to be a little bot more comprehensive.   I have IVs of nursing specialty,  qualification, age, years of experience, work shift, marital status and childberaing status; dependent variable being perceived stress by nurses. I need to see the effect of nursing specialty (as main variable of interest) on perceived stress while controlled for confounders. I will identify confounders by noting crude coefficient of nursing specialty and then noticing the change in its coefficient when each IV is placed in the model with nursing specialty (one variable at a time). If adding a variable in regression model brings a change of more than 10% in coefficient of nursing specialty, I ll treat that variable as a confounder. Since to find out if a variable is a confounder, I have to put that confounder alone along with nursing specialty in regression model, I am not sure if I can treat contrast 1 and contrast 2 (in place of marital status and childbearing status) as individual variables to see how much change each brings about in the coefficient of nursing specialty separately. I hope I have made myself sufficiently clear. Please bear with me and offer your kind insight on this problem.
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 In reply to this post by Maguin, Eugene Rich can speak for himself but I think that he means that the orthogonal contrast (OC) for the three groups would look something like this:   ----------OC1__________OC2 Group1 (75*-2)= -150     (75*0)=0 Group2 (40*1)= 40          (40*-1)= -40 Group3 (15*1)=  15         (15*1)= 15   Elazar Pedhazur cover this situation and compare the use of orthogonal coefficients with one-way ANOVA in the following:   Pedhazur, E. J. (1997). Multiple regression in behavioral research: Explanation and prediction. Fort Worth: Harcourt Brace College Publishers.   See Chapter 11. A Categorical Independent Variable: Dummy, Effect, and Orthogonal Coding.   Page 401-406 cover orthogonal coding with unequal sample sizes..   If I am wrong, I'm sure I will be corrected.   -Mike Palij New York University [hidden email]     ----- Original Message ----- From: [hidden email] Sent: Thursday, October 20, 2016 8:56 AM Subject: Re: contrast (orthogonal) coding with unequal cell frequencies Rich, I need some education about what youre saying in your reply. That first sentence and the phrase using the Ns. How does using the Ns change the construction of the contrast coefficients? To be specific suppose cell Ns of 75, 40, 15 and the two contrasts being (-2, 1, 1) and (0, -1, 1). Thanks, Gene Maguin             From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Rich UlrichSent: Thursday, October 20, 2016 1:24 AMTo: [hidden email]Subject: Re: contrast (orthogonal) coding with unequal cell frequencies   The big virtue of /orthogonal/ coding, using the Ns, is that the two contrasts are created as uncorrelated: which makes them "unconfounded".  If you use that version, then the coefficients are exactly the same whether you look at one contrast or both; the t-test will vary only to the extent that taking into account another variable will reduce the (denominator) error term.   As I just posted, with unequal Ns, you can check to see if the simple contrasts (not using Ns) do give essentially the same outcome. If not, then you either look at them together or discuss the mutual impact or switch to the other contrasts.   -- Rich Ulrich   From: SPSSX(r) Discussion <[hidden email]> on behalf of Sidra <[hidden email]>Sent: Wednesday, October 19, 2016 10:29 PMTo: [hidden email]Subject: Re: contrast (orthogonal) coding with unequal cell frequencies   Note: To be more precise, what I want ask is whether I can treat new contrastcoded variables as individual variables (to represent marital status andchildbearing status)? or I have to treat them essentialiy as a pair for anyanalysis? ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 In reply to this post by Sidra From Rich's comment I'm am getting this impression that my be my previous comment has been taken to mean that I'm interested in noting the confounding effect of two contrast variables on each other but that's not the case.. I need to look for the confounding effect of each of them on the association between nursing specialty (Independent variable of interest) and criterion "perceived stress".
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 In reply to this post by Sidra Are you speaking in your initial question about contrast coefficients (coefficients in a contrast, they sum to zero) or contrast coding (values of contrast variables)? See http://stats.stackexchange.com/a/221868/3277 20.10.2016 19:07, Sidra пишет: ```I'm sorry fellows, I do not have a background of statistics ..that's why I'm having a hard time understanding your suggestions here. Perhaps I need to be a little bot more comprehensive. I have IVs of nursing specialty, qualification, age, years of experience, work shift, marital status and childberaing status; independent variable being perceived stress by nurses. I need to see the effect of nursing specialty (as main variable of interest) on perceived stress while controlled for confounders. I will identify confounders by noting crude coefficient of nursing specialty and then noticing the change in its coefficient when each IV is placed in the model with nursing specialty (one variable at a time). If adding a variable in regression model brings a change of more than 10% in coefficient of nursing specialty, I ll treat that variable as a confounder. Since to find out if a variable is a confounder, I have to put that confounder alone along with nursing specialty in regression model, I am not sure if I can treat contrast 1 and contrast 2 (in place of marital status and childbearing status) as individual variables to see how much change each brings about in the coefficient of nursing specialty separately. I hope I have made myself sufficiently clear. Please bear with me and offer your kind insight on this problem. ``` ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 ﻿ I think that there are bigger problems here than the distinction between contrast coefficient and contrast coding.  Let me point out what I think IMHO are some greater problems:   (1) The OP calls nonexperimental variables "independent variables" which the OP may do by convention (everyone in the area calls them that) but from an experimental design perspective, they are not independent variables -- the OP may want to call them"causal variables" and provide a path diagram that shows how the causal and other variables affect the *outcome* variable.   (2) Given the info below, one would think that one would look at the correlation matrix for all of the variables to determine how all of the variables are interrelated.  In all likelihood, all of the variables -- "causal", outcome, "confounder"/3rd variables" -- are correlated. The concept of "confounder" is peculiar in this situation because it doesn't seem that nurses were randomly assigned to nursing specialty and one now wants to determine whether random assignment worked (i.e., the nursing specialty groups are statistically equivalent on background variables of age, years of experience, etc.). A path diagram explicitly identifying the relationships that one expects on a theoretical basis, would be very helpful in clearing up what is/isn't correlated -- and don't even get started on mediation and moderation effects.   (3) An alternative way of conceptualizing what the OP want to do is think in terms of Analysis of Covariance, that is, does mean level of perceived stress vary significantly as a function of nursing specialty AFTER removing the effects of other variables (i.e., age, etc.). IMHO, this puts the focus on the relationship of greatest interest. I know that the equivalent can be done in multiple regression (indeed, superfans of MR like Pedhazur and other prefer MR to traditional ANOVA analyses) but then we get the situation that we're in right now.  I think that the original question was perhaps misunderstood because complete information was not provided and the issue of orthogonal coding for unequal sample sizes was maybe a side issue or even irrelevant.   (4) I could be wrong but it seems to me that what the OP wants to do is a MR that enters all of the background variables first, determine if the is a significant relationship between perceived stress and these variables (and which ones significant), and then enter the variable nursing specialty (categories appropriately coded) to determine if provides a significant increase in the variance accounted for or R^2.    (5) I think it may become relevant to ask whether orthogonal coding should be used of nursing specialty categories because I don't think it likely that N for all specialties are equal.  The situation is complicated by background variables since it is likely that nursing specialty will differ on some/all of the background variables. Again, I think this is made clearer from an ANCOVA perspective but I'm sure that folks who think in regression terms will disagree.   (6) I could be wrong (probably am) but maybe the following analysis should be conducted:  regress perceived stress on all of the background variables and if there is a significant relationship, save the residuals or studentized residuals, transform them to perceived stress scores by adding the original mean and multiplying by the original standard deviation, and then regress these new scores on an orthogonal contrast representing nursing specialty. The new stress scores should represent the variance that remains after the effects of background variables have been removed (explicitly) and one can ask if there is any relationship between them and the coding for nursing specialty..    (7) Does anyone think that generating propensity scores for the background variables for the regression of perceived stress on nursing specialty categories might be an alternative analysis to consider?   (8) Does anyone wonder if a single nurse might report having multiple specialties?  If so, how is this represented in the data?   (9) My understanding of the OP's situation could be completely wrong, so feel free to ignore everything I said above.  But I do think that maybe we have been focusing on the wrong issues.   -Mike Palij New York University [hidden email]     ----- Original Message ----- From: [hidden email] Sent: Thursday, October 20, 2016 12:36 PM Subject: Re: contrast (orthogonal) coding with unequal cell frequencies Are you speaking in your initial question about contrast coefficients (coefficients in a contrast, they sum to zero) or contrast coding (values of contrast variables)? See http://stats.stackexchange.com/a/221868/3277 20.10.2016 19:07, Sidra пишет: ```I'm sorry fellows, I do not have a background of statistics ..that's why I'm having a hard time understanding your suggestions here. Perhaps I need to be a little bot more comprehensive. I have IVs of nursing specialty, qualification, age, years of experience, work shift, marital status and childberaing status; independent variable being perceived stress by nurses. I need to see the effect of nursing specialty (as main variable of interest) on perceived stress while controlled for confounders. I will identify confounders by noting crude coefficient of nursing specialty and then noticing the change in its coefficient when each IV is placed in the model with nursing specialty (one variable at a time). If adding a variable in regression model brings a change of more than 10% in coefficient of nursing specialty, I ll treat that variable as a confounder. Since to find out if a variable is a confounder, I have to put that confounder alone along with nursing specialty in regression model, I am not sure if I can treat contrast 1 and contrast 2 (in place of marital status and childbearing status) as individual variables to see how much change each brings about in the coefficient of nursing specialty separately. I hope I have made myself sufficiently clear. Please bear with me and offer your kind insight on this problem. ``` ===================== 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: contrast (orthogonal) coding with unequal cell frequencies

 How fine grained is the perceived stress variable?  I.e, how many values occur in a frequency count? How many cases are there? This seems like it would be a very complex model, is there enough power? Art Kendall Social Research Consultants
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## Re: contrast (orthogonal) coding with unequal cell frequencies

 No, I don't think it's a very complex model. The perceived stress was measured on 5 point likert type scale consisting of 14 items.  A mean score of perceived stress for each case and nursing specialty (type of nurse: medical vs psychiatric was calculated). In bivariate analysis (using t-test) i found significant difference between mean stress scores of the two nursing strata. I want to see if the difference is still significant while controlled for confounders (using multiple regression). I'm  not interested in seeing causal effect of any variable on outcome rather just association. I have another outcome variable(DCL stress score) which consists of five factors(domains) measured the same way as "perceived stress". These five domains will be treated as individual variables and will be tested for their association with nursing specialty using the same method I' ll use for the first outcome "perceived stress".