{"id":5522,"date":"2022-09-21T09:09:04","date_gmt":"2022-09-21T09:09:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5522"},"modified":"2022-10-10T18:55:58","modified_gmt":"2022-10-10T18:55:58","slug":"16b-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/16b-coreq\/","title":{"raw":"16B Coreq","rendered":"16B Coreq"},"content":{"raw":"
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In the next preview assignment, you will need to understand complex fractions to calculate the value of an F-statistic and use the DCMP F Distribution tool to calculate the correspondingP-value.<\/div>\r\n
Complex Fractions<\/div>\r\n
A complex fraction is a fraction in which the numerator and\/or the denominator include fractions. An example of a complex fraction is shown below:<\/div>\r\n
[latex]\\frac{\\frac{1}{2}}{\\frac{3}{4}}[\/latex]<\/div>\r\n
In keeping with the order of operations, you should evaluate the numerator and the denominator separately before dividing the numerator by the denominator. When using a calculator, use parentheses to indicate that the operations in the numerator and the denominator should be completed first, as shown:<\/div>\r\n
[latex](1\/2)\/(3\/4)\u22480.667[\/latex]<\/div>\r\n
\r\n
\r\n

Question 1<\/h3>\r\n
1) Use a calculator to evaluate the following complex fractions. Express your answers using decimals. Round to three decimal places.<\/div>\r\n
Part A: 149\u20442139\/12<\/div>\r\n
Part B: 4\u204413\/12<\/div>\r\n<\/div>\r\n<\/div>\r\n
F-statistics always involve complex fractions. For example, In-Class Activity 14.B introduced the one-way ANOVA F-statistic. The formula for the one-way ANOVA F-statistic is:<\/div>\r\n
[latex]\ud835\udc39=\\frac{\ud835\udc40\ud835\udc46\ud835\udc3a\ud835\udc5f\ud835\udc5c\ud835\udc62\ud835\udc5d}{\ud835\udc40\ud835\udc46\ud835\udc38\ud835\udc5f\ud835\udc5f\ud835\udc5c\ud835\udc5f}=\\frac{\ud835\udc46\ud835\udc46\ud835\udc3a\ud835\udc5f\ud835\udc5c\ud835\udc62\ud835\udc5d\/\ud835\udc51\ud835\udc53\ud835\udc3a\ud835\udc5f\ud835\udc5c\ud835\udc62\ud835\udc5d}{\ud835\udc46\ud835\udc46\ud835\udc38\ud835\udc5f\ud835\udc5f\ud835\udc5c\ud835\udc5f\/\ud835\udc51\ud835\udc53\ud835\udc38\ud835\udc5f\ud835\udc5f\ud835\udc5c\ud835\udc5f}[\/latex]<\/div>\r\n
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\r\n

Question 2<\/h3>\r\n2) Use the values given in the following partially filled-in ANOVA table to calculate the F-statistic. Round your answer to three decimal places. Source DfSum sqMean sqF valueGroup2614.6307.3Error69391156.681Total714525.6During In-Class Activity16.B, you will consider how various factors affect the value of the F-statistic.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 3<\/h3>\r\n
3) First let\u2019s try changing some of the values in the complex fractions you saw in Question 1. Fill in the blanks.<\/div>\r\n
Part A: \ud835\udc65\u20442139\/12As \ud835\udc65increases, the size of the overall fraction ______.<\/div>\r\n
Part B: 4\u204413\/\ud835\udc65As \ud835\udc65increases, the size of the overall fraction ______.<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 4<\/h3>\r\n
4) Now let\u2019s try changing some of the values in the formula for the F-statistic.You may assume that we are only changing one value at a time\u2014all other values in the formula are being held constant.<\/div>\r\n
Part A: As SSGroupincreases, the size of the F-statistic ______.<\/div>\r\n
Part B: As the degrees of freedom for Groupincreases, the size of the F-statistic ______.<\/div>\r\n
Part C: As SSErrorincreases, the size of the F-statistic ______.<\/div>\r\n
Part D: As the degrees of freedom for Errorincreases, the size of the F-statistic ______.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
Using the F Distribution Tool<\/span><\/div>\r\n<\/div>\r\n
\r\n
The F Distribution models the values of the F-statistic that would occur if the null hypothesis was true. The F Distribution tool (i.e., data analysis tool) can be used to calculate a P-value\u2014the probability of getting an F-statistic as large or larger than the one from the sample if the null hypothesis was true. Note: This is an upper tail test. There are different F Distributions, depending on the numerator degrees of freedom (\ud835\udc51\ud835\udc531) and the denominator degrees of freedom (\ud835\udc51\ud835\udc532). These degrees of freedom come from the numerator and the denominator of the F-statistic, so for a one-way ANOVA,\ud835\udc51\ud835\udc531is the degrees of freedom for groups and \ud835\udc51\ud835\udc532is the degrees of freedom for error. Follow these steps to calculate a P-value using the DCMP F Distribution tool at https:\/\/dcmathpathways.shinyapps.io\/FDist\/.<\/div>\r\n
\u2022Click the Find Probability tab at the top of the page.<\/div>\r\n
\u2022Change the numerator and denominator degrees of freedom to match the given scenario.<\/div>\r\n
\u2022Switch to \u201cUpper Tail\u201d probability.<\/div>\r\n
\u2022Type the F-statistic into the \u201cValue of x\u201d box.<\/div>\r\n
\u2022The P-value is the percentage shown in orange above the graph. This value can also be converted to a proportion by moving the decimal two places to the left.<\/div>\r\n
<\/div>\r\n
\r\n
\r\n

Question 5<\/h3>\r\n
5) Suppose that F = 2.89, \ud835\udc51\ud835\udc531= 3, and \ud835\udc51\ud835\udc532= 76.<\/div>\r\n
Part A: Use the DCMP F Distribution tool to find the P-value. Express your answer as a percentage. Do not round.<\/div>\r\n
Part B: Convert the P-value to a decimal. Do not round.<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 6<\/h3>\r\n
\r\n
6) Use the values given in the following partially filled-in ANOVA table to carry out a one-way ANOVA F-test. SourceDfSum sqMean sqF valueGroup236.018.0Error21134.66.41Total23170.6<\/div>\r\n<\/div>\r\n
\r\n
Part A: Calculate the F-statistic. Round your answer to three decimal places.<\/div>\r\n
Part B: Use the F Distributiontool (i.e., data analysistool)to find the P-value. Express your answer as decimal. Do not round.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
In the next preview assignment, you will need to understand complex fractions to calculate the value of an F-statistic and use the DCMP F Distribution tool to calculate the correspondingP-value.<\/div>\n
Complex Fractions<\/div>\n
A complex fraction is a fraction in which the numerator and\/or the denominator include fractions. An example of a complex fraction is shown below:<\/div>\n
[latex]\\frac{\\frac{1}{2}}{\\frac{3}{4}}[\/latex]<\/div>\n
In keeping with the order of operations, you should evaluate the numerator and the denominator separately before dividing the numerator by the denominator. When using a calculator, use parentheses to indicate that the operations in the numerator and the denominator should be completed first, as shown:<\/div>\n
[latex](1\/2)\/(3\/4)\u22480.667[\/latex]<\/div>\n
\n
\n

Question 1<\/h3>\n
1) Use a calculator to evaluate the following complex fractions. Express your answers using decimals. Round to three decimal places.<\/div>\n
Part A: 149\u20442139\/12<\/div>\n
Part B: 4\u204413\/12<\/div>\n<\/div>\n<\/div>\n
F-statistics always involve complex fractions. For example, In-Class Activity 14.B introduced the one-way ANOVA F-statistic. The formula for the one-way ANOVA F-statistic is:<\/div>\n
[latex]\ud835\udc39=\\frac{\ud835\udc40\ud835\udc46\ud835\udc3a\ud835\udc5f\ud835\udc5c\ud835\udc62\ud835\udc5d}{\ud835\udc40\ud835\udc46\ud835\udc38\ud835\udc5f\ud835\udc5f\ud835\udc5c\ud835\udc5f}=\\frac{\ud835\udc46\ud835\udc46\ud835\udc3a\ud835\udc5f\ud835\udc5c\ud835\udc62\ud835\udc5d\/\ud835\udc51\ud835\udc53\ud835\udc3a\ud835\udc5f\ud835\udc5c\ud835\udc62\ud835\udc5d}{\ud835\udc46\ud835\udc46\ud835\udc38\ud835\udc5f\ud835\udc5f\ud835\udc5c\ud835\udc5f\/\ud835\udc51\ud835\udc53\ud835\udc38\ud835\udc5f\ud835\udc5f\ud835\udc5c\ud835\udc5f}[\/latex]<\/div>\n
\n
\n

Question 2<\/h3>\n

2) Use the values given in the following partially filled-in ANOVA table to calculate the F-statistic. Round your answer to three decimal places. Source DfSum sqMean sqF valueGroup2614.6307.3Error69391156.681Total714525.6During In-Class Activity16.B, you will consider how various factors affect the value of the F-statistic.<\/p>\n<\/div>\n<\/div>\n

\n
\n

Question 3<\/h3>\n
3) First let\u2019s try changing some of the values in the complex fractions you saw in Question 1. Fill in the blanks.<\/div>\n
Part A: \ud835\udc65\u20442139\/12As \ud835\udc65increases, the size of the overall fraction ______.<\/div>\n
Part B: 4\u204413\/\ud835\udc65As \ud835\udc65increases, the size of the overall fraction ______.<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 4<\/h3>\n
4) Now let\u2019s try changing some of the values in the formula for the F-statistic.You may assume that we are only changing one value at a time\u2014all other values in the formula are being held constant.<\/div>\n
Part A: As SSGroupincreases, the size of the F-statistic ______.<\/div>\n
Part B: As the degrees of freedom for Groupincreases, the size of the F-statistic ______.<\/div>\n
Part C: As SSErrorincreases, the size of the F-statistic ______.<\/div>\n
Part D: As the degrees of freedom for Errorincreases, the size of the F-statistic ______.<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
Using the F Distribution Tool<\/span><\/div>\n<\/div>\n
\n
The F Distribution models the values of the F-statistic that would occur if the null hypothesis was true. The F Distribution tool (i.e., data analysis tool) can be used to calculate a P-value\u2014the probability of getting an F-statistic as large or larger than the one from the sample if the null hypothesis was true. Note: This is an upper tail test. There are different F Distributions, depending on the numerator degrees of freedom (\ud835\udc51\ud835\udc531) and the denominator degrees of freedom (\ud835\udc51\ud835\udc532). These degrees of freedom come from the numerator and the denominator of the F-statistic, so for a one-way ANOVA,\ud835\udc51\ud835\udc531is the degrees of freedom for groups and \ud835\udc51\ud835\udc532is the degrees of freedom for error. Follow these steps to calculate a P-value using the DCMP F Distribution tool at https:\/\/dcmathpathways.shinyapps.io\/FDist\/.<\/div>\n
\u2022Click the Find Probability tab at the top of the page.<\/div>\n
\u2022Change the numerator and denominator degrees of freedom to match the given scenario.<\/div>\n
\u2022Switch to \u201cUpper Tail\u201d probability.<\/div>\n
\u2022Type the F-statistic into the \u201cValue of x\u201d box.<\/div>\n
\u2022The P-value is the percentage shown in orange above the graph. This value can also be converted to a proportion by moving the decimal two places to the left.<\/div>\n
<\/div>\n
\n
\n

Question 5<\/h3>\n
5) Suppose that F = 2.89, \ud835\udc51\ud835\udc531= 3, and \ud835\udc51\ud835\udc532= 76.<\/div>\n
Part A: Use the DCMP F Distribution tool to find the P-value. Express your answer as a percentage. Do not round.<\/div>\n
Part B: Convert the P-value to a decimal. Do not round.<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 6<\/h3>\n
\n
6) Use the values given in the following partially filled-in ANOVA table to carry out a one-way ANOVA F-test. SourceDfSum sqMean sqF valueGroup236.018.0Error21134.66.41Total23170.6<\/div>\n<\/div>\n
\n
Part A: Calculate the F-statistic. Round your answer to three decimal places.<\/div>\n
Part B: Use the F Distributiontool (i.e., data analysistool)to find the P-value. Express your answer as decimal. Do not round.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":68,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5522","chapter","type-chapter","status-publish","hentry"],"part":5514,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5522\/revisions"}],"predecessor-version":[{"id":5631,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5522\/revisions\/5631"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5514"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5522\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5522"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5522"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5522"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}