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Title screen: Conducting ANOVA: Two-Factor Without Replication. Copyright ©2017 McGraw-Hill Education. All rights reserved.
Narrator: "This video will demonstrate how to conduct a two-way analysis of variants. We will study the separate or independent effects of two variables, also called factors, on a response variable by applying Excel's ANOVA: Two-Factor Without Replication tool. In this data set, a company runs production for three shifts five days a week. Employees rotate shifts, and management is interested in determining whether there is a difference in production output by employee depending on which shift is worked. A random sample of five workers is selected, and their output recorded on each shift. At the . 05 significance level, is there a difference in the mean production rate by shift or by employee? The rows correspond to our blocking variable—the five employees."
Cells A3 to D7 are circled.
Narrator: "The columns correspond to our treatment variable—the mean output per shift."
Cells B2 to D7 are circled.
Narrator: "We have two sets of hypotheses."
The first set: H0: mu subscript one equals mu subscript two equals mu subscript three; H1: mu subscript one does not equal mu subscript two does not equal mu subscript three. Second set: H0: mu subscript S equals mu subscript L equals mu subscript C equals mu subscript T equals mu subscript M; H1: mu subscript s does not equal mu subscript L does not equal mu subscript C does not equal mu subscript T does not equal mu subscript M.
Narrator: "The test of hypothesis for our treatment variable is that production means are the same regardless of time of day, therefore the null hypothesis is mu1 = mu2 = mu3."
Arrows point from the mu values of the first set of hypotheses to the column headers Day (mu subscript one), Afternoon (mu subscript two), and Evening (mu subscript three).
Narrator: "The alternative hypothesis is they are not equal. For the hypothesis of equal-block means, we will use employees' initials to tell them apart in our notation. MuS = MuL = MuC = MuT =MuM, where the 'S' stands for Skaff, the 'L' for Lum, and so on."
Arrows point from the mu values of the second set of hypotheses to the row headers in the Employee column.
Narrator: "The alternative hypothesis is that the means are not equal. Go to Data, Data Analysis, and select ANOVA: Two-Factor Without Replication."
Data Analysis is selected from the Analysis section of the Data tab. The Data Analysis dialog box appears with a list of Analysis Tools. Anova: Two-Factor Without Replication is selected, which opens a new dialog box.
Narrator: "In the input range, select from 'Employee' through 'Evening,' and down through Morgan's output. I've included labels, so I click 'Label.' Leave the alpha at . 05. Output can stay in this tab. Let's have it here in Excel F1. And click 'Okay.'"
Within the Anova: Two-Factor Without Replication dialog box, Input Range is set to $A$2:$D$7, the Labels checkbox is checked, Alpha is left at 0.05, and Output Range is set to $F$1. When OK is clicked, new tables appear in the sheet.
Narrator: "Here is my output. We have descriptive statistics at the top for each variable. A summary of the blocking variable is first, then the treatment, and that corresponds to the order in the ANOVA table."
Arrows point to the rows headers in cells F17 and F18: Row, blocking variable equals employees; Columns, treatment variable equals shift.
Narrator: "We can compare 'F' with the 'F' critical value, or look at 'P' value for our rows and our columns. For the test of employee-production equality, which is our rows or blocking variable, 'F' of 1. 55 is smaller than 'F' critical,"
Cell J17 (F), 1.552147, is less than cell L17 (F crit), 3.837853.
Narrator: "and the 'P' value is larger than alpha. With either outcome, we fail to reject the null hypothesis. We cannot conclude that there is a difference in output by employee. For the treatment—that is, for the Columns row—'F' of 5. 75 is larger than 'F' critical of 4. 46, and our 'P' value is smaller than our alpha. We reject the null hypothesis, and conclude that there is a difference in mean output per shift. Note that we are not able to conclude which shift is different from another. We can only conclude that there is a difference. Further testing would be needed to determine where the difference lies. This video demonstrated how to conduct a two-way ANOVA of two independent factors on a response variable using Excel's tool ANOVA: Two-Factor Without Replication."
Video has ended.
Described transcript ©2023 McGraw Hill. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.
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