Friday, August 21, 2020

Social Contract essays

Implicit agreement papers It probably won't be conceivable to live a moral and well behaved life and still have the option to keep up control of our predetermination without being squashed by outside forces. In any case, we should attempt on the off chance that we need to live as a feature of a network, we should attempt since we'll be returning to a province of Nature on the off chance that we don't. At the point when Jean Jacques Rousseau composed The Social Contract he expressed that ...a point was reached throughout the entire existence of humanity when the snags to proceeding in a province of Nature were more grounded than the powers which every individual could utilize as far as possible of proceeding in it. (Rousseau, p.179) and that ...mankind would have died had it not changed its way of presence. (Rousseau, p.179). On account of this Social Contract people have deserted a territory of Nature where ethic and laws didn't exist and they became rather a network building up an ...a focal heading... (Rousseau, p.179) and figuring out how ...to act in show... (Rousseau, p.179). In any event, when outside forces can control our fate we ought to try constantly to live a moral and decent life. On the off chance that we do stop well be influencing us and every other person around us. It will be the initial move towards downhill on the tricky slant. The tricky slant can be characterized as: on the off chance that An is allowed, at that point by a progressive arrangement of little strides through B, C, ..., X, Y, inevitably Z will be as well. We ought not allow Z so in this way, we ought not allow A. Applying living a moral and honest life to this idea we can express that on the off chance that I quit doing it, my neighbor will quit doing it, and his neighbor will quit doing it, et cetera until the whole society will quit doing it, leaving us in a totally territory of Nature. Jean Jacques Rousseau certified that What a man loses because of the Social Contract is his normal freedom and his unfit right to lay hands on all that entices him..... <!

Tuesday, July 7, 2020

Research The Use of Marijuana among Medical Students - 2200 Words

Research The Use of Marijuana among Medical Students (Research Paper Sample) Content: Name:Instructor:Subject:Date: The Use of Marijuana among Medical Students Problem StatementDrugs are used for a number of beneficial purposes when directed by qualified medical personnel. However, some drugs can have detrimental effects when used wantonly, and one such drug is Marijuana. Within the medical profession, specifically in medical schools, the problem experienced is the incorrect use of marijuana by the medical students, and it involves using it incorrectly for medicinal purpose, to improve brain function, and to promote social interaction.Description of the ProblemMarijuana is derived from the hemp plant known as Cannabis sativa. It is the mainly used illegal drug in the US. In most cases, the plants leaves are dried and smoked, as well as its seeds, stems, and flowers. Marijuana can also be mixed and taken with food or brewed as tea. It has many street names, such as herb, weed, and pot. In adults, the rates of smoking marijuana have been stable since th e 1990s. However, statistics show that about 30% of young people are today smoking marijuana. Since the majority of youthful people are in colleges, they have abused this drug in a number of ways.Using Marijuana for Medical Purpose IncorrectlyNumerous states in the United States are passing legislations advocating the use of marijuana as medicine. This raises questions as to what marijuana treats, as well as who should use it. According to Dehaas (par. 7), medical students have grabbed this opportunity and are incorrectly using marijuana for medicinal value. As medicine, Marijuana is used for alleviating pain in the body, regardless of the disease. In states that have legalized marijuana, doctors and medical students prescribe it when they believe it can take away any pain or illness. A patient is given a marijuana card to help him, or her buy marijuana from a seller authorized to run a marijuana dispensary. Following marijuana legalization, medical students have taken advantage of the situation and are using it to treat a myriad of diseases. Some of these include seizure disorders, muscle spasm from multiple sclerosis, nausea caused by cancer chemotherapy, and weightless and poor appetite caused by chronic illnesses, such as nerve pain or HIV AIDs (Dehaas par. 9). A key ingredient in Marijuana called Tetrahydrocannabinol (THC) is responsible for improving appetite and treating nausea. Once taken as medicine, Marijuana is absorbed in the body as a chemical affecting inflammation and pain, among others. Also, it can catalyze the working of natural chemicals. Marijuana is used through smoking, vaporization, eating, or taking it as a liquid extract. Although Marijuana has medicinal value, it has a number of side effects, including drowsiness, euphoria, dizziness, and a short-term memory loss. However, there are some serious effects such as severe psychosis and anxiety (Emmett and Nice 19).Medical marijuana does not lie in the category of FDA-approved medicines. This is because when using it, it is not easy to tell its ability to cause cancer, as well as its side effects, purity, and potency. People with a marijuana card are the only ones allowed to use marijuana medicinally. Doctors should not prescribe medical marijuana to people under 18. Others who are not allowed to use it are those suffering from heart disease, those with a history of psychosis and pregnant women. However, these guidelines are not being followed by the university students (Emmett and Nice 23). Using Marijuana to Improve Brain FunctionThe information by Engs and Teijlingen (439) indicates that at least 18% of medical students use Marijuana to improve brain functioning to carry out their day-to-day activities. Engs and Teijlingen (441) attribute the use of marijuana to tiring academic work, which forces a number of students to use the drug as a stimulant for reading. The functioning of a human brain depends on a multifaceted interplay of chemicals referred to as neurot ransmitters that function as information carriers between the brain cells known as neurons. THC, the main active ingredient in marijuana, interferes with this interplay and alters the strength of some of the signals. THC also interrupts the normal communication of neurons and brain circuits.THC interacts with proteins in the brain known as cannabinoid receptors. A high concentration of these proteins is present in the critical areas of the brain, essential for reward processing, learning, pain perception, and memory. Scientists believe that activating cannabinoid receptors in a humans brain may cause the likelihood of abusing Marijuana. Abuse of marijuana can cause some enduring changes to the working of the brain, particularly to people with a greater risk of psychiatric disorders (Engs and Teijlingen 442). According to Solowij (74), when the use of marijuana is repeated during a youthful stage, it can increase the risk of psychosis and decrease adulthood IQ. It can also alter the brain and increase its vulnerability to harmful illicit drugs. This means if the continued use of marijuana will be left in the hands of medical students the new breed of graduates will have a reduced IQ and will thus not cope with the rigors of their profession (Solowij 78). The addictive and medicinal properties of marijuana have impelled the search for new drugs to exhibit a reduced ability for abuse while maintaining therapeutic value. A recent discovery shows that the brain produces chemicals naturally and these targets cannabinoid receptors, opening avenues for drug discovery. New studies promise that drugs that target the natural cannabinoid system of the brain may offer relief to patients that suffer from devastating conditions, including mental health disorders, chronic pain, and obesity (Solowij 79).Using Marijuana to Promote Social InteractionThere are several factors causing university students to use marijuana, and curiosity is one of them. The study by the DrugScope A lcohol Concern (24) indicates that students use marijuana for the sake of fitting into a social group, and the medical students are not exempted. Although peer pressure is most rampant during the adolescent stage, the university students are equally affected. Interacting with marijuana users influences one to follow suit. Also, those already exposed to smoking cigarettes or taking alcohol are at a great risk of using marijuana. According to Tashkin (635), about 85% students from top universities in the US smoke to fit in a social norm. This means about 85% of university students are likely to use marijuana in the course of their studies. University students use marijuana to cover up past assaults on their lives. When one is sexually or physically abused, this heightens a risk of using marijuana, as well as other drugs. This is done to forget the abuse, but the victim becomes addicted rather than finding help. Research by the Seatle Hospital Reseach Foundations (5) indicates that the utilization of marijuana in university students occurs as a result of ones background. When role models of such students are people using drugs, this heightens the risk of the students to use marijuana or other drugs, as well. This depicts that the environment of a university student is a determinant of whether they should use marijuana or not. There is no magic bullet to prevent drug use among university students. As a result, a one-on-one discussion about the use of marijuana is very important. Research holds that parents are very influential to university students even when it does not seem so. However, the study by the Seatle Hospital Reseach Foundation (4) indicates that parents do not talk openly to their children in the university. This has shielded active engagement between the parent and the university student, and thus students fail to differentiate between myths and facts so as to make the right decision per the current evidence. Impact AnalysisIf marijuana is left in th e hands of medical students, a number of adverse effects are likely to take place and this will impact their professional development. First of all use of marijuana for medicinal value is likely to lead to abuse of the same drug, and this will result into poor physical and social health. At the same time, if the drug will be used as brain booster in academic work, it will lead to detrimental effects. Social misfits cannot be solved by the drug, and this implies a further deterioration in health. The impact of uncontrolled use of marijuana among medical students is analyzed in below:Psycho-social HealthAccording to investigation by the University of Oregon (par. 5), marijuana addicts about 9% of people who begin using it the age of 18 years. This addiction is accompanied by withdrawal symptoms, such as anxiety, sleep disturbances, which often causes relapse, and irritability. Given that the brains of university students are still growing, marijuana use will results to high addiction rates amounting to 17% in a period of 2 years. This will disrupt the students live to a great deal following the great risk of using it at the schooling age. In this case, it will be impossible for them to focus on their profession. Negative Effects on Mental HealthMarijuana causes fluctuations in anxiety and mood to the extent of persistent beyond description. Frequent marijuana users experience increased depressive and anxiety disorders to a point that the direction of causality is indescribable. However, inasmuch as the effect of marijuana cannot be defined, it is evident that heavy use of the drug causes depression and anxiety disorders. The endogenous cannabinoid system is known to modulate the hypothalamus-pituitary- adrenal axis. Exogenous cannabinoids, including THC activate the main neuroendocrine system of response to stress through the HPA axis. Dysregulation of responses to stress...

Tuesday, May 19, 2020

What Is Astronomy and Who Does It

Astronomy is the scientific study of all objects in space. The word comes to us from the ancient Greek term for star law. Astrophysics, which is part of astronomy, goes a step further and applies the  laws of physics  to help us understand the origins of the universe and the objects in it. Both professional and amateur astronomers observe the universe and devise theories and applications to help understand the planets, stars, and galaxies.   Branches of Astronomy There are two main branches of astronomy: optical astronomy (the study of celestial objects in the visible band) and non-optical astronomy (the use of instruments to study objects in the radio through gamma-ray wavelengths). Non-optical is sorted into wavelength ranges, such as infrared astronomy, gamma-ray astronomy, radio astronomy, and so on.   Optical observatories operate both on the ground and in space (such as the Hubble Space Telescope).  Some, like HST, also have instruments sensitive to other wavelengths of light. However, there are also observatories dedicated to specific wavelength ranges, such as radio astronomy arrays. These instruments allow astronomers to create a picture of our universe that spans the entire electromagnetic spectrum, from low-energy radio signals,o ultra high-energy gamma rays. They give information about the evolution and physics of some of the most dynamic objects and processes in the universe, such as neutron stars,  black holes, gamma-ray bursts, and supernova explosions. These branches of astronomy work together to teach about the structure of the stars, planets, and galaxies.   Subfields of Astronomy There are so many types of objects that astronomers study, that it is convenient to break astronomy up into subfields of study. One area is called planetary astronomy, and researchers in this subfield focus their studies on planets, both within and outside our solar system, as well as objects like asteroids and comets.Solar astronomy is the study of the Sun. The scientists who are interested in learning how it changes, and to understand how these changes affect the Earth, are called solar physicists. They use both ground-based and space-based instruments to make nonstop studies of our star.  Stellar astronomy is the study of stars, including their creation, evolution, and deaths. Astronomers observe these objects across all wavelengths and apply the information to create physical models of the stars.Galactic astronomy focuses on the objects and processes at work in the Milky Way Galaxy. Its a very complex system of stars, nebulae, and dust. Astronomers study the motion and evolution of the Milky Way in order to learn how galaxies are formed.Beyond our galaxy lie countless others, and these are the focus of the discipline of extragalactic astronomy. Researchers study how galaxies move, form, break apart, merge, and change over time.  Cosmology  is the study of the origin, evolution, and structure of the universe in order to understand it. Cosmologists typically focus on the big picture and attempt to model what the universe would have looked like only moments after the Big Bang. Meet a Few Pioneers of Astronomy Over the centuries there have been countless innovators in astronomy, people who contributed to the development and advancement of the science. Today there are more than 11,000 trained astronomers in the world dedicated to the study of the cosmos. The most famous historical astronomers are those who made major discoveries that improved and expanded the science.   Nicolaus Copernicus  (1473 - 1543), was a Polish physician and lawyer by trade. His fascination with numbers and the study of the motions of celestial objects made him the so-called father of the current heliocentric model of the solar system. Tycho Brahe  (1546 - 1601) was a Danish nobleman who designed and built instruments to study the sky. These were not telescopes, but calculator-type machines that allowed him to chart the positions of planets and other celestial objects with such great precision. He hired  Johannes Kepler  (1571 - 1630), who started out as his student. Kepler continued Brahes work, and also made many discoveries of his own. He is credited with developing the  three laws of planetary motion. Galileo Galilei  (1564 - 1642) was the first to use a telescope to study the sky. He is sometimes credited (incorrectly) with being the creator of the telescope.  That honor probably belongs to Dutch optician Hans Lippershey.  Galileo made detailed studies of heavenly bodies. He was the first to conclude that the Moon was likely similar in composition to planet Earth and that the Sun’s surface changed (i.e., the motion of sunspots on the Sun’s surface). He was also the first to see four of Jupiter’s moons, and the phases of Venus. Ultimately it was his observations of the Milky Way, specifically the detection of countless stars, that shook the scientific community. Isaac Newton  (1642 - 1727) is considered one of the greatest scientific minds of all time. He not only deduced the law of gravity but realized the need for a new type of mathematics (calculus) to describe it. His discoveries and theories dictated the direction of science for more than 200 years  and truly ushered in the era of modern astronomy. Albert Einstein  (1879 - 1955), famous for his development of  general relativity, a correction to Newton’s  law of gravity. But, his relation of energy to mass (EMC2) is also important to astronomy, as it is the basis for which we understand how the Sun, and other stars, fuse hydrogen into helium to create energy. Edwin Hubble  (1889 - 1953) is the man who discovered the expanding universe. Hubble answered two of the biggest questions plaguing astronomers at the time. He determined that so-called spiral nebulae were, in fact, other galaxies, proving that the Universe extends well beyond our own galaxy. Hubble then followed up that discovery by showing that these other galaxies were receding at speeds proportional to their distances away from us. The Stephen Hawking  (1942 - 2018), one of the great modern scientists. Very few people have contributed more to the advancement of their fields than Stephen Hawking. His work significantly increased our  knowledge of black holes  and other exotic celestial objects. Also, and perhaps more importantly, Hawking made significant strides in advancing our understanding of the universe and its creation. Updated and edited by Carolyn Collins Petersen.

Wednesday, May 6, 2020

The Benefits and Risks of Outsourcing - 1269 Words

Out sourcing Development of specific skills: Out sourcing benefits the development of specific skills at a corporation level the same way off shoring does at a global level. Companies outsource in order to take advantage of specialized skills and knowledge that itself does not own or that can’t be efficiently acquired. In this case out sourcing leads to higher efficiency and better quality provided by third parties for a specific business processes. Moreover the third parties can further specialize to take advantage of the resulting economies of scale and mitigate the possible shortage of specific skilled and talented workers. Focus on core competencies: Similar to the effect on the third parties, out sourcing provides out-sourcing companies the opportunity to focus on specific business competencies in which they possess clear comparative advantage. Therefore resources and capitals are not used in tasks where the company does not possess comparative advantage, but are utilized at their full potential and highest efficiency in their core business processes. Labor flexibility: Out sourcing means that a company does not actually own or invest in the capital and resources required for that specific business process, but it acquires it from a third part. As a consequence, it posses the flexibility to increase or decrease the quantity of services or merchandise provided by the third party according to its needs, as long as it does not breach the contract. In extreme cases, theShow MoreRelatedThe Risk And Benefits Of Outsourcing Supply Chain And Risk Management Essay961 Words   |  4 Pages The Risk and Benefits of Outsourcing Supply Chain and Risk Management. How Boeing 787 Supply Chain Issues Affected Other Industries? 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The New York City Emergency Plan free essay sample

A paper which discusses the way the N.Y.C. Emergency plan should be revised after it was put to the test on September 11th. The paper shows that currently the New York City Emergency Plan is solid and has been tested and re-tested many times over. The World Trade Tower bombing of September, 11, 2002 put the plan to the ultimate test. The paper discusses that, overall, the emergency plan worked very well, considering the size and scope of the emergency. However, it also brought out some areas in need of improvement. The paper shows that the key issues which need to be addressed are the need for secondary and tertiary backup plans for the command control center and hospital scheme. Also, it shows that it has become painstakingly clear, that even though the plan is in place, when the actual emergency occurred, police officers and other key authority figures did not know where to tell the public where to go or what to do. We will write a custom essay sample on The New York City Emergency Plan or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The paper discusses the potential disasters N.Y.C. might face and the steps taken to plan for them. The theme of the program will be a simple question, What would you do? This question will be followed by a scenario involving a disaster. All ads will be designed to spark thoughts of the possibility of the occurrence suggested and evoke thoughts of what they would do if the same disaster struck right now. Information on certain disasters, such as hurricane and storm safety, fire safety, and other safety issues will be an integral part of this program. The ads are not supposed to invoke panic, but rather to alleviate it. Panic occurs when there is a lack of a plan of action. This advertising campaign is aimed at getting people to develop plans, where-ever they happen to be. People who have a plan do not panic as easily and will respond in a more efficient manner to unexpected events.

Wednesday, April 22, 2020

Racial Profiling Against Aboriginal People free essay sample

For the historical reason, First nation people seldom get involved in the white-dominated society. To begin with, many aboriginal people, especially in North Saskatchewan, live in the Indian reserves, which is far away from cities. In the reserve, native people have their own way of dealing with matters, and quite a few of them that do not fit the modern society standards. According to an exclusive Ipsos Reid poll conducted for Postmedia News More than four out of five Canadians don’t want more money sent to aboriginal reserves unless proper, independent audits are conducted to ensure financial accountability. Secondly, 30 percent of the aboriginal population are tax-exempt. In other words, first nation group make less contribution to the society than any other group do and get more rewards than any other race groups in Canada though aboriginal welfare system. Also, the contrary between the extremely low fee on the aboriginal students and the very limited amount of them are willing to receive higher education is very disturbing to many Canadians, therefore, it’s no surprise that many people are questioning is it wise for government to pay huge amount of taxpayer’s money on aboriginal education. We will write a custom essay sample on Racial Profiling Against Aboriginal People or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page What’s more, given certain Indian culture backgrounds, it seems like amongst all racial groups in Canada, First nation people are most likely to get involved in serious social problems, such as illegal Gambling, drug problem, female abusing and even the high suicide rate in aboriginal youth. In 2004-05, Aboriginal offenders represented 16. 2% of the total federal offender population and 20% of the provincial/territorial offender population, while Aboriginal adults accounted for only 2. % of the Canadian adult population in the last Canadian census(Tanya Rugge). Due to the overrepresentation within the criminal justice system, the stereotyped image of uneducated, violent aboriginal people is rooted in many people’s head even they often denying for being racists. Like Mrs. Wegner, the mother of one of the victims said in the documentary:† We are not valued as human being—we are Indians. †(Hubbard). Lastly, the authority structures failed to address raci al profiling effectively. In the documentary, RCMP did not hold a clean and full investigation on those two officers who were the top suspects of murdering Rodney Naistus and Lawrence Wegner, they ended up to serve 4 months sentence behind the bar, they almost gone scot-free. Even though in the movie, a new chief is hired and he meant to fix the relationships with aboriginals, but individual’s effort can’t fix the flaws in the whole criminal justice system, nor stopped another native man, Neil Stonechild, to die out of cold shortly after his meeting with aboriginal elderly. In a word, the racial profiling is seems to be inevitably, since the legal system produces and reproduces the essential character of law as a means f rationalizing, normalizing, and legitimizing social control on behalf of those who hold power and the interests they represent(Carol. Tator,Henry, Frances 2006) In conclusion, racial profiling leaves real and direct consequences to people who experiencing it. Isolating and distorting is no way near the solutions, only with joined efforts, we could forge an empowering future for both aboriginals and non-aboriginals people. Reference 1 â€Å"two worlds Colliding†, Tasha Hubbard . 10 February 2005 (Canada). 2 Michael Woods, â€Å"Majority of Canadians concerned about financial accountability on First Nations reserves: poll†. Postmedia News , 13/01/15. 3 Tanya, Rugge. lt;Risk assessment of male aboriginal offenders: A 2006 perspectivegt;. Public Safety and Emergency Preparedness Canada, 2006. 4 Carol,Tatoramp;Henryamp; Frances.? Racial Profiling in Canada: Challenging the Myth of a Few Bad Apples?. University of Toronto Press Incorporated 2006.

Monday, March 16, 2020

What Is Statistical Significance How Is It Calculated

What Is Statistical Significance How Is It Calculated SAT / ACT Prep Online Guides and Tips If you've ever read a wild headline like, "Study Shows Chewing Rocks Prevents Cancer," you've probably wondered how that could be possible. If you look closer at this type of article you may find that the sample size for the study was a mere handful of people. If one person in a group of five chewed rocks and didn't get cancer, does that mean chewing rocks prevented cancer? Definitely not. The study for such a conclusion doesn't have statistical significance- though the study was performed, its conclusions don't really mean anything because the sample size was small. So what is statistical significance, and how do you calculate it? In this article, we'll cover what it is, when it's used, and go step-by-step through the process of determining if an experiment is statistically significant on your own. What Is Statistical Significance? As I mentioned above, the fake study about chewing rocks isn't statistically significant. What that means is that the conclusion reached in it isn't valid, because there's not enough evidence that what happened was not random chance. A statistically significant result would be one where, after rigorous testing, you reach a certain degree of confidence in the results. We call that degree of confidence our confidence level, which demonstrates how sure we are that our data was not skewed by random chance. More specifically, the confidence level is the likelihood that an interval will contain values for the parameter we're testing. There are three major ways of determining statistical significance: If you run an experiment and your p-value is less than your alpha (significance) level, your test is statistically significant If your confidence interval doesn't contain your null hypothesis value, your test is statistically significant If your p-value is less than your alpha, your confidence interval will not contain your null hypothesis value, and will therefore be statistically significant This info probably doesn't make a whole lot of sense if you're not already acquainted with the terms involved in calculating statistical significance, so let's take a look at what it means in practice. Say, for example, that we want to determine the average typing speed of 12-year-olds in America. We'll confirm our results using the second method, our confidence interval, as it's the simplest to explain quickly. First, we'll need to set our p-value, which tells us the probability of our results being at least as extreme as they were in our sample data if our null hypothesis (a statement that there is no difference between tested information), such as that all 12-year-old students type at the same speed) is true. A typical p-value is 5 percent, or 0.05, which is appropriate for many situations but can be adjusted for more sensitive experiments, such as in building airplanes. For our experiment, 5 percent is fine. If our p-value is 5 percent, our confidence level is 95 percent- it's always the inverse of your p-value. Our confidence level expresses how sure we are that, if we were to repeat our experiment with another sample, we would get the same averages- it is not a representation of the likelihood that the entire population will fall within this range. Testing the typing speed of every 12-year-old in America is unfeasible, so we'll take a sample- 100 12-year-olds from a variety of places and backgrounds within the US. Once we average all that data, we determine the average typing speed of our sample is 45 words per minute, with a standard deviation of five words per minute. From there, we can extrapolate that the average typing speed of 12-year-olds in America is somewhere between $45 - 5z$ words per minute and $45 + 5z$ words per minute. That's our confidence interval- a range of numbers we can be confident contain our true value, in this case the real average of the typing speed of 12-year-old Americans. Our z-score, ‘z,' is determined by our confidence value. In our case, given our confidence value, that would look like $45 - 5(1.96)$ and $45 + 5(1.96)$, making our confidence interval 35.2 to 54.8. A wider confidence interval, say with a standard deviation of 15 words per minute, would give us more confidence that the true average of the entire population would fall in that range ($45Â ± \bo{15}(1.96)$), but would be less accurate. More importantly for our purposes, if your confidence interval doesn't include the null hypothesis, your result is statistically significant. Since our results demonstrate that not all 12-year-olds type the same speed, our results are significant. One reason you might set your confidence rating lower is if you are concerned about sampling errors. A sampling error, which is a common cause for skewed data, is what happens when your study is based on flawed data. For example, if you polled a group of people at McDonald's about their favorite foods, you'd probably get a good amount of people saying hamburgers. If you polled the people at a vegan restaurant, you'd be unlikely to get the same results, so if your conclusion from the first study is that most peoples' favorite food is hamburgers, you're relying on a sampling error. It's important to remember that statistical significance is not necessarily a guarantee that something is objectively true. Statistical significance can be strong or weak, and researchers can factor in bias or variances to figure out how valid the conclusion is. Any rigorous study will have numerous phases of testing- one person chewing rocks and not getting cancer is not a rigorous study. Essentially, statistical significance tells you that your hypothesis has basis and is worth studying further. For example, say you have a suspicion that a quarter might be weighted unevenly. If you flip it 100 times and get 75 heads and 25 tails, that might suggest that the coin is rigged. That result, which deviates from expectations by over 5 percent, is statistically significant. Because each coin flip has a 50/50 chance of being heads or tails, these results would tell you to look deeper into it, not that your coin is definitely rigged to flip heads over tails. The results are statistically significant in that there is a clear tendency to flip heads over tails, but that itself is not an indication that the coin is flawed. What Is Statistical Significance Used For? Statistical significance is important in a variety of fields- any time you need to test whether something is effective, statistical significance plays a role. This can be very simple, like determining whether the dice produced for a tabletop role-playing game are well-balanced, or it can be very complex, like determining whether a new medicine that sometimes causes an unpleasant side effect is still worth releasing. Statistical significance is also frequently used in business to determine whether one thing is more effective than another. This is called A/B testing- two variants, one A and one B, are tested to see which is more successful. In school, you're most likely to learn about statistical significance in a science or statistics context, but it can be applied in a great number of fields. Any time you need to determine whether something is demonstrably true or just up to chance, you can use statistical significance! How to Calculate Statistical Significance Calculating statistical significance is complex- most people use calculators rather than try to solve equations by hand. Z-test calculators and t-test calculators are two ways you can drastically slim down the amount of work you have to do. However, learning how to calculate statistical significance by hand is a great way to ensure you really understand how each piece works. Let's go through the process step by step! Step 1: Set a Null Hypothesis To set up calculating statistical significance, first designate your null hypothesis, or H0. Your null hypothesis should state that there is no difference between your data sets. For example, let's say we're testing the effectiveness of a fertilizer by taking half of a group of 20 plants and treating half of them with fertilizer. Our null hypothesis will be something like, "This fertilizer will have no effect on the plant's growth." Step 2: Set an Alternative Hypothesis Next, you need an alternative hypothesis, Ha. Your alternative hypothesis is generally the opposite of your null hypothesis, so in this case it would be something like, "This fertilizer will cause the plants who get treated with it to grow faster." Step 3: Determine Your Alpha Third, you'll want to set the significance level, also known as alpha, or ÃŽ ±. The alpha is the probability of rejecting a null hypothesis when that hypothesis is true. In the case of our fertilizer example, the alpha is the probability of concluding that the fertilizer does make plants treated with it grow more when the fertilizer does not actually have an effect. An alpha of 0.05, or 5 percent, is standard, but if you're running a particularly sensitive experiment, such as testing a medicine or building an airplane, 0.01 may be more appropriate. For our fertilizer experiment, a 0.05 alpha is fine. Your confidence level is $1 - ÃŽ ±(100%)$, so if your alpha is 0.05, that makes your confidence level 95%. Again, your alpha can be changed depending on the sensitivity of the experiment, but most will use 0.05. Step 4: One- or Two-Tailed Test Fourth, you'll need to decide whether a one- or two-tailed test is more appropriate. One-tailed tests examine the relationship between two things in one direction, such as if the fertilizer makes the plant grow. A two-tailed test measures in two directions, such as if the fertilizer makes the plant grow or shrink. Since in our example we don't want to know if the plant shrinks, we'd choose a one-tailed test. But if we were testing something more complex, like whether a particular ad placement made customers more likely to click on it or less likely to click on it, a two-tailed test would be more appropriate. A two-tailed test is also appropriate if you're not sure which direction the results will go, just that you think there will be an effect. For example, if you wanted to test whether or not adding salt to boiling water while making pasta made a difference to taste, but weren't sure if it would have a positive or negative effect, you'd probably want to go with a two-tailed test. Step 5: Sample Size Next, determine your sample size. To do so, you'll conduct a power analysis, which gives you the probability of seeing your hypothesis demonstrated given a particular sample size. Statistical power tells us the probability of us accepting an alternative, true hypothesis over the null hypothesis. A higher statistical power gives lowers our probability of getting a false negative response for our experiment. In the case of our fertilizer experiment, a higher statistical power means that we will be less likely to accept that there is no effect from fertilizer when there is, in fact, an effect. A power analysis consists of four major pieces: The effect size, which tells us the magnitude of a result within the population The sample size, which tells us how many observations we have within the sample The significance level, which is our alpha The statistical power, which is the probability that we accept an alternative hypothesis if it is true Many experiments are run with a typical power, or ÃŽ ², of 80 percent. Because these calculations are complex, it's not recommended to try to calculate them by hand- instead, most people will use a calculator like this one to figure out their sample size. Conducting a power analysis lets you know how big of a sample size you'll need to determine statistical significance. If you only test on a handful of samples, you may end up with a result that's inaccurate- it may give you a false positive or a false negative. Doing an accurate power analysis helps ensure that your results are legitimate. Step 6: Find Standard Deviation Sixth, you'll be calculating the standard deviation, $s$ (also sometimes written as $ÏÆ'$). This is where the formula gets particularly complex, as this tells you how spread out your data is. The formula for standard deviation of a sample is: $$s = √{{∑(x_i – Â µ)^2}/(N – 1)}$$ In this equation, $s$ is the standard deviation $∑$ tells you to sum all the data you collected $x_i$ is each individual data $Â µ$ is the mean of your data for each group $N$ is your total sample So, to work this out, let's go with our preliminary fertilizer test on ten plants, which might give us data something like this: Plant Growth (inches) 1 2 2 1 3 4 4 5 5 3 6 1 7 5 8 4 9 4 10 4 We need to average that data, so we add it all together and divide by the total sample number. $(2 + 1 + 4 + 5 + 3 + 1 + 5 + 4 + 4 + 4) / 10 = 3.3$ Next, we subtract each sample from the average $(x_i – Â µ)$, which will look like this: Plant Growth (inches) $x_i – Â µ$ 1 2 1.3 2 1 2.3 3 4 -0.7 4 5 -1.7 5 3 0.3 6 1 2.3 7 5 -1.7 8 4 -0.7 9 4 -0.7 10 4 -0.7 Now we square all of those numbers and add them together. $1.32 + 2.32 + -0.72 + -1.72 + 0.32 + 2.32 + -1.72 + -0.72 + -0.72 + -0.72 = 20.1$ Next, we'll divide that number by the total sample number, N, minus 1. $20.1/9 = 2.23$ And finally, to find the standard deviation, we'll take the square root of that number. $√2.23=1.4933184523$ But that's not the end. We also need to calculate the variance between sample groups, if we have more than one sample group. In our case, let's say that we did a second experiment where we didn't add fertilizer so we could see what the growth looked like on its own, and these were our results: Plant Growth (inches) 1 1 2 1 3 2 4 1 5 3 6 1 7 1 8 2 9 1 10 1 So let's run through the standard deviation calculation again. #1: Average Data $1 + 1 + 2+ 1 + 3 + 1 + 1 + 2 + 1 + 1 = 14$ $14/10 = 1.4$ #2: Subtract each sample from the average $(x_i – Â µ)$. $0.4 + 0.4 + (-0.4) + 0.4 + (-1.6) + 0.4 + 0.4 + (-0.4) + 0.4 + 0.4 = 0.4$ #3: Divide the last number by the total sample number, N, minus 1. $0.4/9=0.0444$ #4: Take the square root of the previous number. $√0.0444 = 0.2107130751$ Step 7: Run Standard Error Formula Okay, now we have our two standard deviations (one for the group with fertilizer, one for the group without). Next, we need to run through the standard error formula, which is: $$s_d = √((s_1/N_1) + (s_2/N_2))$$ In this equation: $s_d$ is the standard error $s_1$ is the standard deviation of group one $N_1$ is the sample size of group one $s_2$ is the standard deviation of group two $N_2$ is the sample size of group two So let's work through this. First, let's figure out $s_1/N_1$. With our numbers, that becomes $1.4933184523/10$, or 0.14933184523. Next, let's do $s_2/N_2$. With our numbers, that becomes $0.2107130751/10$, or 0.02107130751. Next, we need to add those two numbers together. $0.14933184523 + 0.02107130751 = 0.17040315274$ And finally, we'll take the square root: $√0.17040315274 = 0.41279916756$ So our standard error $s_d$, is 0.41279916756. Step 8: Find t-Score But we're still not done! Now you're probably seeing why most people use a calculator for this. Next up: t-score. Your t-score is what allows you to compare your data to other data, which tells you the probability of the two groups being significantly different. The formula for t-score is $$t = (Â µ_1 – Â µ_2)/s_d$$ where: $t$ is the t-score $Â µ_1$ is the average of group one $Â µ_2$ is the average of group two $s_d$ is the standard error So for our numbers, this equation would look like: $t = (3.3 - 1.4)/0.41279916756$ $t = 4.60272246001$ Step 9: Find Degrees of Freedom We're almost there! Next, we'll find our degrees of freedom ($df$), which tells you how many values in a calculation can vary acceptably. To calculate this, we add the number of samples in each group and subtract two. In our case, that looks like this: $$(10 + 10) - 2 = 18$$ Step 10: Use a T-Table to Find Statistical Significance And now we'll use a t-table to figure out whether our conclusions are significant. To use the t-table, we first look on the left-hand side for our $df$, which in this case is 18. Next, scan along that row of variances until you find ours, which we'll round to 4.603. Whoa! We're off the chart! Scan upward until you see the p-values at the top of the chart and you'll find that our p-value is something smaller than 0.0005, which is well below our significance level. So is our study on whether our fertilizer makes plants grow taller valid? The final stage of determining statistical significance is comparing your p-value to your alpha. In this case, our alpha is 0.05, and our p-value is well below 0.05. Since one of the methods of determining statistical significance is to demonstrate that your p-value is less than your alpha level, we've succeeded! The data seems to suggest that our fertilizer does make plants grow, and with a p-value of 0.0005 at a significance level of 0.05, it's definitely significant! Now, if we're doing a rigorous study, we should test again on a larger scale to verify that the results can be replicated and that there weren't any other variables at work to make the plants taller. Tools to Use For Statistical Significance Calculators make calculating statistical significance a lot easier. Most people will do their calculations this way instead of by hand, as doing them without tools is more likely to introduce errors in an already sensitive process. To get you started, here are some calculators you can use to make your work simpler: How to Calculate T-Score on a TI-83 Find Sample Size and Confidence Interval T-Test Calculator T-Test Formula for Excel Find P-Value with Excel What's Next? Need to brush up on AP Stats? These free AP Statistics practice tests are exactly what you need! If you're struggling with statistics on the SAT Math section, check out this guide to strategies for mean, median, and mode! This formula sheet for AP Statistics covers all the formulas you'll need to know for a great score on your AP test!