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Factors for Data Analysis: Margin of Error and Null Hypothesis

Paper Type: Free Essay Subject: Data Analysis
Wordcount: 1893 words Published: 8th Feb 2020

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1.  What does the margin of error tell us about a sample taken from a large population?  How does the confidence level for a sample outcome differ from the sample’s margin of error?

First, the margins of error and sample size are considered an inverse relationship (Rumsey, n.d.).  Second, increasing the sample size furthermore than what you already may have will give you a reduced return since the increases accuracy will be negligible (Rumsey, n.d.).

A notion, indispensable in estimating the chances that a sample is accurate is considered the margin of error (Carey, 2011).  The population is defined as the average value of a variable, where the reference class is a population interest, and the sample can be defined as the same; however, the reference class is a sample from the population.  When taking samples from a larger population one must keep in mind that the larger the population, the greater the chances the results took will be accurate (Carey, 2011).  In lamest terms, the margin of error decreases and as the sample size increases (Carey, 2011).  The aforementioned relationship is called an inverse because both, the margin of error and sample size, move in opposite directions.

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The population is gauged by two important statistics, the margin of error and confidence level.  The confidence level can be defined as the percentage of all samples, which can be expected to include the true population parameter or in lamest terms, how confident we are in a given margin of error.  Both margins of error and confidence level are closely related.  Both depend on the sample size and not the population size.  As known, with the increase of the sample size, the margin of error decreases.  However, as the population increases, the margin of error increases as well.  Lastly, as the confidence level increases so does the margin or error increases.

2.  What is a null hypothesis in causal research and what does it mean to say a study has failed to reject the null hypothesis?

A hypothesis is defined as a theory or speculation, which is based on insufficient evidence that lends it to further experimentation and testing (Gonzalez, n.d.).  However, the null hypothesis can be defined as a hypothesis, which says there is no statistical significance between the two variables in the hypothesis (Gonzalez, n.d.).  The following are a couple of examples of the null hypothesis.  Question: do teens access the Internet more than adults using a cellular phone?  Null hypothesis: age, teens or adults, has zero effect when a cellular phone is used to access the Internet.  Question:  does taking a daily dose of aspirin to reduce your chances of a heart attack?  Null hypothesis: taking a daily dose of aspirin does not reduce your chances of a heart attack.

However, in causal research, unable to establish a causal link is often seen as a failure to reject the null hypothesis.  Furthermore, an experiment, which establishes a successful large enough difference in levels of effect between control and experimental groups, will often be said to reject the null hypothesis (Carey, 2011).  With the aforementioned stated there must be null and alternative hypotheses.  If it is concluded, during the experimentation and testing, that a null hypothesis is rejected; then we must be inclined to accept the alternative hypothesis (Taylor, 2018).  However, if the null hypothesis were not rejected, then we would say that we accept the null hypothesis (Taylor, 2018).

In a nutshell, researchers are attempting to provide enough evidence to prove and accept the alternative hypothesis, not the null hypothesis (Taylor, 2018).  The null hypothesis is considered to be a true statement until evidence proves otherwise (Taylor, 2018).

3.  How do randomized, prospective and retrospective studies differ from one another?  What are the major advantages and disadvantages of each type of study?

As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) randomized causal studies can be explained as a selection of subjects, dividing the selected into two groups, and administering the suspected causal agent to the selected subjects of one of the two groups.  One advantage of randomized causal studies is that they are capable of providing strong evidence because it enables us to control other potential causal factors.  Another advantage is that subjects are chosen prior to being exposed to the suspected cause, combined with being indiscriminately divided into control and experimental groups.  The aforementioned allows controlling for extraneous cause factors.  However, one of the biggest disadvantages of randomized causal studies is that they tend to be time consuming and expensive.

As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) prospective causal studies can be explained as two groups of subjects, one that is the experimental group and already has the suspected causal factor while the other group does not.  A huge advantage of prospective causal studies versus the abovementioned study is that they require less direct manipulations of the experimental subjects, therefore, are considered easier and less expensive to conduct.  Furthermore, they provide the most accurate analysis of the effect (Why randomize?” n.d.) A downfall of prospective causal study is although if properly conducted it can indicate a strong causal link; however, the link would not be as strong as what a randomized causal study would provide.

As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) retrospective causal studies can be explained as a beginning with two groups, control, and experimental groups; however, both are comprised of subjects who do and do not have the effect in question.  Advantages of retrospective causal studies are similar to randomized causal studies in which they can be conducted fairly quickly and inexpensive.  A few limitations of retrospective causal studies are they provide no way of estimating the level of differences of the effect being experimented.  Furthermore, retrospective causal studies provide weak evidence of a causal link.

4.  Describe each of the fallacies listed below and make up an example of each.

a) False anomalies: As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) false anomalies are defined as omitting facts intentionally, which would show how something is not as bizarre as it may seem.   For example, many of the conspiratorial theories, which surrounded the events of September 11, 2001, were considered false anomalies (Carey, 2011).  One of the events, which could not be explained as many people felt as if a plane did not crash into the Pentagon due to the fact of little wreckage; however, an American Airlines fuselage was located in the front lawn of the Pentagon.

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b) Questionable arguments by elimination: As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) questionable arguments by elimination is defined as having one true alternative by eliminating the possibility of the other alternative, which may be false.  An example of this is telepathy.  Case studies in the past have shown people to somehow receive unexplained messages from one person to another.  Although telepathy may not be the scientific answer other explanations are far-fetched and are eliminated.

c) Illicit causal inference: As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) illicit casual inference is defined as saying one thing caused another when there is clearly only a correlation.  For example, students who sit in the front of the class tend to get better grades than those who sit in the back of the class; however, the answer might just be that students who sit in front of the class are more motivated to do better than those who sit in the back of the class (Carey, 2011).

d) Unsupported analogies and similarities: As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) are defined as showing similarities between one speculative theory and a different well-established theory in science.  An example of this would be luminiferous ether.  Physicists hypothesized of certain similarities between light and sound; however, after much experimentation, they were able to conclude there was no there were no such similarities thus establishing light as a well-understood phenomenon (Carey, 2011).

e) Untestable explanations and predictions: As mentioned in A Beginner’s Guide to Scientific Method (Carey, 2011) untestable explanations is defined as presenting a theory, which by definition alone, cannot be tested.  Furthermore, untestable predictions can be seen as providing a prediction, which cannot be tested or explained.  Predictions should be testable, allowing the prediction to either be verified or invalidated (Brennan, 2017). 

f) Empty jargon can be defined as a phrase or word, which changes or loses its meaning when used with people who do not understand the meaning of the phrase or word used.  An example of empty jargon can be seen at the hospital.  Doctors and nurses use of medical jargon to explain an issue their patient may be having is sometimes more confusing rather than telling their patient they have the flu or a simple cold.


  • Brennan, J. (2017). What is a testable prediction? Sciencing. Retrieved from
    • https://sciencing.com/testable-prediction-8646215.html
  • Carey, S. S. (2011). A beginner’s guide to scientific method (4th ed.). Boston, MA: Wadsworth, Cengage Learning.
  • Gonzales, K. (n.d.). What is a null hypothesis? Study. Retrieved on October 12, 2018 from https://study.com/academy/lesson/what-is-a-null-hypothesis-definition-examples.html
  • Rumsey, D. (n.d.) How sample size affects the margin of error. Dummies. Retrieved on October 12, 2018 from https://www.dummies.com/education/math/statistics/how-sample-size affects-the-margin-of-error/
  • Taylor, C. (2018). Why say “fail to reject” in a hypothesis test? Thought Co. Retrieved from https://www.thoughtco.com/fail-to-reject-in-a-hypothesis-test-3126424
  • Why randomize? (n.d.). Yale University. Retrieved on October 10, 2018 from https://isps.yale.edu/node/16697


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