 Now, how to ensure precision and accuracy in experiments and how to design apparatus, how to conduct experiments? So, these are the things that we will discuss in this session. So, more specifically we will discuss what are the essential elements of all scientific methods. We will discuss some things about variables and errors in experiments. Then we will talk about control precision and accuracy and finally, fitting a straight line to measure data. Now, all scientific methods have some things in common. So, what are the common features? So, normally often we start with a hypothesis which we verify using an experiment. Now, hypothesis itself is born out of observation. So, you are making observation and you want to find a pattern in the observation. So, your mind by intuition tries to come up with some sort of a statement about the pattern that is called hypothesis. Now, whatever your mind conceives based on observation alone may or may not be the truth or may or may not be correct. So, you must devise an experiment to conclusively establish that the hypothesis is correct. Only when hypothesis is verified, it becomes a law. Now, verification itself involves experiment and observation in the experiment and then drawing of inference. So, when you can generalize your observations or your hypothesis, then it becomes a law. So, that is the final step generalization. Now, a few points about each aspect, observation. Observation is not passive acquisition of sensory information. So, it is not as though you are just passively sitting when the experiment is going on and then just a few things are occurring to you and you call them as observations. No, but it is a critical purposeful process needing high level of awareness. So, you must have a high level of awareness to observe things. There is a reason why we choose to observe a specific portion of the whole domain of possible objects of observation. Now, what is the meaning of a high level of awareness? So, you see supposing for instance, being a chemical reaction, there may be many things happening. Say the color of the solution may be changing, temperature of the solution may be rising. There may be some inadvertent agitation of the solution. Light is falling on the reactants. Now, all these things can have an effect or impact on the reaction and the products. Rate of reaction also may be affected. Now, the point is just how many variables can be there which affect the reaction. So, nobody can tell you beforehand what are all the things you should observe. So, it is dependent on your level of awareness that you will be able to identify variables which may be influencing the reaction. So, being aware of the temperature changes, the agitation of the solution, the color change of the solution, change of the intensity of lighting, presence of vibration and so on. All of these things will be able to observe simultaneously. So, this is what is meant by a high level of awareness, hypothesis. It is an imaginary preconception or an inspired guess about some particularly interesting aspect of the world. Every discovery begins as an experiment. It is an act undertaken to verify the hypothesis. So, what does it do? It discriminates between possibilities and gives directions for further thought. Another way of looking at the experiment is to look to realize that it is happening device to apprehend the truth. Finally, it is the method of discovering causal interconnection. Now, before I move on to this topic of hypothesis. Let me tell you what is the difference between a scientific method and non-scientific approaches. So, when you say methods are scientific, we have said that all scientific methods have this observation hypothesis, then experiment and then generalization. So, the key point in scientific methods is verification of the hypothesis. Now, this importance of verification has been realized only in the last few hundred years. So, earlier how a non-scientific approach can be problematic. Now, one great philosopher in Greece remarked that women have less teeth than men. So, this was his hypothesis. He said that women have less teeth than men. Now, evidently this hypothesis he would have made based on some common sense reasoning like you know average height, average weight and average size of women is less than that of men and then you know you extrapolate to the number of teeth. Now, what is surprising was that people during when he was alive and even a few hundred years after his death continue to believe whatever statement he made, whatever hypothesis is made namely that women have less teeth than men. It is only when someone actually counted the number of teeth, realize that there is no difference between the number of teeth a woman has and a man has. Now, that is where the importance of verification comes. So, you can see that even though a person may be a great thinker, what he or she comes up by purely intuition alone may or may not be correct. So, even good thinkers can have wrong intuition. Therefore, knowledge which is developed only by intuition and which has not been verified through experiment normally should not be taken as final. In fact, jokingly someone had remarked that this great philosopher had two wives, but how was it that he never asked them to open the mouth and count the teeth. So, you must see that the concept of verification has come much later in the tradition of intellectual tradition of the mankind. So, in all scientific endeavors normally the verification is very, very important. Now, I would like to reference at this point yesterday while discussing our productive thinking we discussed how asking new questions alters the domain and makes new contributions. I discussed an experiment related to obesity. How using an experiment a particular scientist showed that external factors are as much responsible for over eating habits of fact people apart from internal factors. So, that example is very useful to understand the various elements of scientific method. How it is an art to devise the right experiment to disprove or prove your hypothesis. Now, hypothesis that can be tested by practical experiments is an art. For instance, hypothesis such as on all men are mortal is not a testable hypothesis because the word all means that you must check whether every human being is mortal. So, all includes those people who are going to be born in future also. So, evidently this is not a testable hypothesis. We can only talk about people who were born in the past and whom we have seen that they are dying at some time or the other. Now, it is a common practice to state the hypothesis in a null form that is the hypothesis stated in negative term. What this means in simple terms is the following supposing your hypothesis is cast in the form A implies B or A is the cause of B. Now, the same hypothesis can be cast as follows. Instead of saying A implies B, you can say not B implies not A. This means if A is present then A is the cause of B. So, you will see the effect B. On the other hand you can say if you do not see the effect B that is complement of B not B implies not A. So, if you do not see the effect B then you find that the cause A is not present. So, this form of framing of the hypothesis in the form of not B implies not A can be regarded as the null form. A lot of thought has been has gone on to decide why null form of hypothesis is a good method of framing the hypothesis and testing the hypothesis. So, this topic I will leave it to you as an assignment. You do a internet search on null hypothesis, how hypothesis can be cast in the null form and why this form of hypothesis is considered superior from the point of view of testing. Now, some examples here these are some hypothesis or commonly held beliefs are they correct or not? I will leave it to you. If a woman wants to have good teeth she should not have children. Second memory of an event fades with time because if you do not use material you have learnt it disappears due to disuse. So, we are likely to believe this hypothesis because it is our common experience that supposing something is taught to you in the beginning of a course you know that towards the end of the course you do not remember. Now, you find that that particular concept which was introduced in the beginning you never utilized any purpose you never solved any problems never applied that concept and you do not remember. So, you try to connect the two and then you say yes because I did not use that concept probably I forgot. However, there are many other things that you have to note for instance after that concept was introduced in the beginning many other concepts have been introduced and you are simultaneously doing many courses. So, it is that because you have introduced to many other ideas apart from that particular idea that you have forgotten. So, in other words can forgetting happen because of interference from other ideas. So, in fact it has been found that this interference is primarily responsible for forgetting and not just the disuse of an idea. So, a lot of forgetting or predominantly forgetting happens because of interference from other ideas and not because of disuse. So, you see hypothesis needs to be tested using a proper experiment. So, if you want to prove if you want to prove that the forgetting is happening because of disuse you have to ensure that after you are introducing a concept you should not teach anything else. You should ensure that nothing else is taught and the person is not exposed to any other ideas. Now, this may be somewhat difficult to achieve. So, this kind of conditions will have to be achieved if you want to prove the connection between lack of use of a concept and forgetting of that. So, this is what brings us to the topic of variables. What are all the things which are affecting or influencing the experiment? So, you can divide the variables which are influencing an experiment into three types. So, independent variable, dependent variable and confounded variable. Independent variable. So, independent variable is also called as the cause. So, stimulus, input, cause all these are other terms, equivalent terms for an independent variable. So, it is a condition manipulated to determine its effect on an observed phenomenon. So, you will vary the condition of this variable and try to see the effect of this variable on the phenomenon. The dependent variable on the other hand is nothing but the response output or the effect that is being measured. So, it is the condition that appears, disappears or varies as the independent variable is introduced, removed or varied. Now, in some cases it may be difficult to decide which of a pair of variables is the cause and which is the effect. So, just because two variables exist together, presence of A and presence of B always appears together, it means that one of them is independent and one of them is dependent. But which one is independent and which is dependent can sometimes be difficult to ascertain. Confounded variable is one whose effect cannot be separated from the supposed independent variable. Now, let us illustrate with an example. So, suppose you are trying to find out color preferences of men and women. So, you want to know whether some particular color is preferred by men and some other color is preferred by women. So, you want to do an experiment to ascertain this. Now, one of the problems with this is the men and women whom you will consider for experiments will have a particular age and until that age, until reaching that age, they would have been exposed to various colors. Now, you have no idea what kind of colors the people in your experiment have been introduced to in their past. It can happen that some color was, some set of people were exposed to a particular set of colors far too often and it is possible that some set of colors were rarely, some people were rarely exposed to another set of colors. Now, this is this sort of past experience can also affect the choice of colors of men and women. So, unless and until you ensure that all the men and women whom you are considering for testing your hypothesis or finding out the color preferences have all been exposed to all the various colors in some sort of equitable manner. So, the past experience, past exposure of people to various colors is a confounded variable because it is something whose effect you cannot separate from the supposed independent variable. So, like this often in experiments you can have variables, you know that this variable is important it can have an effect, but unfortunately you have no way of separating that effect. So, unless and until you choose a set of people and ensure that over a sufficiently long period of time they are all exposed to the same set of colors and then do an experiment to find out their color preferences you will not be able to remove this effect. So, the types of variables broadly you can divide the variables into quantitative, categorical and continuous and discrete. So, quantitative variables are those which vary in amount. So, you can assign some number to this variable, categorical variables they vary in kind. So, categorical gender is a categorical variable and then you can the amount or a number associated with the variable may change discreetly or it may change continuously accordingly you can have discrete and continuous variables. Now, let us talk about the errors in any measurement the goal is to measure the effect and the cause accurately, but you know this is not possible always some sources of inaccuracy will be there. So, some source of errors so therefore, we must know what are the types of errors that can be present in an experiment and how to reduce them. So, broadly the errors can be divided into two parts random and systematic. Random errors are those random error varies equally likely to be positive or negative. So, it varies and then it is equally likely to be positive or negative then it is random systematic. So, systematic error on the other hand it remains throughout the experiment or it is constant throughout the experiment. Now, the word constant is put in inverted commas here because you must interpret the meaning of the word correctly. So, it exists throughout the experiment and it has a particular trend for instance it can tend to be always positive or it may be always negative. So, it is in this sense that the word constant is used. So, probably it may be a better idea to simply divide the errors into random and non random instead of calling it as systematic. However, traditionally the word systematic has been used to designate this type of errors. Now, let us take some examples to illustrate this presence of these errors how they arise. So, the experiment the example that I am considering here involves an experiment in which you are measuring the terminal velocity of a ball in a viscous medium like glycerin. So, here is a diagram of the experiment that I am talking about. So, measurement of terminal velocity of a ball in glycerin. So, this is the ball and this is the tube in which you have a liquid namely glycerin basically a viscous fluid. Now, you know that if you drop a ball in vacuum then it will go on accelerating because of gravity or even in air air is not that viscous as a fluid. Now, in a fluid which is viscous if you drop a ball then it will accelerate in the beginning, but ultimately it will its acceleration will go on decreasing and will reach a constant velocity after some time that constant velocity is called terminal velocity. Now, why does it reach a constant velocity why does not it accelerate continuously because there is a opposing tendency from the fluid. This opposing tendency or viscous force something like a frictional force is proportional to the velocity of the ball therefore, if the velocity increases the resistance in the form of viscous force also increases and ultimately the gravitational force and the viscous force they become equal and beyond that point there is no net force on the ball and therefore, the velocity remains constant. So, if I have to illustrate this on a diagram so, you are dropping this ball and the ball moves down and may be beyond a point say somewhere here it goes down with a constant velocity and you have markings on this tube. So, until reaching this point from the top it will accelerate, but the acceleration will go on decreasing because this is the downward force Mg and on the ball you have an upward force exerted by the fluid that is the viscous force. Downward force is Mg and this resistance is viscous force it is proportional to the velocity of the ball. Now, since it is accelerating its velocity is going on increasing and at some point the viscous force which is proportional to velocity becomes equal to the force Mg and there it reaches a constant velocity thereafter when it is falling it will reach a constant velocity that velocity is called terminal velocity. Now you want to measure the terminal velocity of a ball let us say like this in viscous medium. Now what are the sources of errors in this experiment? So, random errors can occur in starting and stopping the clock or in estimating the ball location on a scale. So, going back to this diagram how will you measure the terminal velocity? So, well you will have a stop clock so, whenever the ball crosses a particular marking on the tube you will start the clock and then you will stop the clock when it crosses some other mark and you know the distance between these two markings and you know the time shown on the clock if you divide the that distance by time then you get the velocity. So, this is how you are going to estimate the terminal velocity random errors can be there in starting and stopping of the clock see you are trying to do the two things simultaneously right. So, you are observing the crossing of the ball or the crossing of the mark by the ball and at that instant you want to start the clock now it is not clear what do you when do you decide that the ball has crossed the mark because the ball has a particular diameter let us say you choose to start the clock when the top of the ball top edge of this ball crosses the horizontal mark ok the top edge of the ball crosses the horizontal mark now it is not possible for anyone to locate this precisely and also after your mind has detected that the ball has crossed this mark you may take some time to start the clock or you might start the clock little before the crossing right. So, you are trying to coordinate both these things this kind of error can arise. So, this error can arise both while starting the clock and while stopping the clock. So, this is one source of error that is a random error you cannot really control now what is the source of systematic error in an experiment like this. So, suppose your clock is running slow. So, in this case systematically you are going to get a shorter time duration ok. So, in other words even though the time elapsed is maybe 20 seconds your clock will only show it as 18 seconds. So, you will be systematically noting as smaller time another source of systematic error is the change in temperature of the fluid. So, here you are doing this experiment repeatedly and because of friction when you drop a number of balls like this and you are making measurements the temperature of glycerin in the tube is going on increasing right as you progress with your experiments and as you do many trials. So, this increase in temperature is a systematic error because slowly the temperature keeps in always increasing it is not a random error. So, this is how you can have systematic and random errors. Now, in the experiment that you are doing you must similarly find out what are the sources of random and systematic errors. So, it requires a certain amount of expertise in doing experiments to identify such errors because in different experiments there are different sources of this random and systematic errors. Now, in terms of this these errors the random and systematic errors let us define the meanings of the words accuracy and precision. Now, a measurement is said to be accurate if small if the systematic and random errors are small then it is accurate. So, this is illustrated by a diagram here this diagram is you can regard it as an analogy. So, in this diagram solid circle here indicates the target that is sought to be fired upon by a shooter. So, a shooter is shooting bullets at this target, but you know he may or may not get the target. So, where the bullet is try a bullet strikes it is shown by the cross. So, the shooter is making several attempts right. So, every shooting event the bullet reaches a certain point and that point is shown by as a cross. Now, you can say that the shooter is accurate if all these various locations of the bullet strikes are very close to the target which is the solid circle. So, this is an example of small systematic and random errors. Now, let us see what would how would you show the systematic and random errors in this analogy. Now, this is an alternative that can happen. So, the shooter is always missing the mark, but he is always misses the mark by the same amount right. So, in repeated trials he is shooting at a location which is away from the target, but he always gets a different, but the location that he gets in repeated trials is the same though it is not the same as the target. Now, this is an example of a precise, but inaccurate measurement. So, where random errors are small. So, you see every time you are getting the same reading almost the same reading, but systematic error can be present. So, you can your measurements may be precise, but they may be inaccurate. So, another word for precision is repeatable. So, if you repeatedly get the same value you cannot conclude that your measurement is accurate. You can conclude that it is precise to decide to conclude that it is accurate you must know the true value that you should try to get and only then you can compare your measured value with the true value and then say whether it is accurate or not. Now, imprecise and inaccurate. So, this is an example where you have lot of random errors the shooter is not getting a particular location at all every time he gets a different location right and all the locations are different from the target. So, both systematic and random errors are present in this case. So, your measurement may be precise, but inaccurate and it may be imprecise and inaccurate both. So, there is no repeatability and therefore, there is no accuracy also. Now, often you find readings reported as follows for example, here is what we are showing is the reading of a resistance in an experiment. Now, the question is when you write the reading as some value plus or minus some other value in this case plus or minus 0.001 ohm does it represent systematic or random error. I am leaving it to you as an assignment after I complete this section on experimental skills I am going to ask you to tell me whether 0.001 ohm in this particular case does it represent a systematic error or random error. So, please be ready with the answers. Now, detection of errors how do you detect random and systematic errors. So, random errors can be detected by repeating the experiment and minimise and minimise by simply averaging the readings obtained in repetition. So, there is a simple way of detecting and reducing random errors. So, when you repeat an experiment if your value if the measured values in successive trials are all different, then you know that errors exist random errors exist. Now, you want to remove this source of random error well you take a number of readings and average them evidently you take more and more readings and average your random error will be reduced more and more. Now, I want to emphasise the fact that by averaging you do not remove the systematic errors. Removal of systematic errors or reduction of systematic errors is a much more tricky and difficult exercise. So, please note that by averaging you do not remove systematic errors you should not think if you average you will get accurate results no if you average you will reduce the random errors, but if there are any systematic errors present they will not be removed. Now, let us talk about control in an experiment. Control implies awareness of all the variables in an experiment and the ability to vary them at will this enables one to restrain sources of variables sources of variability in research. Control also means a standard against which the effect of a particular variable can be compared. The effects of all, but the independent variable can be eliminated by removing them, maintaining them constant screening them counterbalancing and systematic randomisation. Now, this is an important topic namely how do you remove the effects of variables except the independent variable that you want to study whose effect you want to study. So, various methods are available I am told that there is a more detailed discussion on experimental skills perhaps this topic will be discussed there. If not please note down these various methods names you can do an internet search to understand what are these various methods of removing the effects of variables other than independent variable. So, maintaining them constant is a very a state forward statement I mean you can understand very easily. Now what is the meaning of screening counterbalancing and systematic randomisation this you can find out you do an internet search and find out. Now I am going to discuss some examples to show how difficulties arise in controlling an experiment. Now first example is magnetostriction in ferromagnetic material. Let me draw a diagram to illustrate what we are talking about magnetostriction is nothing but you have a magnetic material let us say a rod of a magnetic material and you change the strength of the magnetic field in which this rod is immersed. So, the rod is put in a magnetic field and when you change the strength of the magnetic field you find that there is a change in length. So, this phenomenon is called magnetostriction. So, magnetic field changing the dimension of the material a ferromagnetic material. Now suppose you want to find out and measure whether and measure the amount of magnetostriction of a particular material. So, the experiment that you would do is something like the following. So, you will take this rod and then you will insert it in a coil. So, you will surround a coil surround the rod by a coil like this and through which you will pass a current. So, when you pass a current through this coil a magnetic field will be set up inside you know. So, for example, if I pass a current like this and this is clockwise the coil is clockwise then you know that a magnetic field will be set up something like this. Now, this magnetic field is what will affect the length of the rod. Now, suppose you do an experiment like this in the absence of the voltage you measure the length to be something and in the presence of the voltage you measure a slightly different length. Now, you will jump and you jump to the conclusion that your material has magnetostriction. Now, this is where there is a problem because when you pass current through a coil it dissipates power and as a result the temperature of the rod is going to increase it dissipates heat. The dissipated power will appear as heat. So, when you pass current through the coil the coil and the rod will get heated up. Now, unfortunately heating also increases the length of the rod. Therefore, how can you be sure that the increase in length of the rod in your experiment is due to magnetic field and not due to increase in temperature because of energy dissipation. So, this is what is important. So, if you forget that the temperature is increasing then you will attribute the increase in length of the rod to magnetostriction. Now, this is where again the awareness issue of awareness comes. We said in the beginning that you require a high level of awareness to do a good observation and it is difficult to tell what are all the things you should observe. So, only a very alert person will be aware of all the variables which are going to be present in the experiment and will monitor the values of these variables and then carefully conclude whether all the variables are having an effect or not. So, in this case the temperature also is a variable whose effect you have to take into account. So, if you want to conclude make a conclusion about magnetostriction what you will have to do is you will have to do another experiment in which you raise the temperature of the rod but do not apply the magnetic field and then you find out how much is the increase in length in that case and then you check whether when you apply magnetic field and by you know winding a coil around the rod what is the change in length in this case how much is the increase in temperature and then you remove the effect of temperature increase the increase of the length because of temperature increase and then you can find out whether there is a change in length because of magnetic field. So, this is how the control of variables in an experiment is not always easy you always have many variables affecting the phenomenon influencing the phenomenon. The other example is terminal velocity of a body in a viscous liquid like glycerin. So, we just discussed an experiment of measuring the terminal velocity and we said even there there can be temperature rise. So, the terminal velocity of the ball can be affected by a factor such as a diameter of the ball and it may be affected by temperature also because as the temperature increases the liquid becomes less viscous and that can have an effect on terminal velocity. So, if you forget about the increase in temperature of the viscous liquid then your conclusions can be inaccurate. Gender differences in color preferences. So, I mentioned this already that gender gets confounded with past experience. So, past experience is a confounding variable exposure of the control population used in experiment to different kinds of colors in their past life this can affect your conclusion. So, why precision is important why you should bother about precision and accuracy when experiments give results at variance with the theoretical ideas new discoveries are made. So, many new discoveries have been made when the measurements were at variance with the theoretical predictions even small variations can lead to significant results provided you realize that the word small is a relative word and now here is an example to illustrate that this fact discovery of argon by Rayleigh and Ramsey how was argon discovered now in an experiment in which nitrogen was produced by two different methods it was found that the density of nitrogen dependent on the method used to produce the gas. For example, in one method nitrogen was produced by from air by removing oxygen and moisture at that point it was believed that air consists of nitrogen oxygen and moisture. So, people said well you remove oxygen by some chemical means and you remove the moisture whatever remains is nitrogen they measured the density of the remnant gas and they said you know that is the density of nitrogen then someone else I did another experiment to produce nitrogen from ammonia by a different method right use this is a different method of producing nitrogen. It was found that the density of nitrogen produced from ammonia was slightly lower than the density of nitrogen produced from air. So, slightly means how much it is important to always give numbers it was 0.5 percent different. So, density of nitrogen from air was 0.5 percent more than density of nitrogen from ammonia. Now, normally if you are not a strong researcher you would say well 0.5 percent error in an experiment is you know it can always happen right. So, this kind of an error is insignificant, but the people who are doing experiments they were very careful and they said well we want to find out why repeatedly they are getting this much difference 0.5 percent difference between the nitrogen produced from air and from ammonia. And then investigation showed that this difference was because air consisted of a rare gas apart from nitrogen and oxygen and moisture argon as well. So, after this was discovered after this was realized then that the nitrogen produced from air also had a small amount of argon in it and that is what was responsible for the higher density. So, this is how you can see that you should be very careful about errors and sources of errors. In many cases if you investigate the sources of errors you might make new discoveries. Now, one more point about precision how much precision should be there. So, or rather that point comes later first significance of results depend on precision. So, here is an example let us say you measured resistance at two different temperatures. So, your resistance readings were 200 plus 0.25 ohm at 10 degrees and 200.034 ohm at 20 degrees. Now, can we say that the temperature has an effect on the resistance. Now, if you look at the readings as presented here then you will say yes when the temperature increases the resistance increases, but you know if you are a careful experimenter you will not jump to such conclusions and you will say that the data provided is inaccurate in adequate to come to any conclusion why because you have not reported the error in the reading. So, you see reporting experimental errors is not trivial doing a good experiment can be very strenuous and painful and many factors need to be taken into account. So, at least after undergoing this set of lectures all those who are doing experimental work should always report the measured value of any variable together with the error right there should be that plus or minus term. Now, coming back to this topic can we say the temperature has an effect on the resistance. Now, it depends on the error if the error is plus or minus 0.001 ohm in your experiment now how do you decide how much is the error that is a separate topic that we will come to but supposing this is the error plus or minus 0.001 ohm then your conclusion will be correct that the temperature has an effect on the resistance. On the other hand if you find that the error in your measurements is 0.01 ohm plus or minus 0.01 ohm then you cannot draw any conclusion from this set of readings. Now, this is very easy to understand let me just still let me just explain why now supposing your error is plus or minus 0.001 ohm now what does it mean. So, your readings are 200.025 ohm at 10 degree centigrade so this is though this is the reading this is an average in practice the reading can vary between this plus 0.001 that is 200.035 to sorry 200.026 and you can subtract 0.001 ohm and you will get 200.024. So, in actually your value can be anywhere in between you cannot say with certainty now you take the reading at 20 degree centigrade it can vary between 200.035 and 200.033 now you see if your error is 0.001 ohm plus or minus then at 10 degree centigrade your value can be anywhere in between these two and at 20 degree centigrade it could be between these two. Now, clearly this interval is such that the value is all at 10 degree centigrade will always be less than the value at 20 degree centigrade. So, the lower limit at 20 degree centigrade at 200.035 ohms and the upper limit at 10 degree centigrade is 200.024. So, this upper limit at 10 degree centigrade is less than the lower limit at 20 degree centigrade therefore, you are right in concluding that temperature has an effect on the resistance. Now, just repeat this exercise with a higher error of 0.01 in that case your numbers would be as follows. So, 200.015 and 200.035 at 10 degree centigrade. So, your resistance can be anywhere between this range and at 20 degree centigrade the numbers would be 200.024 and 200.044. So, now you see that the upper limit at 10 degree centigrade is 200.035 let me write it I think bigger 200.035 upper limit at 10 degree centigrade and the lower limit at 20 degree centigrade is 200.024. So, you see that now the lower limit at 20 degree centigrade is less than the upper limit at 10 degree centigrade. Now, in this case you really cannot conclude whether the temperature has any effect because your temperature resistance at 10 degree centigrade range can also be equal at to the temperature to the resistance at 20 degree centigrade the ranges are such. So, that is how precision is very important to draw conclusions from experiment. Yes, now we come to the point how much precision. So, it all depends on the purpose of the experiment. In our resistance example if a resistance is to be used as a standard in the range of 10 to 20 degree centigrade and the precision required is 0.01 percent and error of plus or minus 0.01 ohm is adequate and it is not necessary to reduce the error to plus or minus 0.001 ohm. So, you in your experiment how much care you should take to reduce the error it depends on what is the purpose of your experiment. So, unnecessarily one need not try to reduce the error we come to the topic of how do you find out that number which you write as plus or minus. So, when you say your resistance is let us say 200 plus or minus 0.01 ohm how do you get that number plus or minus 0.01 ohm. So, this is what we are now discussing. So, here is an example let us say we have done 1, 2, 3, 4, 5, 6, 7, 8. 8 trials of a resistance measurement and in these 8 trials we got these values. Now clearly these values are changing and they are going in either direction. So, therefore, this variation in the values represents random errors. You can average all these values and you will get a number shown here 4.625 ohms. So, add up all these values and divide by 8 you get the average. You can get the standard deviation. How do you get the standard deviation? So, you find out this average that is 4.625 ohms. You subtract the average from each of these quantities and you get a difference. Now you square all these differences sum them up and then divide by the number of trials that is 8 and you take a square root of this quantity. So, sum of all the deviations from the mean, sum of the squares of deviations from the mean. So, it is you can also call it as root mean square value. So, that is the standard deviation. So, that value you will get in this case as 0.017 ohms from your measured readings. Now the error in a mean of observations denoted as sigma m is equal to the error in a single observation that is sigma by square root of n. This sigma value is related to the standard deviation s. So, we just discussed how to find out the standard deviation s. From the standard deviation you can get the error that is sigma. So, let me write this down. So, what we are saying is the resistance R is equal to average of the standard deviation plus or minus a term dependent on standard deviation that we are calling it as sigma m. So, this plus or minus term is sigma m and the formula for this sigma m is what is shown in the slide that is sigma by square root n where sigma itself is dependent on standard deviation as shown here. Now for simplicity you can assume this term square root of n by n minus 1 to be almost 1 in which case you get an approximate value of sigma as standard deviation. So, if you put sigma as approximately standard deviation then the plus or minus value that you are putting against your resistance measurement is the standard deviation divided by the square root of the number of trials. So, in our case for example, standard deviation is 0.017 ohm your sigma m will be equal to the standard deviation 0.017 divided by square root of the number of trials that is 8. So, that is the number that you will put as the plus or minus quantity in your reading. So, this is important for you to know how do you write this plus or minus quantity. Now this formula also shows why repeating measurement and taking the average reduces error. So, you see from here that the error in your average depends on the number of readings n you take. So, if you take two readings then your error will reduce by a factor of 1 by root 2. If you take nine readings it will reduce by factor of 3 because square root of 9 is 3. What this also shows formula also shows is increasing the number beyond a point may not have that much increase that much benefit because the behavior goes as square root of the reduction of error happens as square root 1 by square root of n. So, because of the square root dependence normally it is suggested that you know you restrict your number of readings to between 7 and 9 around that should be sufficient even if you go to 16 readings you know the reduction in error as compared to 9 readings will not be significant. So, please make note of this ballpark figure you must make 7 to 8 measurement 7 to 9 measurements and take the average of this measurements to get the value after reduction of the after removal of the random error. Now, estimation of random error in a function of several variables we discussed how you know you can estimate the error in a single variable. If you have many variables then you know there is a formula and that is given here this is standard all of you know I have just put it here for the sake of completeness. So, if you have a result that is a function of several variables and you want to know the error in z as a function of error in a, b, c and so on then you use this kind of a formula. So, I think I will skip this I will spend a few minutes on reduction of systematic error as I mentioned the reduction of systematic error is not a straight forward matter. First of all identification of source of systematic error or presence of systematic error itself is a difficult exercise unlike identification reduction of random errors. Because if you repeat measurements and you find that there is a variability you know random errors are present and you can take an average of several readings about 7 to 9 readings and then you can reduce the random error fine systematic error not straight forward. First of all you do not know how it is hidden in the experiment and even after you know how it is hidden it may not be easy to remove the this particular error. Now broadly there are two methods simple methods that are available it does not mean these are the only methods for reading systematic error. In fact depending on the type of systematic error you will have different methods and there are very many sources of systematic errors in different experiments. We will discuss two very simple techniques which should be used and in case they work. If they do not work of course you should go to more sophisticated techniques. Now the first one is choosing a proper sequence of the measurements and the second one is using the symmetry in an apparatus to reduce the systematic error. So let us illustrate these two techniques with examples. Let us take the first technique that is choosing a proper sequence for making your measurements. So let us say you are talking about measuring the terminal velocity as a function of the diameter of the ball and now the glycerin experiment. Now let us say you have four balls of diameters A, B, C and D and let us say the diameter is decreasing in that order. So how many readings will you make? Now you want to find out the dependence of the terminal velocity on the ball. Now as we said each measurement should be repeated. Let us say we repeat each measurement we just now said 7 to 8 times to reduce the random error. So how many readings you will have to take? So you take ball A and you repeat the experiment 7 times. So 7 times you are going to drop the ball of diameter A and every time you will measure the terminal velocity. Like this you will do for all the four balls. So in other words you have 28 readings. So you are going to do 28 experiments. So 28 measurements and what sequence they should be done is very important. For instance if you do not apply your mind critically to this particular problem and simply use the following method. Let us say I take the ball A and I take all the 7 readings for ball A for averaging. Then I go to ball B, I repeat the experiment 7 times. Then I go to ball C and ball D. Now what is going to happen is because there is a systematic error due to temperature rise in glycerin all the measurements of ball A will be at a lower temperature as compared to the measurements of ball D. Therefore the terminal velocity that you measure for ball D will also incorporate the effect of this temperature rise. And therefore your conclusions that you draw may not be correct. Now how to remove the effect of temperature rise? Now here is one trick that can be used. Now somebody can say well you use a constant temperature bath. That is a straight forward looking solution but then you will have to buy a constant temperature bath and then make the setup so that you can maintain the temperature constant. Instead a simple technique exists you choose a proper sequence for the measurements. For instance you can use a sequence like this. So I measure the terminal velocity with ball A, then I measure the terminal velocity with ball B, then C and D. Now next I start with the ball D and measure the terminal velocity of this ball. And then I make a measurement of the velocity with C, then B, then A. Notice that this order D, C, B, A is a mirror reflection of A, B, C, D. So I first choose sequence A, B, C, D then I choose D, C, B, A. Now I choose a different sequence. Now I do the experiment with ball B first then B, C, D, A and then I take the mirror image of this sequence later on. So this is how I do all my 28 measurements. Now see when I use averaging technique for each diameter in this case what will happen is the effect of temperature would have got averaged out. Why because let us say I start with ball A, the glycerin is at some temperature. By the time I have come to ball D let us say there is a delta T rise in temperature. Now since I am repeating the measurement of ball D immediately, these two readings are all happening both taken at T plus delta T. Now when I come to the reading A, the next time there will be another delta T rise in temperature. So the reading with this ball A now is at a temperature T plus 2 times delta T. Now when I average this first very first reading of A which is at temperature T with the reading at T plus 2 delta T, the average temperature would be T plus T plus 2 delta T by 2 which is T plus delta T, which is the same as the temperature for D and you can easily show that all readings in this case will be at temperature T plus delta T for B and for C and so on. Now in this fashion you can easily show that in effect the temperatures for all the diameters would be the same. So this is how one can reduce the systematic error due to temperature rise in this case. So please remember if you are taking a large number of readings, different readings by varying the variable then pay careful attention to the sequence or order in which you make the measurement. It can help you, choice of a proper order can help you reduce the systematic error. Let me discuss the use of symmetry in apparatus. How? This can be used for reducing the systematic error. Let us consider another experiment. So let us say you are measuring thermal conductivity, you are measuring thermal conductivity of a material. So how do you make this measurement? So let us say this is your material. Now you will maintain a temperature difference between the two phases. So let us say you maintain a temperature T1 here and T2 here. You will find out how much is the heat flux from this end to the other end. And then thermal conductivity sigma is nothing but heat flux divided by the temperature difference T1 minus T2. So this involves measurement of heat flux and measurement of temperature T1 and T2 and then you take the ratio. Now a source of systematic error can be in this case you will use, supposing you use different thermometers to measure temperature T1 and measure temperature T2. Now each of these two thermometers may have different zero errors. Now let us say the thermometer used for measuring T2 tends to give a higher temperature than the actual temperature. How can you remove the error, this sort of an error? Well what you can do is you measure a T1 using one thermometer as well as the second thermometer and you measure T2 also with both the thermometers. This means that I put thermometer 1 at phase number 1 and thermometer 2 at phase number 2, I measure T1 minus T2. In the next trial I put thermometer 2 at phase number 1 and I put thermometer 1 at phase number 2 and then I measure the temperature difference T1 minus T2 again. Now I can repeat this sort of a thing and take an average and in this way any zero error or different zero error of the two thermometers can be removed. So this is where we have used the symmetry of the experimental setup to remove the source of systematic fitting a straight line by method of least square. I only want to point out that knowing the theory behind fitting of a straight line and the method to be used for fitting a straight line so as to reduce the least square error is a very important part of doing an experiment because often we plot the experimental results in a way in which the dependent variable and the independent variable the relationship is shown as a in a straight line form. So fitting of a straight line is very straight forward and therefore you cast it in this form. This is not to say that the dependent variable always varies linearly with the independent variable. For example, dependent variable y to the power 3 can be a square law function of independent variable. So y power 3 by 2 is equal to x square but still you will fit the result of measurements as a straight line as follows. So you can plot y cube as a function of x square for example or it can be even more complicated as a x square plus b. So you can plot y cube as a function of x square and you know it will be a straight line. You need not plot y as a function of x though you are interested in the relation between y and x depending on the relationship you can always choose your axis or the variables along the axis in such a way that ultimately the relationship gets plotted in a straight line form because this is the simplest way of checking the theory. So now here you will have various measurements data with their errors and you would like to fit a straight line through all these points minimizing the errors. So now this is a topic that you should know so I will leave this as an assignment. So how to decide the slope and intercept of the line depending on the measurement. So this is the formula. So with this we come to the end of the discussion on experimental skills. I will entertain any comments or questions on whatever we have discussed on experimental skills. Let us take St. Francis Institute of Technology Boreubli. Your sessions are very informative. Thank you so much for that. But I need one kind suggestion regarding publishing work that is from your earlier session in the morning. Like I have done my MFIL and my work has been acknowledged in a book chapter Springer where my name is there in the acknowledgement part where my supervisor and my one of my PhD senior they have written my name and thankful to so and so for their work which has been published in their MFIL dissertation work. Now the query is like they have used my data tables and everything my thing my MFIL work and I have heard from one of my senior that there is a difference between the book chapter and the paper which is to be given in the journal. Now can I write my paper through like this is my work and using the same data the same table but these data and other tables which is given here it is available to the entire world is accessible to the entire world or maybe you can have a slight you know twist and turn discussion part. Okay let me reframe your question. What you have said is that some matter has already been published in a book. Can you now use data from that book chapter to write a paper and further you are saying that in that book chapter you are not a co-author you have been acknowledged in the acknowledgement section but you are not a co-author but you want to write a paper with yourself as an author. Yeah yes sir. Definitely you cannot use tables and numbers as it is from the material published in a book the reverse is possible for instance supposing some material has been published in a paper and you are writing a book chapter after publication you can use that information to you know publish in a book chapter form. The reverse first it something has appeared in a book chapter and then now you want to publish it. I think that will not be correct you cannot use it as it is because normally a journal publication requires if you see the requirements for submission you will find all journals will state that you must certify that this work has not been published elsewhere or sent for publication elsewhere. Yeah so that is why you cannot even send the same paper simultaneously to different journals. Now there is a small exception to this suppose you have published your work in a conference. Now you can write a fuller paper for a journal which is about 30 percent which contains about 30 percent new material as compared to the conference right. So you can add to some further work and you can use the data presented in a conference and your results plus some additional thing but as it is you cannot publish right but by adding a few more things to that you can publish in a journal that is fine. Just elaborate on random and systematic error with a real example because we are a bit confused with the question which you have given to us that is 0.001 ohms will be a systematic or a random error. So we will just brief about a real take a real time example real world example and just brief about it. Actually if you have carefully followed my talk I already gave the answer right. I will repeat I gave the example of how you calculate random error. So this is the example I have given multiple readings of the same resistance 8 readings and I have mentioned how to report this these readings you know convert them into a single reading and a single error. So the effect the resultant of all these trials would be reported as follows. The resistance is equal to the average of all these readings that is 4.625 ohms plus or minus a number which is nothing but the standard deviation 0.017 ohms divided by square root of n where n is equal to the number of trials in this case 8. So 4.625 plus or minus 0.017 upon square root of 8. Now if you want to be even more accurate then as shown in the slide it will be 0.017 that is s into square root of 8 divided by square root of 8 minus 1 multiplied by 1 by square root of 8. So which means it is nothing but s by square root of n minus 1 that is more accurate result would be 4.625 plus or minus 0.017 divided by square root of 8 minus 1 that is 7. So that is how you will report your results. Now this is an example of random errors. So I already told you that you can detect random errors in your experiment if in repeated trials you are getting different values your repeated measurements are all different from each other then it means random error is presented and also the trials are showing values which are do not have a trend it is not as though all your readings are going on increasing in repeated trials or going on decreasing. So they are going here and there then you know that random errors are present and you can take an average and this is how you can reduce the random error. Now systematic error I have shown is much more difficult to detect and reduce. So I cannot give a general method of detecting systematic errors or removing systematic errors it all depends on what is the type of systematic error. So does that clarify your doubt? Yes sir. Thank you sir. Now you should answer my question when you write the resistance as does 0.001 ohm represent random error or systematic error. Now please tell me what does it represent? I think it must be random error because it is varying in both the direction that is positive and negative direction. That is one thing and always whenever you are reporting your reading in this form it is a random error that you report because it is always present in any experiment. Systematic error may or may not be there. Okay fine. Thank you sir. This is Radhe Krishna from SFIT sir. I have a doubt regarding the publication research paper published in different journals. Suppose there is I want to publish three papers. First paper I am going to present in a conference and I am getting the conference proceeding. The second paper I am submitting to the journal directly and it is getting published and the third paper I am going to attend the conference. I am presenting my paper in the conference and the conference convener sends the paper to the same journal and it is getting published. So I have three papers, one conference proceeding, one paper that is published through the conference convener and the third paper that is directly published through the journal editor and the author. So which one has got more weightage in terms of the quality and in terms of the standard of publication? Let me repeat your question. You are saying case one, paper published in conference proceedings. Case two, the same work published in a journal which is reviewed, peer reviewed journal. But I think it is not really important for us whether we are talking about different papers or not. In fact, I should consider these three different modes for the same paper and see which one is better because then I should follow that. So always a peer reviewed journal paper has a higher status. Now in case the paper appears in a journal after publication in a conference and it is sent by the conference convener to the journal, it will always go through the review process because the journal is not going to accept without review process. You are saying it is going to the same journal. So in both these cases there is a peer review process. So I think ultimately what matters is publication in that journal. If there is a publication in that journal, it does not matter whether it is directly sent to that journal or it is appearing through a conference convener. I think either of them, you know, ultimately it is the same journal where it is getting published. So as against this paper published in a conference proceeding definitely has less standard than paper published in a journal because in general as I said conferences adopt a lenient criteria criterion for lenient standard for reviewing because they want to allow a large number of people to come and meet each other. What is the goal of a conference? The goal of a conference is for researchers to come and meet and then discuss something technical and then maybe establish collaborations and so on. You get to know what other people are doing. So in conferences, they always allow you some leniency because the goal is to allow more and more people to come and meet each other. Sir the paper that I have published in conference proceeding can I rewrite and publish it in a journal over to you, sir? I answered that question already. You can add about 30 percent more material and then send it to a journal. Journals do not accept whatever you have published in a conference as it is. There should be some addition and some journals are saying 30 percent addition should be there. Now you should see, please note 30 percent addition does not mean simply increasing the length of the work by 30 percent. It is not that your number of pages should be more. The original contribution should be more. So it is not so easy to decide whether 30 percent original contribution is there or not. You know it is a subjective judgment but does give you some sort of a feel for how much different it should be. Thank you, sir. Over to you. Let me go to KMEA engineering college, Alua. Sir normally once you apply for patents, how much is the duration in India and in US? I do not have the exact numbers for this. You can keep a patent alive for different periods of time depending on how much payment you are prepared to make. But all patents become, you know, they die out beyond a certain number of years. Unfortunately I do not have that number right now. There is a certain number of years beyond which you cannot keep any patent alive. That is one thing. Other thing is, suppose you want to keep a patent alive for seven years, there is certain amount you have to pay. If you want to keep it alive for say 15 years, you know, you have to pay a bigger amount. So you have to renew. But beyond a point you cannot renew. Anyway, because work becomes obsolete. So I do not know the number. Maybe you should do an internet search. I will also, you know, see that. I do not have this number ready in my mind. Okay. Thank you. Right. I should stop the interaction now.