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Is there a statistically significant correlation between religious faith and total family income in the US?

Introduction and Aim of the Study

The main target of this study (which is available here in pdf) is to investigate any possible relation between religion and financial income in the US in the last decade. More precisely I decided to focus on Protestants, Catholics and the ones who claimed to belong to no religious community at all (identified as None). These three categories, according to the data, have been the most common ones in the United States in the period 2000-2012.
Therefore the target of the investigation may be summarized by the following question: “Is there a relationship between the religious faith of a US citizen (Protestant, Catholic or None) and his/her total family income?”
My personal interest derives from a general conviction that there could be some religious communities wealthier than others, due to historical, social or political reasons and the exploration of this kind of aspects may lead to underline some specific features going on behind the scenes. More generally I thing that digging this matters may enlighten some subtle pattern hiding behind the data, such as religious discrimination at work resulting in people belonging to a specific community getting higher, more qualified and more paid jobs. Highlighting this kind of aspects is a starting point for a broader research about social and financial conditions among and within different religious communities.

General Discussion about the Data of Interest

The research project was based on the data collected in the online-available database of the General Social Survey, 1972-2012 (Citation: Smith, Tom W., Michael Hout, and Peter V. Marsden. General Social Survey, 1972-2012 [Cumulative File]. ICPSR34802-v1. Storrs, CT: Roper Center for Public Opinion Research, University of Connecticut /Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributors], 2013-09-11. doi:10.3886/ICPSR34802.v1) (GSS), which since 1972 has been monitoring societal change and studying the growing complexity of American society. The GSS aims to gather data on contemporary American society in order to monitor and explain trends and constants in attitudes, behaviors, and attributes; to examine the structure and functioning of society in general as well as the role played by relevant subgroups; to compare the United States to other societies in order to place American society in comparative perspective and develop cross-national models of human society.

The dataset is composed by 57061 cases corresponding to an equal number of interviewed citizens. Each person may be considered as a single case, as there are several pieces of information (variables) which were recorded for each case. In particular, cases are single individuals respecting the following characteristics: all non institutionalized, English and Spanish speaking persons 18 years of age or older, living in the United States. As just mentioned each candidate was asked several questions about a number of aspects of his own life, his family, his community, the society he lives in.
The data were collected by three main methods:

  • computer-assisted personal interview (CAPI). Data are inserted directly into an electronic sheet over a PC and the interviewer and the respondent are both present at the moment of the survey, in front of the computer. The difference with CASI is that in the latter the interviewed is left alone in order to answer the questions more privately.
  • face-to-face interview.
  • telephone interview.

The two variables I took into account from the data set are the following:

  • income06: categorical variable. The interviewed was asked which of the proposed groups he/she thought his/her total-tax-less-family income of the previous year would fall. There are 25 possible interval varying from a minimum of less than 1000$ to a maximum of more than 150.000$, plus a category named “Refused”, including all the cases who did not accept to reveal their financial condition.
  • relig: categorical variable. The interviewed was asked by which of the proposed communities his/her religious faith would better be identified. A more proper description of the variable is going to be provided during the exploratory data analysis.

The study is observational because researchers recorded data “in a way that does not directly interfere with how the data arise”. The structure of the survey and the data collection methods are clearly not typical of an experimental setup. In the latter case, in fact, researchers would have sampled individuals and divided them into groups organizing an experiment in order to investigate the possibility of a causal connection between two or more variables.
From the point of view of the generalizability of the study it is crucial to focus on the population of interest, whic,h in this very case, includes all non institutionalized, English and Spanish speaking persons 18 years of age or older, living in the United States. According to 2011 American Community Survey Data on Language Use 79.2205% of american families speak English at home, while the 20.7794% speak Spanish which added up result in a global 99.9999%.

This means that we can reasonably generalize the results to the totality of US population 18 years of age or older. Furthermore the used data collection methods compensate each other in terms of any potential source of sampling bias. For instance, CAPI is mainly addressed to computer friendly persons. This bias may be prevented by phone interviews which enable researchers to reach and convince less “technology-friendly” people. The last but not the least is the face-to-face survey which compensates the unavoidable bias introduced by a phone call. The latter gives for granted the connection to a phone line which may not always be respected. In addition to that it is necessary to consider that generally children, youngsters or more generally minors do not have a clear financial overview over the family. Despite their belonging to a particular religious community they may have great insights into the total family income, which means that their contribution to the survey, at least on this very aspect, would have been pointless.

All this considerations lead us to the conclusion that the results of the study may be generalized to all US families. However, since the survey is observational, the findings do not imply causal relationships.

Exploratory Data Analysis

In the present section a brief exploratory data analysis is performed. The relevant statistics is provided together with the associated R code.

The first two used functions R are summary and str, which help to get a broader and in the mean time synthetic view over the data. As ir is clear the gss.after.subsetting data set is composed by only two variables , Income and Religion. Both are factors consisting respectively in 26 (actually 25 as I did not take into account the Refused category) and 13 levels. In particular Religion mantains all the original 13 levels despite only three of them have been selected (Protestant, Catholic and None).

In order to visualize the data in a cleaner way a plot is provided too. The whole data set has been converted into a contingency table, which has been properly plotted in the figure below.

The figure below shows pretty clearly the distribution of incomes among and within the three investigated communities. Nevertheless it is quite hard to identify any particular pattern hiding behind the data. It is necessary to proceed with a more complete and rigorous analysis in order to draw any conclusion concerning a possible correlation between religious community and family financial income. For further details about the data see the Appendix at the end of the report.



As stated at the end of the previous section in order to end up with a proper conclusion and answer the original question at the base of the study it is necessary to perform a rigorous statistic test on the data set. First a purpose of clearness, first of all we recap the main target of the project which is to answer the following question: “Is there a relationship between the religious faith of a US citizen (Protestant, Catholic or None) and his/her total family income?”

As we are dealing with two categorical variables (Income and Religion), both of which with more than two levels (respectively 25 and 3), only an hypothesis test is admittable. In particular, as no defined parameter of interest can be highlighted, I have performed a theroretical Chi-square test for independence, which is allowed by the fact that each particular scenario (i.e. cell count) has at least 5 expected cases. The proof of this condition being met is provided in the following table, which summarizes the whole dataset with each case joined by its expected value. As you can see all scenarios have expected value well above 5.

Income Protestant Catholic None
(x$1000) Real Expected Real Expected Real Expected
Below-1 67.00 65.90 23.00 30.80 30.00 23.20
1-2.999 62.00 56.60 22.00 26.50 19.00 19.90
3-3.999 40.00 41.80 17.00 19.50 19.00 14.70
4-4.999 26.00 28.00 11.00 13.10 14.00 9.90
5-5.999 36.00 42.30 22.00 19.80 19.00 14.90
6-6.999 48.00 51.10 21.00 23.90 24.00 18.00
7-7.999 63.00 59.90 27.00 28.00 19.00 21.10
8-9.999 98.00 94.00 33.00 43.90 40.00 33.10
10-12.499 181.00 179.70 72.00 84.00 74.00 63.30
12.5-14.999 172.00 160.50 70.00 75.00 50.00 56.50
15-17.499 156.00 156.10 70.00 73.00 58.00 55.00
17.5-19.999 118.00 114.80 47.00 53.70 44.00 40.40
20-22.499 174.00 173.60 81.00 81.20 61.00 61.10
22.5-24.999 166.00 169.80 83.00 79.40 60.00 59.80
25-29.999 256.00 241.80 109.00 113.10 75.00 85.10
30-34.999 252.00 263.20 133.00 123.10 94.00 92.70
35-39.999 270.00 250.00 109.00 116.90 76.00 88.00
40-49.999 440.00 417.10 199.00 195.00 120.00 146.90
50-59.999 369.00 370.40 175.00 173.20 130.00 130.40
60-74.999 471.00 453.90 206.00 212.30 149.00 159.80
75-89.999 349.00 345.10 176.00 161.40 103.00 121.50
90-109.999 279.00 284.10 142.00 132.90 96.00 100.00
110-129.999 185.00 185.70 87.00 86.90 66.00 65.40
130-149.999 100.00 116.50 64.00 54.50 48.00 41.00
150-Over 228.00 284.10 155.00 132.90 134.00 100.00

The total number of degrees of freedom is df = (R-1) X (C-1) which is equal to df = (25-1) X (3-1) = 48, well above the minimum allowed of 2.
As for the independence issue, the GSS sampling has been randomic and in any case the number of cases in each scenario as well as the total amount of cases is below the 10% of the population of the US.

Given that, we can state our hypothesis:

  • H0 : (nothing going on): Religion and Total Family Income are independent, meaning that the amount of money earned by a US family per year does not vary by belonging to either the Protestant or the Catholic community, or no religious community at all.
  • HA : Religion and Total Family Income are dependent, meaning that the amount of money earned by a US family per year does vary by belonging to either the Protestant or the Catholic community, or no religious community at all.

Let’s recall that applying the Chi-square test for independence means that we are to evaluate whether there is convincing evidence that a set of observed counts O11, O12, O13… ORC in RC categories are unusually different from what might be expected under a null hypothesis. Call the expected counts that are based on the null hypothesis, E11, E12, E13 … ERC computed as

$$E_{row \hspace{1mm} i,\hspace{1mm} col \hspace{1mm} j} = \frac{(row \hspace{1mm} i \hspace{1mm} total) \times (column \hspace{1mm} j \hspace{1mm} total)}{table \hspace{1mm} total}$$

If certain conditions are met, then the test statistic below follows a chi-square distribution with (R-1)X(C-1) degrees of freedom:

$$ \chi^2 = \frac{(O_{11}-E_{11})^2}{E_{11}} + \frac{(O_{12}-E_{12})^2}{E_{12}} + \cdots + \frac{(O_{RC}-E_{RC})^2}{E_{RC}} $$

The p-value for this test statistic is found by looking at the upper tail of this Chi-square distribution. We consider the upper tail because larger values of chi squared would provide greater evidence against the null hypothesis.

The result of the Chi-square test for independence over the data set of interest is the following:

Because we typically test at a significance level of α = 0.05 and the p-value is less than 0.05, the null hypothesis is rejected. That is, the data provide convincing evidence that there is some association between the amount of money earned by a US family per year and belonging to either the Protestant or the Catholic community, or no religious community at all.


The aim of the research project was to investigate whether there could be any association between the total tax-free income of an American family and their belonging to the Protestant, Catholic or none religious community at all. The dataset was taken from the General Social Survey 1972-2012 (GSS), which since 1972 has been monitoring societal change and studying the growing complexity of American society. the original database was subset in order to take into account only the two variables of interest, Income and Religion; the latter has been subset itself to select only three inner levels, Protestant, Catholic and None. Due to the tipology of the investigated data, only a hypothesis test based on the Chi-square test for independence can be performed.

The result of the statistical analysis leads us to reject the null hypothesis and then to state that there is some association between the amount of money earned by a US family per year and belonging to either the Protestant or the Catholic community, or no religious community at all.

This could be only the beginning of a wider study about correlation between religion and financial condition in the US. Deeper insights must be get into the matter and more complex statistical tools and techniques must be used in order to infer complete and satisfying conclusions.

APPENDIX – Attached Dataset

by Francesco Pochetti

Endocrine Disruptors: how we are poisoned by everyday chemicals

How many chemicals do we get in touch with every day? Are they safe? In which doses? What kinds of chemicals are they?

If you have ever tried to find an answer to the previous questions probably this is the right place to check it out. In order to be as rigorous as possible I report the transcript of the first part of a very interesting and together frightening video I found on the net on Earth Focus web page, which you can find here and which I embed hereafter. Therefore I limited myself to simply watching the video and carefully writing down what I heard.


The topic dealt is crucial and is about Endocrine Disruptors (ED), a class of compounds, well known to science, which tend to interfere with the biological processes at the base of hormonal control. Basically,  ED have a molecular structure which resembles very closely the one of the most important human hormones (testosterone, progesterone, estrogens…) ; this feature gives them the ability to deceive cellular receptors which cannot recognize the real hormones from the fake ones. The result is that even at very tiny doses these chemicals might be very dangerous, altering irreversibly the most basic physiological human processes.

The above video (which I highly recommend) has been built gluing together pieces of interviews from the highest world experts in this field, whom I list below, before pasting the transcript, and whom I report within the transcript itself in order to clarify the respective contributes.

  • Andy Igrejas (National Campaign Director/ Safer Chemicals, Healthy Families)
  • Theo Colborn, Phd (President & Founder, The Endocrine Disrupting Exchange)
  • Erin Switalski (Executive Director, Women’s voices for the Earth)
  • Cecil Corbin-Mark (Deputy Director, WE ACT)
  • Sean G. Palfrey, MD (Clinical Professor of Pediatrics & Public Health/ Boston University School of Medicine, MA)
  • Heather White (Executive Director, Environmental Working Group)
  • Judith Robinson (Executive Director, Coming Clean)
  • Mia Davis (Vice President of Health & Safety, Beauty Counter)
  • Johanna Congleton, Phd (Senior Scientist,  Environmental Working Group)
  • Linda S. Birnbaum, Phd (Director, National Inst of Environmental Health Sciences/ National Toxicology Program, NH)
  • Julia Brody, Phd (Executive Director, Silent Spring Institute)
  • Tracey Woodruff, Phd, MPH (Director, Program on Reproductive Health in the Environment/ University of California, San Francisco)




“They are everywhere in our environment, in the air we breath, the water we drink, the food we eat, they are in everyday products we use for personal care and cleaning, they are in our furniture, our children toys and the products we use in gardening and agriculture and almost all of us have them inside our bodies.

Andy Igrejas “Chemicals right now according to the best evidence we have are contributing to the chronic disease burden in this country in ways that are substantial.”

Sean G. Palfrey “We are seeing increases clearly in certain kinds of illnesses, asthma is one, autism in another, ADHD (Attention Deficit Hyperactivity Disorder) is a third”

endo5Theo Colborn “One out of every third child born today is going to have diabetes and if you are a minority it’s one out of two”

Andy Igrejas “Chemicals contribute to the incidents of leukemia”

Mia Davis “breast cancer, infertility”

Theo Colborn “alzhaimer’s and parkinson’s”

Tracey Woodruff “People are more obese […] than they were up to 20 years ago”

Judith Robinson “Child’s cancers are going on”

Linda S. Birnbaum “We’re seeing effects on sperm count in men […]”

Andy Igrejas “They are more of these bizarre heart effects particularly around male reproductive development”

Theo Colborn “If I were a parent I would be very concerned”

endo2They were meant to make life easier and they do. Chemicals fight diseases […] and support manufacturing. They’re big business, a key stone of the us economy from consumer goods to high technology almost all aspects of modern life depend on the chemical industry. Chemical production in the US has grown 25 fold since World War II. It sales above 763 billion dollars in 2011. The chemical industry supports over 3 million US jobs and invest billions in the research and development. Our bodies take in […] chemicals every day and this exposure has consequences for out health, our safety and our future.

Andy Igrejas “There are 84 thousand chemicals that are legal for commercing in the US and could be used to make all kinds of things, going to the products we bring into our homes, our workplaces and they are basically unregulated”

Theo Colborn “And of course every year new chemicals are coming on the line that have not been fully tested”

Erin Switalski “There are almost 13000 chemicals that are used in cosmetics and just about 10% of them have actually been evaluated for their safety. We found lead in lipsticks, there is mercury out there in skin lightening creams. We have found phormaldeid in products”

Cecil Corbin-Mark “[…] products that people apply to their faces and their skin daily”

pestSean G. Palfrey “Pesticides are clearly poisonous and it should be obvious to us that if they kill insects they are going to have the possibility of hurting us”

Judith Robinson “In our kitchen cabinet. If you open up the doors and you count up all the tin cans in there, all of them are going to be lined with Bisphenol A unless they are labeled that say they are not”

Sean G. Palfrey PCBs (Polychlorinated Biphenyls) might be in plastics, might be in cups, might be in containers we put in our microwaves, might be perfectly safe when they are first put on the shelf but quite dangerous once they start to break down”

Heather White “All we have is chemical companies that have created products that have contaminated literally every living thing on the planet”

Judith Robinson “I think that the corporations who are profiting from this really have run away with our system”

Heather White “Industrial chemical pollution begins in the womb”

Erin Switalski “Everything that we are bringing into our bodies if we choose to have children, we actually pass our rate on through to a developing child”

Mia Davis “Some of the chemicals we know can cross the placenta and enter the womb and have effects at incredibly tiny tiny doses”

Sean G. Palfrey “About ten years ago a seminal study was done on ten newborns cord blood. The cord blood as the baby was born contained several hundred toxic elements which terrified all of us”

endo3Heather White “Chemicals like Bishenol A, many different classes of flame retardants, we found DDT and PCBs, […] chemicals that we interact with every day from consumer products”

We now know that along with the nutrients and oxygen that the mother supplies to the baby comes a […] toxic chemicals.

Sean G. Palfrey “We know that chemicals will affect younger children, fetuses, new born babies and young children in general more than older children and adults and the reason for that is that younger children and fetuses are developing much more rapidly, their organ systems are much more sensitive”

Erin Switalski “What science is starting to show now is that early exposure to toxic chemicals at critical points when a child is in the womb has effects later in life”

Endocrine disruptors are chemicals of growing concern, fetuses and children exposed to even minute amounts may develop a wide range of health conditions from diminished intelligence to cancers. Our endocrine glands produce hormones that regulate the basic processes of our body like metabolism, growth reproduction and development. Endocrine disruptors disturb how these processes work.

baby1Johanna Congleton “Endocrine disrupting chemicals interfere with hormones signaling. Proper hormone signaling is very important for fetal development and for childhood development as well as sexual maturation. Therefore compounds that interfere with these processes could have very profound effects”

Linda S. Birnbaum “Many of these and other chemicals appear to be associated with lower IQs and/or behavioral problems in children”

Theo Colborn “If you look at what these chemicals can do to the brain we know now these chemicals are also interfering with how we process information”

Sean G. Palfrey “They affect our genetic outcome, they increase the possibility that we lose a baby, they change the activity of our hormones, our sex hormones in a variety of different ways”

Linda S. Birnbaum “We’re seeing children starting puberty at younger ages. So there are many little girls that have, for example, breast at the age of seven in the african american community and eight in the white community. This is too young for our children”

980 endocrine disrupting chemicals have now been identified. Among the most ubiquitous are a class of compounds called Phthalates, Bishpenol-A and flame retardants including PBDEs, chemicals so common that almost all of us have them inside our bodies.


ftalaJudith Robinson “So you may have vinyl floors, you may have vinyl shower curtains, you may have vinyl toys that your kids are using, […] leaching Phthalates which are known to be toxic into the environment where you get exposed”

Phthalates are in many common products, including food packaging, building materials and pharmaceuticals; they’re in our cars and even in new cars’ smell. They’re used in cosmetics to hold fragrance and health products to more effectively penetrate and moisturize the skin.

Julia Brody “We’re concerned about their effects on males, on baby boys…”

Johanna Congleton “We see problems with testicular development, problems with sperm development. They can be associated with a decrease in testosterone levels.”

Tracey Woodruff “So if you interfere with the testosterone levels they don’t quite go up all the way. In animal studies it has been shown to be linked to cryptorchidism, so undescended testicles and hypospadias, which is incomplete formation of the male reproductive organ”

babyPhthalates may also be feminizing boys; scientists found that Phthalates may be associated with a shorter anogenital distance, the distance between the genitals and anus, a subtle marker of feminization in boys. The American Chemistry Council which represents chemical manufacturers says Phthalates are among the most thoroughly studied family compounds in the world and have a history of safe use. But Phthalates are banned from children toys in more than 10 countries and the European Union. In the US 3 Phthlates were permanently banned from children toys […] in 2008 because of their potential to leach frel plastic if chewed or sucked.

Johanna Congleton “The worst actors have been taken out of children’s toys but they are still widely used in many other types of consumer products and a monitoring study showed that these chemicals are still showing up in people”



Tracey Woodruff “BPA is of concern because it looks like an estrogen and it has been shown to have a weak estrogenic effect and so if you are exposed to a chemical that might interfere with your hormone levels, in this case estrogen, it can have effects particularly during development.”

Linda S. Birnbaum “And there are preliminary data that say that it may infact […] directly increase the risk of breast cancer in animal”

BPA1Julia Brody “If they are chemicals that affect the development of the breast even before birth, if they are chemicals that cause breast thumors in animals, these are chemicals that we want to be worried about and start thinking about reducing exposure”

In addition to breast cancer BPA may be associated with genetic damage and a wide variety of reproductive, methabolic, behavioral and developmental problems. It’s one of the top industrial chemicals in the world. About 6 billion punds of BPA are produced globally each year, earning manufacturers a profit of some 8 billion dollars.

Johanna Congleton “We’ve made some progress with eliminating BPA from infant productsBPA2 including infant formula packaging, baby bottles and plastic drinking cups.”

But BPA remains widely used in many consumer products from electronic to medial equipmentsand it’s in the resin of cans […] and in plastic bottles where it can leach into the food or liquid contents inside. The Food And Drug Administration, which has jurisdiction over food packagings says BPA is safe at the low doses that occur in food but many research and health organisations remain concerned about BPA’s impact on human health at current levels of exposure.


PBDEOver 1,5 million tons of flame retardants are used worldwide each year. They’re added to consumer products to meet flamability standards, though their effect remains questionable.

Judith Robinson “Any furniture that you have that has polyurethane in it, that is most of our furniture, may contain toxic flame retardants and those flame retardants don’t stay put in the foam, they leach out and they end up in the dust in our house where we are all exposed, in particular kids who are on the ground, low, picking things up with their hands in their mouth. They are exposed to that dust which is gonna have flame retardants chemicals in it”

There are many different kinds of flame retardants. Among the most studied are PolyBrominated Diphenyl Ethers (PBDEs). Scientists have linked PBDEs to a wide range of conditions from delayed development to learning problems and diminished intelligence. […] Two PBDEs, pentaBDE and octaBDE were taken out the US market voluntarily in 2004 because of growing health concerns. Production of PBDEs deca is in the process of of being terminated.

flameLinda S. Birnbaum “The problem with all PBDEs is that they are very persistent in the environment”

Johanna Congleton “The issue with PBDEs is that they’ve been replaced with other types of chemicals that may have very similar concerns and perhaps even the same mechanism action in terms of their ability to disrupt the endocrine system”

The flame retardants Clorinated Tris and Fire Master 550, which may be linked to DNA damage, cancer or neurological defects continue to be widely used in polyurethane foam and in a number of children’s products.

Linda S. Birnbaum “So I think that the whole issue of flame retardants is one for which there is some concern and I think the real question we should ask, and maybe we need to ask this more broadly about other kinds of chemicals as well, is do we really need them?




by Francesco Pochetti

How does a photocopier work?

DADF_(Canon_IR6000)We all know the difference between an insulating and a conductor. Despite that there are also materials which, depending on their conditions, may change their main inner characteristics: photoconductors, for example, are insulating substances which, after absorbing light, turn into conductors. This feature is exploited by a procedure known as xerography, which is at the base of copying machines and laser printers. The working principle of photocopiers consists in creating an electric image of the to-be-copied document over the photoconductor. Some colored pigment particles (toner) are layered on the electric image in order to get stuck to a blank sheet of paper, reproducing the original document.

A thin layer of photoconducting material is applied to a grounded metallic belt.


  1. The free photoconducting surface is electron sprayed by a metallic wire, as if a nebulizer covered it with paint. The electrons polarize the photoconductor and get stuck to it: the effect of the polarization is to form a collection of negative charges on the opposite face of the photoconductor, in contact with the metallic belt. This negative charge attracts a correspondent positive charge which gathers on the upper face of the belt.
  2. At this point, the document is lightened up and its image is projected over the photoconductor. Its exposed areas become conductive and, as this surface has a smaller potential level compared to the ground, the electrons scattered over these regions are immediately grounded. The shadowed areas, instead, keep their charge: over the free photoconductor surface a negative charged copied image is created (whilst a correspondent positively charged picture is kept on the surface facing the metallic belt).
  3. It is now necessary to transfer onto the paper the charged image. By a special brush device, some toner particles (plastic insulating dust containing colored pigments) get positively charged and approached to the photoconductor.  The toner, attracted by charged areas (negative), gets scattered according to the original picture.
  4. In order to let toner particles detach from the photoconductor and attach to the paper, it is necessary to get rid of the electrostatic attraction. The photoconductor gets lightened again and the charged image gets erased. The positive toner particles are kept on the photoconducting layer, in correspondence to the original picture.
  5. After that a previously negatively charged sheet of paper is pressed over the photoconducting layer. The toner particles gets attracted without modifying the original drawing.
  6. The final image gets eventually pressed whilst the toner melted by proper heating. Before a new copy the photoconductor is lightened for a third time to wipe the residual electrons and cleaned, in the very end, from the not transferred toner.

That’s it! Cool, isn’t it?


by Francesco Pochetti