Neil, don't confuse terms, please. Data is neither parametric nor non-parametric. It's metric or categorial. 0/1 is categorial, more specifically dichotomous. Logistic regression is not a non-parametric method. It puts strict assumptions on the data, especially, the residuals must be binomially distributed. And, it estimates linear parameters (on a logit scale).

Catherine, please follow the advice of the others and use logistic regression. Setting up the model and interpretation is straight forward if you are familiar with classic linear models. The only issue to understand is that parameters are on a logit scale. This sort of stretches your 0/1 response to [-Inf,Inf]. In order to obtain estimated group means (or slopes in case of cont. predictors), you have to apply the logistic transformation (which happens to be the inverse of the logit):

logist(B) = exp(B) / (1 + exp(B))

So, assuming you have a simple design with two groups. You may get something like

beta

(Intercept) 1.2

group2 0.4

This means your first group has an estimated group means of

logist(1.2) = 0.77

whereas the second has

logist(1.2 + 0.4) = 0.83

Note that you don't have to transform your response variable in any way. Also note that all linear combinations of the estimates must be done before the logistic transformation. This ensures that you can't get predictions outside the range [0;1]. You can do the same thing for confidence limits. I'm not sure whether there is any way to interpret estimates after arcsine transformation.

Another difference to linear models is that the F-test does not apply. You can resort to either the Wald test or the Likelihood Ratio test. Should be part of the output of your program and is reported in much similar way.

If you have a number of trials per subject, there are two more things to take care for: First, you have to make the number of trials known to the program. This can even vary by subject or group. I'm not using Statistica myself, so you have to refer to the manual.

Second, as I said above, the logistic regression has strict assumptions, one of them being that the residual variance is exactly np(1-p). Typically, the residual variance is larger, which is then called overdispersion. My advice: Run a quasi-logistic regression. This is about the same thing, but confidence limits are inflated by the amount of overdispersion.

For a quick tutorial of how to do logistic regression and report it:

Peng, C.-Y.J., Lee, K.L., and Ingersoll, G.M. An Introduction to Logistic Regression Analysis and Reporting. The Journal of Educational Research 96, 1 (2002), 3–14.

A very comprehensive (digestible, yet) treatment:

Hilbe, J.M. Logistic regression models. CRC Press, Boca Raton, FL, 2009.

Good luck!

Use a binomial model to estimate the effects.

https://www.google.com/search?q=binomial+model&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:de:official&client=firefox-a#client=firefox-a&hs=PFP&hl=de&rls=org.mozilla:de%3Aofficial&sclient=psy-ab&q=generalized+linear+model+binomial&oq=generalized+linear+model+binomial&gs_l=serp.3..0i19l2j0i30i19l2.11545.19560.0.19856.33.18.0.15.15.0.165.1307.17j1.18.0...0.0...1c.1.11.psy-ab.eJ03gclojk0&pbx=1&bav=on.2,or.r_qf.&bvm=bv.45645796,d.Yms&fp=75f24052190d1691&biw=915&bih=859

The model you need in Statistica is called "logit regression model".

Regarding the arcsin-transformation (as the alternative mentioned by the reviewer):

Just calculate the arcsin values for your percentages. This might be possible in Statistica (I don't know). Look for "transformation of variables" or similar. If you don't find it, you can use a spreadsheet program like Excel or Calc:

In Excel or Calc you can use the function =ASIN(x) to get the arcsin of x (x is one of your percentage values). Just calculate the arcsins for all you percentage values and substitute the response (the percentages) in Statistica by their arcsin values and redo the analysis.

Thank you so much Jochen for your clarity and concision :-)

Dear Catherine,

FIrst you have to turn the percentage of use per child and experimental condition into a "decimal of use" by dividing the percentage value by 100. Then you take the square root of that decimal and apply the arcsine (= inverse sine function) transformation to that result; finally you should multiply the value attained with 2. How you can create a new variable per experimental condition in Statistica I do not know but there should be a transform option (like in SPSS) or similarly in Excel with which you do the transformation indicated by me.

One nice reference for this transformation is Roger E. Kirk (2013) Experimental Design - Procedures for the Behavioral Sciences (4th ed.).Los Angeles: Sage. ISBN 978-1-4129-7445-5 on p. 107.

This transformation is particularly useful when the percentages observed are close to 0 or 100.

Best regards

Klaus Willmes

Hi Catherine.

The Jochen's tip is adequate. You can do the transformation manually in statistica through arcsin function, or in any spreadsheet application.

Despite the percentage of use, is it of interest to know when did the first success occur ( e.g. they used something)? if so, a negative binomial should be used.

Best regards

Pedro J.. Rosa

As Klaus correctly stressed: your "percentages" should actually be first expressed as fractions/proportions, that is, numbers between zero and one (for instance 31% = 0.31). These fractions (for example 0.31) have to be re-scaled to fit in the range from -1 to +1. This is obtained by multiplication with 2 and subtracting 1 (example: 0.31*2-1 = -0.38). These scaled values can then be arcsin-transformed (example: arcsin(-0.38)=-0.39).

So, if x is a fraction (e.g. 0.31), the transformed value is calculated in Calc or Excel by =ASIN(x*2-1)

Sorry that I missed to say this earlier.

PS: Please always act on the assuption that I greet the reader/questioner and that I always send my best regards. I don't mean to be impolite by dropping the corresponding phrases - I just want to keep the text focussed and short.

Write function =Arcsin('name of percentage variable') in specification of new variable in spreadsheet with data

More - variance of binomial data will be stable after transformation =Arcsin(Sqrt(percentage)), not alone arcsine transformation. About this and similar transformation you can read http://rfd.uoregon.edu/files/rfd/StatisticalResources/arcsin.txt. Generalized Linear Model with logit or probit link is also the solution.

Catherine,

Your original data is "0" and "1"'s. This is non-parametric data and should be analyed as such. Using the logistic model suggested by one of the others or other nonparametric methods. You should look at the original data as distinct assessments and also then assess the data in a combined total if you wish. Combining the data and using that as the only analysis may hide important data.

Neil, don't confuse terms, please. Data is neither parametric nor non-parametric. It's metric or categorial. 0/1 is categorial, more specifically dichotomous. Logistic regression is not a non-parametric method. It puts strict assumptions on the data, especially, the residuals must be binomially distributed. And, it estimates linear parameters (on a logit scale).

Catherine, please follow the advice of the others and use logistic regression. Setting up the model and interpretation is straight forward if you are familiar with classic linear models. The only issue to understand is that parameters are on a logit scale. This sort of stretches your 0/1 response to [-Inf,Inf]. In order to obtain estimated group means (or slopes in case of cont. predictors), you have to apply the logistic transformation (which happens to be the inverse of the logit):

logist(B) = exp(B) / (1 + exp(B))

So, assuming you have a simple design with two groups. You may get something like

beta

(Intercept) 1.2

group2 0.4

This means your first group has an estimated group means of

logist(1.2) = 0.77

whereas the second has

logist(1.2 + 0.4) = 0.83

Note that you don't have to transform your response variable in any way. Also note that all linear combinations of the estimates must be done before the logistic transformation. This ensures that you can't get predictions outside the range [0;1]. You can do the same thing for confidence limits. I'm not sure whether there is any way to interpret estimates after arcsine transformation.

Another difference to linear models is that the F-test does not apply. You can resort to either the Wald test or the Likelihood Ratio test. Should be part of the output of your program and is reported in much similar way.

If you have a number of trials per subject, there are two more things to take care for: First, you have to make the number of trials known to the program. This can even vary by subject or group. I'm not using Statistica myself, so you have to refer to the manual.

Second, as I said above, the logistic regression has strict assumptions, one of them being that the residual variance is exactly np(1-p). Typically, the residual variance is larger, which is then called overdispersion. My advice: Run a quasi-logistic regression. This is about the same thing, but confidence limits are inflated by the amount of overdispersion.

For a quick tutorial of how to do logistic regression and report it:

Peng, C.-Y.J., Lee, K.L., and Ingersoll, G.M. An Introduction to Logistic Regression Analysis and Reporting. The Journal of Educational Research 96, 1 (2002), 3–14.

A very comprehensive (digestible, yet) treatment:

Hilbe, J.M. Logistic regression models. CRC Press, Boca Raton, FL, 2009.

Good luck!

A good and comprehensive answer, Martin. Just one question from my side: You write that logistic regression a a "non-parametric" method. But I doubt this. A regression (i.e. [generalized] linear models) always estimates model parameters (as you later also mentioned!), they are based on models about the data itself and the estimated parameters refer to properties of the underlying the data. Therefore, I assume that this is what is called a "parametric" method. Am I wrong?

PS: IMHO the nomenclature is unfortunate anyway, since the "non-parametric" methods are also based on distributional assuptions related to parameters, only that the distributions here are not based on the data but on the ranks (or some other non-quantitative statistic of the data). I thus would prefer the distinction between "quantitative" and "non-quantitative" methods.

Jochen, I said it's not a non-parametric. Unfortunate double negation.

Hallo, i think that you should do double click on the column to be transformed and choice the math function. then click on arcsin but befor you must calculate the percentage of your data and square them.

Dear Catherine, you can transform your data by using the "function" choice on the "variable" set up. It is quite simple. I suggest you to:

1) add a variable just after the variable you want to transform

2) double click on the new variable column head

3) click on the function button and select the "Math" category

4) Within this group you will find the Arcsin function; as the argument of the function you will select the variable you want to transform.

I am sure it will be very easy for you. On the contrary, feel free to contact me.

Regards

Pier Paolo

Hi Catherine,

I think it's better to use a logit transformation to your data than arcsine transformation.

Just use proportion (p) by dividing your percentage by 100 and then use logitX=log(p/(1-p))

Omar

Catherine,

Yes, (binary) logistic regression is probably the best approach. As noted by Martin, you must be careful of the multiple responses per subject, as (among other things) the significance values are affected by the assumption in a standard logistic regression of independence of responses. I suggest using a mixed-model logistic regression. I do not use Statistica, so I cannot give you example code. In Stata, the code could look like:

xtlogit outcome factor1 factor2 covariate || subject:

where outcome is being predicted from two fixed factors with a covariate and repeated measures on subjects. One of the really nice things about mixed models is that they cope with missing data (e.g. different numbers of responses per subject).

Russell