Pdf Worksheet On What Conclusions Can And Cannot Be Drawn From Statistics

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Descriptive statistics generally characterizes or describes a set of data elements by graphically displaying the information or describing its central tendancies and how it is distributed. Inferential statistics tries to infer information about a population by using information gathered by sampling.

Most of this book, as is the case with most statistics books, is concerned with statistical inference , meaning the practice of drawing conclusions about a population by using statistics calculated on a sample. However, another type of statistics is the concern of this chapter: descriptive statistics , meaning the use of statistical and graphic techniques to present information about the data set being studied. Nearly everyone involved in statistical work works with both types of statistics, and often, computing descriptive statistics is a preliminary step in what will ultimately be an inferential statistical analysis. In particular, it is a common practice to begin an analysis by examining graphical displays of a data set and to compute some basic descriptive statistics to get a better sense of the data to be analyzed.

Chapter 9: Determining Conclusions and Recommendations

Statistics , when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.

The false statistics trap can be quite damaging for the quest for knowledge. For example, in medical science, correcting a falsehood may take decades and cost lives. Misuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods, even if they are careful to check everything.

Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests. One usable definition is: "Misuse of Statistics: Using numbers in such a manner that — either by intent or through ignorance or carelessness — the conclusions are unjustified or incorrect. The term is not commonly encountered in statistics texts and no authoritative definition is known. It is a generalization of lying with statistics which was richly described by examples from statisticians 60 years ago.

The definition confronts some problems some are addressed by the source : [2]. How to Lie with Statistics acknowledges that statistics can legitimately take many forms. Whether the statistics show that a product is "light and economical" or "flimsy and cheap" can be debated whatever the numbers. Some object to the substitution of statistical correctness for moral leadership for example as an objective. Assigning blame for misuses is often difficult because scientists, pollsters, statisticians and reporters are often employees or consultants.

An insidious misuse? The poor state of public statistical literacy and the non-statistical nature of human intuition permits misleading without explicitly producing faulty conclusions.

The definition is weak on the responsibility of the consumer of statistics. A historian listed over fallacies in a dozen categories including those of generalization and those of causation.

Many of the fallacies could be coupled to statistical analysis, allowing the possibility of a false conclusion flowing from a blameless statistical analysis. An example use of statistics is in the analysis of medical research.

The report is summarized by the popular press and by advertisers. Misuses of statistics can result from problems at any step in the process. The statistical standards ideally imposed on the scientific report are much different than those imposed on the popular press and advertisers; however, cases exist of advertising disguised as science.

The definition of the misuse of statistics is weak on the required completeness of statistical reporting. The opinion is expressed that newspapers must provide at least the source for the statistics reported. This tactic becomes more effective the more studies there are available. Organizations that do not publish every study they carry out, such as tobacco companies denying a link between smoking and cancer, anti-smoking advocacy groups and media outlets trying to prove a link between smoking and various ailments, or miracle pill vendors, are likely to use this tactic.

Ronald Fisher considered this issue in his famous lady tasting tea example experiment from his book, The Design of Experiments. Regarding repeated experiments he said, "It would clearly be illegitimate, and would rob our calculation of its basis, if unsuccessful results were not all brought into the account.

Another term related to this concept is cherry picking. If too few of these features are chosen for analysis for example, if just one feature is chosen and simple linear regression is performed instead of multiple linear regression , the results can be misleading. This leaves the analyst vulnerable to any of various statistical paradoxes , or in some not all cases false causality as below. The answers to surveys can often be manipulated by wording the question in such a way as to induce a prevalence towards a certain answer from the respondent.

For example, in polling support for a war, the questions:. A better way of wording the question could be "Do you support the current US military action abroad? Another way to do this is to precede the question by information that supports the "desired" answer. For example, more people will likely answer "yes" to the question "Given the increasing burden of taxes on middle-class families, do you support cuts in income tax?

The proper formulation of questions can be very subtle. The responses to two questions can vary dramatically depending on the order in which they are asked. Overgeneralization is a fallacy occurring when a statistic about a particular population is asserted to hold among members of a group for which the original population is not a representative sample.

The assertion "All apples are red" would be an instance of overgeneralization because the original statistic was true only of a specific subset of apples those in summer , which is not expected to be representative of the population of apples as a whole. A real-world example of the overgeneralization fallacy can be observed as an artifact of modern polling techniques, which prohibit calling cell phones for over-the-phone political polls.

As young people are more likely than other demographic groups to lack a conventional "landline" phone, a telephone poll that exclusively surveys responders of calls landline phones, may cause the poll results to undersample the views of young people, if no other measures are taken to account for this skewing of the sampling. Thus, a poll examining the voting preferences of young people using this technique may not be a perfectly accurate representation of young peoples' true voting preferences as a whole without overgeneralizing, because the sample used excludes young people that carry only cell phones, who may or may not have voting preferences that differ from the rest of the population.

Overgeneralization often occurs when information is passed through nontechnical sources, in particular mass media. Scientists have learned at great cost that gathering good experimental data for statistical analysis is difficult. Example: The placebo effect mind over body is very powerful. Statisticians typically worry more about the validity of the data than the analysis. This is reflected in a field of study within statistics known as the design of experiments. Pollsters have learned at great cost that gathering good survey data for statistical analysis is difficult.

The selective effect of cellular telephones on data collection discussed in the Overgeneralization section is one potential example; If young people with traditional telephones are not representative, the sample can be biased. Sample surveys have many pitfalls and require great care in execution. The simple random sample of the population "isn't simple and may not be random.

If a research team wants to know how million people feel about a certain topic, it would be impractical to ask all of them. However, if the team picks a random sample of about people, they can be fairly certain that the results given by this group are representative of what the larger group would have said if they had all been asked.

This confidence can actually be quantified by the central limit theorem and other mathematical results. Confidence is expressed as a probability of the true result for the larger group being within a certain range of the estimate the figure for the smaller group. This is the "plus or minus" figure often quoted for statistical surveys. The two numbers are related. This is not mathematically correct. Many people may not realize that the randomness of the sample is very important.

In practice, many opinion polls are conducted by phone, which distorts the sample in several ways, including exclusion of people who do not have phones, favoring the inclusion of people who have more than one phone, favoring the inclusion of people who are willing to participate in a phone survey over those who refuse, etc.

Non-random sampling makes the estimated error unreliable. On the other hand, people may consider that statistics are inherently unreliable because not everybody is called, or because they themselves are never polled. People may think that it is impossible to get data on the opinion of dozens of millions of people by just polling a few thousands. This is also inaccurate. However, often only one margin of error is reported for a survey. When results are reported for population subgroups, a larger margin of error will apply, but this may not be made clear.

For example, a survey of people may contain people from a certain ethnic or economic group. The results focusing on that group will be much less reliable than results for the full population.

When a statistical test shows a correlation between A and B, there are usually six possibilities:. The sixth possibility can be quantified by statistical tests that can calculate the probability that the correlation observed would be as large as it is just by chance if, in fact, there is no relationship between the variables. However, even if that possibility has a small probability, there are still the five others. If the number of people buying ice cream at the beach is statistically related to the number of people who drown at the beach, then nobody would claim ice cream causes drowning because it's obvious that it isn't so.

In this case, both drowning and ice cream buying are clearly related by a third factor: the number of people at the beach. This fallacy can be used, for example, to prove that exposure to a chemical causes cancer. Replace "number of people buying ice cream" with "number of people exposed to chemical X", and "number of people who drown" with "number of people who get cancer", and many people will believe you.

In such a situation, there may be a statistical correlation even if there is no real effect. For example, if there is a perception that a chemical site is "dangerous" even if it really isn't property values in the area will decrease, which will entice more low-income families to move to that area. If low-income families are more likely to get cancer than high-income families due to a poorer diet, for example, or less access to medical care then rates of cancer will go up, even though the chemical itself is not dangerous.

It is believed [22] that this is exactly what happened with some of the early studies showing a link between EMF electromagnetic fields from power lines and cancer. In well-designed studies, the effect of false causality can be eliminated by assigning some people into a "treatment group" and some people into a "control group" at random, and giving the treatment group the treatment and not giving the control group the treatment.

In the above example, a researcher might expose one group of people to chemical X and leave a second group unexposed. If the first group had higher cancer rates, the researcher knows that there is no third factor that affected whether a person was exposed because he controlled who was exposed or not, and he assigned people to the exposed and non-exposed groups at random.

However, in many applications, actually doing an experiment in this way is either prohibitively expensive, infeasible, unethical, illegal, or downright impossible. For example, it is highly unlikely that an IRB would accept an experiment that involved intentionally exposing people to a dangerous substance in order to test its toxicity. The obvious ethical implications of such types of experiments limit researchers' ability to empirically test causation.

If, for example, a tobacco producer wishes to demonstrate that its products are safe, it can easily conduct a test with a small sample of smokers versus a small sample of non-smokers. This can—using the judicial analogue above—be compared with the truly guilty defendant who is released just because the proof is not enough for a guilty verdict. This does not prove the defendant's innocence, but only that there is not proof enough for a guilty verdict.

Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis. Statistical significance is a measure of probability; practical significance is a measure of effect. The cure is practically significant when a hat is no longer required in cold weather and the barber asks how much to take off the top.

The bald want a cure that is both statistically and practically significant; It will probably work and if it does, it will have a big hairy effect. Scientific publication often requires only statistical significance.

Drawing conclusions definition in spanish

Days 4 and 5 of the Unit, Days 2 and 3 of this lesson 1. Pause to define the target word in context. He then took off his dusty overalls. Each worksheet also includes a cross-curricular focus on earth science. Inference definition, the act or process of inferring.

Scientific Method Practice Worksheet Pdf

Click here to bypass the following discussion and go straight to the assignments. Logic is the science that evaluates arguments. An argument is a group of statements including one or more premises and one and only one conclusion.

Communicating your conclusions and recommendations i. Throughout the public health assessment process, you are synthesizing information that will support and enable you to draw public health conclusions. In addition, you are identifying public health actions that might be needed to eliminate or prevent exposures, or you are identifying critical data gaps. This chapter describes the process by which you, with the input of the site team, take the findings of exposure and health effects evaluations and draw conclusions regarding the degree of public health hazard, if any, posed by the exposure situations you have studied at a site Section 9.

Statistics has become the universal language of the sciences, and data analysis can lead to powerful results. As scientists, researchers, and managers working in the natural resources sector, we all rely on statistical analysis to help us answer the questions that arise in the populations we manage. For example:. These are typical questions that require statistical analysis for the answers.

1.E: Sampling and Data (Exercises)

Satta king chart august Welcome! Essential Skills and Concepts: q Know that what is read needs to make sense q Identify details and examples q Draw inferences From Longman Dictionary of Contemporary English draw a conclusion draw a conclusion TRUE to decide that a particular fact or principle is true according to the information you have been given draw a conclusion from It would be unwise to draw firm conclusions from the results of a single survey. Subscribe today.

Statistics in a Nutshell, 2nd Edition by Sarah Boslaugh

These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax. For each of the following eight exercises, identify: a. Give examples where appropriate. A fitness center is interested in the mean amount of time a client exercises in the center each week. A cardiologist is interested in the mean recovery period of her patients who have had heart attacks. Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

Read with purpose and meaning. Drawing conclusions refers to information that is implied or inferred. This means that the information is never clearly stated. Writers often tell you more than they say directly.

The Problem Solving and Data Analysis questions on the SAT Math. Test assess your to analyze and draw conclusions about the given information. These (​although you will not be asked to calculate a standard deviation). provided on the answer sheet.) The first it cannot be accurately interpreted in this context.

Applied Statistics - Lesson 1

Statistics , when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy. The false statistics trap can be quite damaging for the quest for knowledge.

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3 Response
  1. Doreen N.

    When sample data are collected using an inappropriate method, the data cannot be used to draw conclusions about the population. (You will learn more about.

  2. Lourdes B.

    ples of how statistics can be used in various occupations. and draw conclusions from data. Students study and cell phones, so they cannot be surveyed. Finally The name of the worksheet will change from Worksheet 1*** to. MyData.

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