Unit_1_Scientific_Methodology.pdf

UNIT 1 SCIENTIFIC METHODOLOGY The scientific method The practice of attempting to approach the objective truth as closely as possible is known as the scientific method. It is a set of procedures that individuals may use to learn more about the world they live in, advance their un...

UNIT 1 SCIENTIFIC METHODOLOGY The scientific method The practice of attempting to approach the objective truth as closely as possible is known as the scientific method. It is a set of procedures that individuals may use to learn more about the world they live in, advance their understanding of it, and make an effort to explain why and/or how things happen. With this approach, ob- servations are made, questions are formulated, hypotheses are formed, an experiment is conducted, data is analyzed, and a conclusion is drawn. But part of the process is to keep searching for the universe’s laws, keep refining your findings, and ask new questions. A proposed explanation of the scientific process is the hypothetico-deductive model or technique. It states that the process of scientific investigation begins with the formulation of a hypothesis in a form that may be verified or refuted by an experiment on observable data with an unknown consequence. A test result that could have, or really does, defy the hypothesis’s predictions is seen as proof that the hypothesis is false. A test outcome that could have, but does not run contrary to the hypothesis corroborates the theory. The results are then compared with other competing hypotheses to determine (strin- gently) the validity of the proposed theory. Unit 1. Scientific Methodology 2 Hypothesis A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientific hypotheses are often based on past findings that the current body of knowledge is unable to adequately explain. Hypothesis vs Theory A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments. A theory, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. Because of the rigors of experimentation and control, it is understood that theory to be more likely to be true than a hypothesis. In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice. Some Famous Theories In no particular order, below are some of the well known theories that have stood against the face of time. The Big Bang Theory The Heliocentric Theory The Theory of General Relativity The Theory of Evolution by Natural Selection Experiment In science, an experiment is simply a test of a hypothesis in the scientific method. It is a controlled examination of cause and effect. Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 3 The two key parts of an experiment are the independent and dependent variables. The independent variable is the one factor that you control or change in an experi- ment. The dependent variable is the factor that you measure that responds to the independent variable. In a science experiment, a variable is any factor, attribute, or value that describes an object or situation and is subject to change. NOTE: There is another type of variable called confounding variable. A confound- ing variable is a variable that has a hidden effect on the results. Sometimes, once you identify a confounding variable, you can turn it into a controlled variable in a later experiment. Some Famous Experiments Galileo Galilei and the Leaning Tower of Pisa Experiment Aristotle had proposed that objects fell at different rates because gravity would act more strongly on heavier objects, but it turns out that the feather falls slower only because of air resistance. If you could perform the same experiment in a vacuum, the feather and ball will hit the ground at exactly the same time. It is difficult to separate fact from legend, but the story goes that Aristotle’s theory of gravity went unchallenged until Italian polymath Galileo Galilei disproved it. Mendel’s peas Augustinian friar Gregor Johann Mendel crossed-bred peas with varying traits to assess the inheritance patterns of various traits in their progeny. His research concentrated on pea plants and their seven distinguishable characteristics: plant height; flower location; seed, pod, and bloom color; and pod and seed morpholo- gies. He watched about 28, 000 pea plants throughout the course of the eight-year investigation. Mendel discovered that many plant generations displayed varying ratios of green to yellow peas, with yellow being the predominant color, while examining the color of the peas that were generated. He found that genes are paired, and that the dominant and recessive expression of those genes is deter- mined by the mathematical pattern that is observed throughout generations. Rutherford strikes gold Ernest Rutherford — Hans Geiger and Ernest Marsden performed a series of ex- periments between 1908–1913 to prove Rutherford’s theory of an atomic model, which resembled planets orbiting the Sun. The physicists used a radioactive substance to bombard a thin piece of gold foil with positively charged alpha particles. The majority of particles passed through the foil without any deflection, suggesting that atoms had a great deal of open space. some were deflected from the gold foil at different angles, which meant that those particular particles had hit something with the same charge. Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 4 This meant that rather than a positive charge engulfing electrons, a smaller positive charge was held in the dense middle, thus heralding the discovery of the atomic nucleus. Eddington and the eclipse The year 1919 had a total solar eclipse, which gave Eddington a rare chance to see the night sky during the day. Eddington studied star positions at night and again during the false night of an eclipse after sailing to Prı́ncipe Island to witness the finest possible solar eclipse and verify Einstein’s hypothesis. This implied that he could watch to see if the Sun’s gravity had changed the stars’ apparent locations, which it had. This demonstrated that Einstein was right—light had been bent throughout its travel to Earth due to the force of the Sun. Examples of what are NOT experiments Making observations does not constitute an experiment. Initial observations often lead to an experiment, but are not a substitute for one. Making a model or a poster is not an experiment. Just trying something to see what happens is not an experiment. You need a hypothesis or prediction about the outcome. Changing a lot of things at once isn’t an experiment. Error Analysis Science is all about building knowledge based on reliable evidence. But no mea- surement is perfect; errors always creep in, no matter how carefully one performs the experiment. Error analysis is a crucial part of scientific inquiry that helps us understand how much trust we can place in our results. Errors are deviations between the measured value and the actual value. Uncer- tainty on the other hand gives us the range of possible values within which the true value likely lies. Error analysis in science is the process of evaluating the uncertainties associated with measurements and experimental results. It’s not about achieving perfect mea- surements (which are impossible), but understanding how close your results are likely to be to the true value and how much confidence you can have in them. Error analysis involves two main types of errors: Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 5 NOTE: As an exercise try to find out all the possible sources of errors while per- forming an experiment. Random Errors Fluctuations happening by chance, causing measurements to scat- ter. Think of throwing darts randomly around the bullseye. These can be minimized by taking multiple measurements and averaging the results. Systematic Errors Consistent biases that push measurements in one direction (over- estimating or underestimating). Imagine a tilted dartboard where darts consis- tently land off-center. These require careful analysis of the experiment’s setup and instruments. By analyzing errors, we can: Estimate the uncertainty in our measurements. Evaluate the reliability of our results. Draw valid conclusions from the experiment, considering the limitations of the measurements. What Error Analysis Doesn’t Do: It doesn’t eliminate errors entirely. Errors are inevitable in any measurement or experiment. However, error analysis helps us account for these uncertainties and build trust in our findings. Accuracy and Precision Accuracy quantifies how closely a measured value aligns with the actual or true value of the quantity being measured. It reflects the “bullseye” of scientific measurement, striving to hit the mark. For example, a thermometer that consistently reads your body temperature at 98.6◦ F is considered accurate, assuming that’s your true body temperature. A single measurement can, in theory, be accurate. If a surveyor’s instrument yields a building height of exactly 100 meters, and that’s the true height, then the measurement is accurate. Precision describes the closeness of multiple measurements of the same quantity to each other. It reflects the reproducibility or repeatability of a measurement process, like clustering your darts tightly on the dartboard. Precision is assessed by analyzing the spread or variability across a series of measurements. A set of measurements can be precise, exhibiting minimal variation between them, yet inaccurate if they all deviate from the true value. Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 6 Feature Accuracy Precision Definition How close a measurement is to How close repeated measure- the true or actual value ments are to each other Analogy (Think dart- How close a throw lands to the How close multiple throws are board) bullseye grouped together Example A scale that measures your weight Throwing darts that all land exactly at 150 lbs (assuming within a 1-inch radius of each that’s your true weight) is accu- other is precise (even if they’re rate. not on the bullseye). Dependence Depends on the true value Independent of the true value Multiple measurements Not necessarily. A single mea- Yes. Precision refers to consis- needed surement can be accurate by tency across multiple measure- chance. ments. Impact of random errors Random errors can cause inaccu- Random errors can affect pre- racy by scattering measurements cision by causing throws to be away from the true value. spread out more. Impact of systematic er- Systematic errors can cause in- Systematic errors won’t affect rors accuracy by consistently push- precision (throws will still be ing measurements in one direc- grouped together) but will af- tion (over or underestimating). fect their location relative to the bullseye (accuracy). Importance Crucial for ensuring measure- Important for ensuring consistent ments reflect reality. Inaccurate and repeatable results. data can lead to misleading con- clusions. Quantifying errors Significant Figures and Round off The precision of an experimental result is reflected not only in the specific value reported, but also in the way it is written. To convey this precision, scientists use the concept of significant figures. The number of significant figures in a result signifies the digits that are considered reliable and contribute to the measured value. Here are the rules of how to determine significant figures: Most Significant Digit: The leftmost non-zero digit is always significant. Least Significant Digit (No Decimal): If there’s no decimal point, the rightmost non-zero digit is the least significant. Least Significant Digit (With Decimal): When a decimal is present, all digits to the right of the decimal are significant, even trailing zeros. Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 7 Digits Between: All digits between the most and least significant digits are considered significant. Following these rules, several examples illustrate numbers with four significant figures: 1, 234; 123, 400; 123.4; 1, 001; 10.10 and 0.0001010. However, ambiguity arises when dealing with trailing zeros in numbers without a decimal. For instance, the number 1, 010 might have a physically significant last digit, but by convention, it’s interpreted as having only three significant figures. To avoid this ambiguity, it is better to supply decimal points or write such numbers in exponent form as an argument in decimal notation times the appropriate power of 10. Thus, our example of 1, 010 would be written as 1, 010. or 1.010 × 103 if all four digits are significant. Rules of error propagation Error propagation refers to how uncertainties in individual measurements translate into the uncertainty of a final result obtained through calculations. Here’s a concise overview with key equations: Addition/Subtraction: The uncertainty of the sum/difference equals the square root of the sum of the squared uncertainties of individual measurements. p ∆z = (∆x2 + ∆y 2 +...) (1.1) (where ∆z is the combined uncertainty, ∆x, ∆y,... are individual uncertainties) Multiplication/Division: The relative uncertainty of the product/quotient is the sum of the relative uncertainties of individual measurements. (∆z/z) = (∆x/x) + (∆y/y) +... (1.2) (where z is the final result, x and y are individual measurements) Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 8 Relation between Z and (A, B) Relation between errors ∆z and (∆A, ∆B) Z =A+B (∆Z)2 = (∆A)2 + (∆B)2 Z =A−B (∆Z)2 = (∆A)2 + (∆B)2 ∆Z 2 ∆A 2 ∆B 2


Z =A·B Z = A + B ∆Z 2 ∆A 2 ∆B 2


Z = A/B Z = A + B ∆Z ∆A
Z = An Z =n A ∆A Z = ln A ∆Z = A ∆Z Z = eA Z = ∆A Mean, Variance and Standard deviation Mean The mean provides a measure of central tendency, summarizing the dataset with a sin- gle value can give an idea of what is to be expected when the experiment is performed again (sometimes can be referred to as the expected value of the experiment). It allows researchers to compare different groups or conditions in an experiment by simplifying a large dataset to an easily represented and understandable value. This is because most of the results of the experiment follow the Gaussian curve, however one must note that the mean is extremely sensitive to the extreme values. Mathematically, the mean (or average) is the sum of all data points in a dataset divided by the number of data points given by: P X Mean = N Where: P X is the sum of all the observations (data points). N is the total number of observations. Unit 1 - Lecture Notes - Science Team Unit 1. Scientific Methodology 9 Variance Variance tells us how far the data points are from the mean, it allows for comparison between different datasets in terms of their spread. A smaller variance indicates consistent results since the data points are closer to the mean, while a larger variance indicates greater variability since the data points are more spread out. Mathematically, it is given by: (X − µ)2 P 2 Variance(σ ) = N Where: X represents each data point. µ is the mean of the dataset. N is the total number of observations. Standard Deviation Standard deviation is the square root of the variance and is a measure of the amount of variation or dispersion in a dataset. Unlike variance, which is in squared units, standard deviation is in the same units as the data, making it easier to interpret the data. It is useful for identifying outliers, as data points more than two or three standard deviations away from the mean are often considered unusual. In a normally distributed dataset, approximately 68% of data points fall within one standard deviation of the mean, and 95% fall within two standard deviations. It is mathematically given by, rP rP (X − µ)2 X2 Standard Deviation(σ) = =⇒ σ = − µ2 N N Where: σ is the standard deviation. X represents each data point. µ is the mean of the dataset. N is the total number of observations. Unit 1 - Lecture Notes - Science Team