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Title screen: Conducting ANOVA: Single Factor. Copyright ©2017 McGraw-Hill Education. All rights reserved.
Narrator: "In this video, I'll demonstrate how to use Excel's data analysis tool ANOVA Single Factor to run a one-way ANOVA and test the assumed equality of more than two population means. A real-estate developer is evaluating three parcels of land for a retail development. Of importance in the final decision are the mean incomes of nearby households. A random sample of four households' income in the area has been collected. At the 0. 05 significance level, can the developer conclude there is a difference in the mean income between potential locations? Our null hypothesis is that all means are equal. The alternative is that they are not."
Cells A7 to B8 are circled and contain formulas: H0: mu subscript s equals mu subscript f equals mu subscript o. H1: mu subscript s does not equal mu subscript F does not equal mu subscript O.
Narrator: "Go to 'data,' 'data analysis,' and find 'ANOVA Single Factor' and click 'OK.'"
Data Analysis is found in the Analysis section of the Data tab. When clicked, the Data Analysis dialog box appears with a list of Analysis Tools. ANOVA Single Factor is selected from list, which opens a new dialog box.
Narrator: "Our input range will be all of the data from Southwick through Old Orchard. Our data are grouped by columns. That is, each sample is in a column, rather than a row. Labels are in the first row. We will leave it at an alpha of 0. 05 and put our output here in our worksheet."
Within the Anova Single Factor dialog box, Input Range is set to $A$1:$C$5, the Labels in first row checkbox is checked, Alpha is set to 0.05, and Output Range is set to $E$1. When OK is clicked, Summary and ANOVA table appears in the spreadsheet.
Narrator: "Now I'm ready to click 'OK.' And here is my output. At the top, we see some descriptive statistics on our data set—The average and variance and our sample size for each of the three samples. In the analysis of variance table, 'between groups' is Excel's term for treatments. In other words, the sample which represents each population. 'Within groups' is Excel's term for error. The value in SS next to 'between groups' corresponds to the sum of the squares due to the treatments, or SST. And the value in this cell is SSE—the sum of the squared errors."
Within the ANOVA table, cells E and F12 and E and F13 are highlighted. The SS column lists 276.5 in F12 and 87.75 in F13.
Narrator: "MS is mean square, and MS in the 'between groups' row is therefore 'MST' —mean square for treatments, while in the 'within groups' row, it is MSE—mean square error."
Cell H12, MST, 138.25; cell H13, MSE, 9.75.
Narrator: "We can either evaluate the critical value against the test statistic…"
Columns I and K contain F and F crit values in the ANOVA table. P-value is listed in column J.
Narrator: "or use the 'P' value. Starting with the calculated test statistic, the 'F' of 14. 179 is much larger than the 'F' critical value."
Text: F equals 14.1795 greater than F critical of 4.2565.
Narrator: "We would reject the null hypothesis and conclude that the means are not equal. The 'P' value leads to the same result."
Text: p-value equals .0017 less than alpha equals 0.05.
Narrator: "It is the probability of getting the calculated 'F' statistic, if there really were no difference between the means, and 0. 0017 is much smaller than our alpha of 0. 05. Again, we would reject the null. Note that we cannot conclude which of the means may be unequal. Only that the three means do not equal one another. If we want to go a step further and determine which pairs of means are unequal, that would require additional testing. This video demonstrated how to use Excel's ANOVA Single Factor tool to conduct a one-way analysis of variance on sample means to determine whether the population means are equal or unequal."
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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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