01:960:401 Lecture Notes - Lecture 2: Standard Deviation, Becquerel, Contingency Table
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Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.
The students receive the following arithmetic test scores:
Ā | Cola | Black Tea | Coffee | Ā |
Caffeine Content (mg/oz) | 2.9 | 5.9 | 13.4 | Ā |
Ā | 85 | 85 | 92 | āX2 = 147,641 |
Ā | 86 | 89 | 87 | G = 1,755 |
Ā | 82 | 82 | 80 | N = 21 |
Ā | 75 | 75 | 89 | k = 3 |
Ā | 66 | 88 | 96 | Ā |
Ā | 78 | 76 | 83 | Ā |
Ā | 87 | 82 | 92 | Ā |
Ā | T1 = 559 | T2 = 559 | T3 = 559 | Ā |
Ā | SS1 = 338.86 | SS2 = 338.86 | SS3 = 338.86 | Ā |
Ā | n1 = 7 | n2 = 7 | n3 = 7 | Ā |
Ā | M1 = 79.8571 | M2 = 79.8571 | M3 = 79.8571 | Ā |
1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?
(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.
(b) The population mean test scores for all three treatments are equal.
(c) The population mean test scores for all three treatments are different.
(d) The population mean test scores for all three treatments are not all equal.
Ā
2.) Calculate the degrees of freedom and the variances for the following ANOVA table:
Source | SS | df | MS |
Between | - | - | - |
Within | 702.28 | - | - |
Total | 973.14 | - | Ā |
Ā
The formula for the F-ratio is:
Ā
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3.) Using words, the formula of the F-ratio can be written as:
Ā
Ā
4.) Using the data from the ANOVA table given, the F-ratio can be written as:
Ā
5.) Calculate for F-ratio:
Ā
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6.)Ā At the level of significance, what is your conclusion?
(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.
(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.
(d)You can reject the null hypothesis; caffeine does appear to affect test performance.
The Scientific Method
For any controlled scientific study, a scientist starts with an observation, does some research to develop a hypothesis, and then designs an experiment that compares some baseline group with a test group. Data are then collected to confirm or refute the hypothesis.
As you review the following study, consider whether the researchers correctly followed the scientific method.
In the late 1990s, gastroenterologist Andrew Wakefield, along with a research team, set out to determine if bowel disease caused by vaccines led to autism.
He compiled a group of 12 children who had loss of acquired skills, developmental delays in language, diarrhea, and abdominal pain-essentially, those with both bowel disease and autism. He questioned each parent about the behavior and personality of the child before the child was vaccinated with the Measles, Mumps, and Rubella (MMR) vaccine. He then ran tests on the children to determine the health of the gastrointestinal tract, brain, and nervous system.
His reported data (tabulated below) included that children experienced either gastrointestinal or autism-like symptoms, sometimes within a short period after being vaccinated. From these data, the researchers concluded that there was no link between autism and the MMR vaccine. Wakefield though, contradicted this conclusion and stated that the vaccine caused changes in the gastrointestinal tract of the children, which then led to autism (Wakefield, et al., 1998). Currently, he still contends that the MMR vaccine contributes to autism (Ziv, 2015).
Many researchers tried to duplicate this study and could not replicate Wakefield's results. In fact, they found no link between the vaccines, bowel disease, and autism. In the United Kingdom, the MMR vaccine was not introduced until 1988. If Wakefield's conclusions were correct, one would then expect a jump in autism cases after 1988, but this was not observed, even when hundreds of children were studied (Taylor et al., 1999). In these additional studies, children who had not been vaccinated were included as a control group, and no difference in the rates of autism was observed.
In 2011, Brian Deer reviewed Wakefield's study and all available records from the National Health Service (NHS) in the United Kingdom for these 12 children. He found that at most, two children showed symptoms days after vaccinations. At least five children showed developmental delays before being vaccinated. Six out of the 12 children may have had autism symptoms. None of the 12 children tested had all three-regressive autism, colitis, and symptoms days after vaccination.
Symptom | Wakefield | Wakefield NHS Records |
Symptoms days after vaccination | 8 | 2? |
Non-specific colitis | 12 | 3 |
Regressive autism | 9 | 6? |
Intestinal/autism/symptoms after vaccine | 12 | 0 |
(Wakefield, et al., 1998; Deer, 2011)
Wakefield's statements led to a worldwide panic about the safety of vaccines, but after Deer's report, Wakefield's study was retracted and his medical license was revoked for falsifying data. Click on the following links to review materials to enhance your knowledge of the scientific method and to support your analysis of Wakefield's experiment:
Steps of the Scientific Method: A simplified explanation of how the scientific method works, the steps taken to investigate phenomenon with diagrams
Do Vaccines Cause Autism?: A review of research demonstrating that vaccines and their components are not the cause of autism
Fifteen years after a vaccine scare, a measles epidemic: An analysis of vaccination trends and an increase in measles cases seen the UK
Answer the following 4 questions:
What was wrong with Wakefield's study? Discuss at least 1 variable or approach that should have been controlled or assessed.
Consider the source of some of his data (parental memory, for example), the small sample size, and whether he considered other variables (genetics, diet, and so on) that could have resulted in symptoms in these children.
Discuss the importance of a control group when using the scientific method.
Did Wakefield deserve to be barred from medical practice?
What were the consequences of his inflated conclusions?
Chose the correct answers on one through 15(plese help)
1.A research group hypothesizes that successful infection by HIVdepends upon the expression of FSH3, a human gene. They overexpressthis gene in T cells (Which HIV normally infects) so that FSH3protein levels are very high in these cells. In other T-cells, theymutate FSH3 so that none of its encoded protein is made. They thenmeasure HIV infection rate in the control, overexpression, andmutant T cells. The three cultures are otherwise grown in the sameway.
What is the independent variable(s) in this experiment? (Selectall correct answers)
FSH3 protein levels | ||
The medium in which cells are grown | ||
The temperature at which cells are grown | ||
HIV resistance of cells |
Question 2
Which arises from an error in a measurement or observation?
Technical variability | ||
Biological variability | ||
Standard error | ||
Standard deviation |
Question 3
Use the following description of an experiment to answer thenext question.
A research group hypothesizes that successful infection by HIVdepends upon the expression of FSH3, a human gene. They overexpressthis gene in T cells (Which HIV normally infects) so that FSH3protein levels are very high in these cells. In other T-cells, theymutate FSH3 so that none of its encoded protein is made. They thenmeasure HIV infection rate in the control, overexpression, andmutant T cells. The three cultures are otherwise grown in the sameway.
What is the control group(s) in this experiment? (Select allcorrect answers)
The unaltered T cells | ||
The medium in which cells are grown | ||
The T cells in which FSH3 is mutated | ||
The T cells overexpressing FSH3 |
Question 4
How many of the following statements are true?
I. All papers have an abstract, methods, results, and discussionsection
II. The methods always follows the introduction
0 | ||
2 | ||
1 |
Question 5
If scientific convention states that when a P value of less than0.05 is considered significant (in other words, the two groupsbeing measured are actually different), this means that: (Selectall correct answers)
If you were to repeat the experiment 100 times, there would notbe a significant difference between the groups in 5 of theexperiments | ||
95% of all conclusions that state two groups are not differentbased on a 0.5% p-value threshold are false negatives | ||
The groups are actually not different from each other 95% of thetime | ||
5% of all conclusions that state two groups are different basedon a 0.5% p-value threshold are false positives |
What information is typically found in the introduction sectionof a paper? (Select all that apply)
The dependent and independent variables within the study | ||
Which areas of the field are not well understood and whatquestion the study addresses | ||
How the main question of the paper is related to other researchin the field. | ||
How previous work forms the basis for the current study | ||
The purpose of the study | ||
Details of the approaches used | ||
A summary of relevant related studies |
Question 7
How can you judge for yourself whether the conclusions reachedin a paper are valid? (Select all that apply)
Read papers of other authors studying the same question or areaof inquiry | ||
Determine if each hypothesis is supported by different types ofevidence/approaches. | ||
Consider closely whether the data actually both addresses andsupports the authorĆ¢ĀĀs hypothesis. | ||
Examine the amount of data in the paper, and how long the paperis. | ||
Whether the authors find a mechanism, or exactly how on variableaffects another. | ||
Interpret the data for yourself without looking the discussion,then compare your interpretations to that of the authorĆ¢ĀĀs. |
Question 8
Where can you usually find the institutional affiliations (wherethey work) of the authors?
Within the discussion | ||
In the acknowledgements section | ||
Below the authors list | ||
This is not usually included in papers |
Question 9
Other than publishing primary research articles, what is themain way scientists disseminate their results?
Lab meetings | ||
Personal correspondence | ||
Conference seminars | ||
Public lectures |
Question 10
Use the following description of an experiment to answer thenext question.
A research group hypothesizes that successful infection by HIVdepends upon the expression of FSH3, a human gene. They overexpressthis gene in T cells (Which HIV normally infects) so that FSH3protein levels are very high in these cells. In other T-cells, theymutate FSH3 so that none of its encoded protein is made. They thenmeasure HIV infection rate in the control, overexpression, andmutant T cells. The three cultures are otherwise grown in the sameway.
What is the experimental group(s) in this experiment? (Selectall correct answers)
Each group is its own control | ||
The T cells overexpressing FSH3 | ||
The T cells in which FSH3 is mutated | ||
The unaltered T cells |