Probability and Health Statistics: Case Assignment

Probability and Health Statistics: Case Assignment
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Probability and Health Statistics: Case Assignment
Part 1: Classification of Variables
1 A researcher studying lifespan categorizes individuals into single, married, divorced, or widowed. What type of variable measurement is this? The categories single, married, divorced or widowed are subcategories of the variable civil status. This is a nominal data in that the subcategories only provide a way or organizing the data and that none of the various sub-categories are considered higher or lesser in value than the others ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "author" : [ { "dropping-particle" : "", "family" : "Bailey", "given" : "Kenneth", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "edition" : "4th editio", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2008" ] ] }, "publisher" : "Simon and Schuster", "publisher-place" : "New York", "title" : "Methods of Social Research", "type" : "book" }, "locator" : "63", "uris" : [ "/documents/?uuid=67055485-3875-4abc-a851-46f8d969ec8d" ] } ], "mendeley" : { "formattedCitation" : "(Bailey, 2008, p. 63)", "plainTextFormattedCitation" : "(Bailey, 2008, p. 63)", "previouslyFormattedCitation" : "(Bailey, 2008, p. 63)" }, "properties" : { "noteIndex" : 0 }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-citation.json" }(Bailey, 2008, p. 63).
2 A cognitive scientist places her subjects into categories based on how anxious they tell her that they are feeling: "not anxious", "mildly anxious", "moderately anxious" and "severely anxious", and she uses the numbers 0, 1, 2 and 3 to label categories where lower numbers indicate less anxiety. What type of variable measurement is this? Are the categories mutually exclusive? The anxiety levels of subjects are measured in the ordinal scale because each category implies a certain kind of ordering. For example, if a subject answers 1, then it means that his/her anxiety level is higher than those who answered 0, but lower than those who answered 2. It is important to note, however, that the differences between the scores are not equal ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "URL" : "/duval/ps601/Notes/Levels_of_Measure.html", "accessed" : { "date-parts" : [ [ "2015", "4", "13" ] ] }, "author" : [ { "dropping-particle" : "", "family" : "Duval", "given" : "Bob", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "West Virginia University", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "1995" ] ] }, "title" : "Levels of Measurement", "type" : "webpage" }, "uris" : [ "/documents/?uuid=e8b4ad63-e21d-4c41-9ec7-22030f7ecb2e" ] } ], "mendeley" : { "formattedCitation" : "(Duval, 1995)", "plainTextFormattedCitation" : "(Duval, 1995)", "previouslyFormattedCitation" : "(Duval, 1995)" }, "properties" : { "noteIndex" : 0 }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-citation.json" }(Duval, 1995), so those who answered 2 are not twice as anxious as those who answered 1. Yes, the categories are mutually exclusive in that each has a different meaning from the other three choices ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "author" : [ { "dropping-particle" : "", "family" : "Bailey", "given" : "Kenneth", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "edition" : "4th editio", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2008" ] ] }, "publisher" : "Simon and Schuster", "publisher-place" : "New York", "title" : "Methods of Social Research", "type" : "book" }, "locator" : "63", "uris" : [ "/documents/?uuid=67055485-3875-4abc-a851-46f8d969ec8d" ] } ], "mendeley" : { "formattedCitation" : "(Bailey, 2008, p. 63)", "plainTextFormattedCitation" : "(Bailey, 2008, p. 63)", "previouslyFormattedCitation" : "(Bailey, 2008, p. 63)" }, "properties" : { "noteIndex" : 0 }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-citation.json" }(Bailey, 2008, p. 63).
3 A Physician diagnoses the presence or absence of disease (i.e. yes or no). What type of variable measurement is this? Presence or absence of disease is a dichotomous variable and is treated as a nominal ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "URL" : "/duval/ps601/Notes/Levels_of_Measure.html", "accessed" : { "date-parts" : [ [ "2015", "4", "13" ] ] }, "author" : [ { "dropping-particle" : "", "family" : "Duval", "given" : "Bob", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "West Virginia University", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "1995" ] ] }, "title" : "Levels of Measurement", "type" : "webpage" }, "uris" : [ "/documents/?uuid=e8b4ad63-e21d-4c41-9ec7-22030f7ecb2e" ] } ], "mendeley" : { "formattedCitation" : "(Duval, 1995)", "plainTextFormattedCitation" : "(Duval, 1995)", "previouslyFormattedCitation" : "(Duval, 1995)" }, "properties" : { "noteIndex" : 0 }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-citation.json" }(Duval, 1995) because it merely categorizes subjects and does not provide any sort of relationship between the categories.
4 A person weighing 200 lbs. is considered to be twice as heavy as a person weighing 100 lbs. In this case, what type of measurement is body weight? Body weight is an interval variable. Just like nominal variables, the weight of a person categorizes every subject, but unlike nominal variables, there is ordering in the body weight. It is not a simple ordinal variable because we know the actual difference between the two categories mentioned (200lbs, is twice as heavy as 100 lbs.).
5 A nurse takes measurements of body temperature on patients and reports them in units of degrees Fahrenheit as part of a study. What type of variable measurement is this? Just like body weight, temperature is an interval variable ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "author" : [ { "dropping-particle" : "", "family" : "Lane", "given" : "Dan Osherson and David M.", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Online Statistics Education: An Interactive Multimedia Course of Study", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2015" ] ] }, "publisher" : "Rice University", "title" : "Levels of Measurement", "type" : "book" }, "uris" : [ "/documents/?uuid=3f486f54-300c-4e0b-99bd-c869866f37fd" ] } ], "mendeley" : { "formattedCitation" : "(Lane, 2015)", "plainTextFormattedCitation" : "(Lane, 2015)", "previouslyFormattedCitation" : "(Lane, 2015)" }, "properties" : { "noteIndex" : 0 }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-citation.json" }(Lane, 2015).
6 Patients rate their experience in the emergency room on a five point scale from poor to excellent ( 1 = very poor, 2 = not very good, 3 = neither good nor bad, 4 = quite good, and 5 = excellent). What type of variable measurement is this? Is the difference between a 1 and a 2 necessarily the same as the difference between a 3 and a 4? Explain briefly. 
This is called a likert scale and is designed to measure attitudes and opinions of respondents ADDIN CSL_CITATION { "citationItems" : [ { "id" : "ITEM-1", "itemData" : { "URL" : "/likert-scale.html", "accessed" : { "date-parts" : [ [ "2015", "4", "13" ] ] }, "author" : [ { "dropping-particle" : "", "family" : "McLeod", "given" : "Saul", "non-dropping-particle" : "", "parse-names" : false, "suffix" : "" } ], "container-title" : "Simply Psychology", "id" : "ITEM-1", "issued" : { "date-parts" : [ [ "2008" ] ] }, "title" : "Likert Scale", "type" : "webpage" }, "uris" : [ "/documents/?uuid=31182ded-d66b-4c2a-b402-5ce253b43da9" ] } ], "mendeley" : { "formattedCitation" : "(McLeod, 2008)", "plainTextFormattedCitation" : "(McLeod, 2008)", "previouslyFormattedCitation" : "(McLeod, 2008)" }, "properties" : { "noteIndex" : 0 }, "schema" : "https://github.com/citation-style-language/schema/raw/master/csl-citation.json" }(McLeod, 2008). While it can be treated as an interval data (because one can compute for mean), it is definitely used for measuring ordinal variables. Likert scales assume that "the strength/intensity of experience is linear, i.e. on a continuum from strongly agree to strongly disagree", which means that one category is higher than the others. Yet, one cannot say that categories 1 and 2 have the same difference as 3 and 4. In fact, if we look at category 3 alone, one cannot say that it is three times better or worse than category 1 (very poor). In fact, from the wording of this category, it looks like a "neutral" response.
Part 2: Statistics
By combining two of the examples above, I would like to know the relationship between anxiety level and civil status. Collecting the data on these two variables and utilizing various statistical tools, one can discover several patterns. For example, descriptive analysis will show how many of the respondents are single, married, divorced or widowed. It will also show the civil status to which a majority of the respondents belong to. It will also show how many of the respondents experience high levels of anxiety or no anxiety at all. Several statistical tools can also determine the average level anxiety of the chosen sample. Statisticians can also utilize various correlational statistical tools, to discover which group of people can experience high anxiety levels, and which groups experience no anxiety at all. Of course, they can also discover whether the general levels of anxiety is statistically the same or different from each group.
Once the researcher has discovered which groups are prone to anxiety, he or she can then proceed studying the possible causes of anxieties by looking at previous literature, and then perhaps later on, propose audience-appropriate interventions to prevent anxiety. Part 3: Quantita...