Question

Tax Research. A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case containing a set of facts, a tax issue, and a key word index consisting of 1336 key words. They were asked to select the key words they believed would refer them to a tax authority relevant to resolving the tax case. Prior to the experiment, a group of tax experts determined that the text contained 19 relevant key words. Subjects in the naive group had little or no declarative or procedural knowledge, subjects in the declarative group had significant declarative knowledge but little or no procedural knowledge, and subjects in the procedural group had significant declarative knowledge and procedural knowledge. Declarative knowledge consists of knowledge of both the applicable tax rules and the technical terms used to describe such rules. Procedural knowledge is knowledge of the rules that guide the tax researcher's search for relevant key words. Subjects in the low time pressure situation were told they had 25 minutes to complete the problem, an amount of time which should be "more than adequate" to complete the case; subjects in the moderate time pressure situation were told they would have "only" 11 minutes to complete the case. Suppose 25 subjects were selected for each of the six treatment combinations and the sample means for each treatment combination are as follows (standard deviations are in parentheses). (TABLE CAN'T COPY) Use the ANOVA procedure to test for any significant differences due to time pressure, knowledge, and interaction. Use a . 05 level of significance. Assume that the total sum of squares for this experiment is 327.50 .

Name: Problem 33, Chapter 13: Essentials of Statistics for Business & Economics
Uploaded: 2022-12-23T12:33:59-08:00
Duration: 23 min 23 s
Channel: Shu Naito

Tax Research. A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case containing a set of facts, a tax issue, and a key word index consisting of 1336 key words. They were asked to select the key words they believed would refer them to a tax authority relevant to resolving the tax case. Prior to the experiment, a group of tax experts determined that the text contained 19 relevant key words. Subjects in the naive group had little or no declarative or procedural knowledge, subjects in the declarative group had significant declarative knowledge but little or no procedural knowledge, and subjects in the procedural group had significant declarative knowledge and procedural knowledge. Declarative knowledge consists of knowledge of both the applicable tax rules and the technical terms used to describe such rules. Procedural knowledge is knowledge of the rules that guide the tax researcher's search for relevant key words. Subjects in the low time pressure situation were told they had 25 minutes to complete the problem, an amount of time which should be "more than adequate" to complete the case; subjects in the moderate time pressure situation were told they would have "only" 11 minutes to complete the case. Suppose 25 subjects were selected for each of the six treatment combinations and the sample means for each treatment combination are as follows (standard deviations are in parentheses).
(TABLE CAN'T COPY)
Use the ANOVA procedure to test for any significant differences due to time pressure, knowledge, and interaction. Use a . 05 level of significance. Assume that the total sum of squares for this experiment is 327.50 .

Essentials of Statistics for Business & Economics

David R. Anderson;… 9th Edition

Chapter 13, Problem 33

Instant Answer

Solved by Expert Shu Naito

12/23/2022

Step 1

The factors in this experiment are time pressure (2 levels: low and moderate) and knowledge (3 levels: naive, declarative, and procedural). This results in a 2x3 factorial design, leading to 6 treatment combinations. Show more…

Show all steps

Thanks for your feedback!

Tax Research. A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case containing a set of facts, a tax issue, and a key word index consisting of 1336 key words. They were asked to select the key words they believed would refer them to a tax authority relevant to resolving the tax case. Prior to the experiment, a group of tax experts determined that the text contained 19 relevant key words. Subjects in the naive group had little or no declarative or procedural knowledge, subjects in the declarative group had significant declarative knowledge but little or no procedural knowledge, and subjects in the procedural group had significant declarative knowledge and procedural knowledge. Declarative knowledge consists of knowledge of both the applicable tax rules and the technical terms used to describe such rules. Procedural knowledge is knowledge of the rules that guide the tax researcher's search for relevant key words. Subjects in the low time pressure situation were told they had 25 minutes to complete the problem, an amount of time which should be "more than adequate" to complete the case; subjects in the moderate time pressure situation were told they would have "only" 11 minutes to complete the case. Suppose 25 subjects were selected for each of the six treatment combinations and the sample means for each treatment combination are as follows (standard deviations are in parentheses). (TABLE CAN'T COPY) Use the ANOVA procedure to test for any significant differences due to time pressure, knowledge, and interaction. Use a . 05 level of significance. Assume that the total sum of squares for this experiment is 327.50 .

Play audio

Feedback

Shu Naito and 82 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Sum of Squares

The sum of squares is a measure used in the context of ANOVA to quantify the total variability present in the data. It is divided into portions that represent the variability due to the effects of the independent variables (between-group variability) and the variability due to random error (within-group variability), providing a foundation for statistical comparison.

Analysis of Variance (ANOVA)

ANOVA is a statistical procedure used to assess whether there are significant differences among the means of different groups. It achieves this by partitioning the total variability observed in the data into components attributable to different sources (e.g., between-group and within-group variance) and comparing these components to determine if the group means differ more than would be expected by chance.

Factorial Design

A factorial design is an experimental framework that involves two or more independent variables, each with multiple levels. This design allows researchers to explore not only the individual (main) effects of each factor on the outcome but also to investigate how these factors may interact with one another, which is critical in understanding complex real-world scenarios.

Main Effects

Main effects refer to the isolated influence that each independent variable exerts on the dependent variable, regardless of the levels of other variables in the study. In an analysis involving multiple factors, examining main effects helps determine if changing a single factor has a significant impact on the outcome.

Interaction Effects

Interaction effects occur when the effect of one independent variable on the dependent variable changes depending on the level of another independent variable. These effects are important because they indicate that the combined influence of two factors is not simply additive, suggesting a more complex relationship between the variables.

Significance Testing

Significance testing is the process of using statistical methods to decide whether the observed effects in a study are likely to be genuine or could have occurred by random chance. By setting a predetermined threshold (such as a 0.05 significance level), researchers can evaluate if the differences among groups are statistically meaningful.

Recommended Videos

Transcript

00:01 Okay, we're going to do 13 .33.

00:05 The first thing we need to do is to make the adjusted table.

00:10 And the way we make this table here is by multiplying the entries in the original table by 25.

00:19 So, for example, for this cell, we have 1 .13 times 25.

00:27 And then this is equal to the 28 .25.

00:33 The reason why we do this is because the original table is in terms of the means, and we're basically trying to convert it to the sum, and these numbers are going to be used in order to do the necessary calculations.

01:00 We're going to fill this table as in the text.

01:04 The next thing we do is to first find a, b, r, and n t.

01:10 So for a, we have, and b, we have 3, and r we have a 25.

01:28 And nt, this is equal to a, b, which is 2 times 3 times 25.

01:39 And this is equal to 150.

01:41 50.

01:45 The next thing we do is to calculate xi, xi dot and x.

01:54 Excuse me, this is a x bar .j.

02:01 Okay, so for x bar 1.

02:11 To find this we are going to use the adjusted table.

02:17 So for example if you look at the first row we're gonna sum these numbers in the first row and divide it by 25 times 3 because the because each entry entails a 25 people so this is equal to 28 .25 plus 39 plus 50 over 25 times 3 and this is equal to 1 .563.

03:00 Similarly we're going to calculate x bar 2 dot and basically the same thing we're going to sum the moderate roll and then divide it by 25 times 3.

03:15 So this is 12 plus 42 plus 71 .5 over 25 times 3 and this equals 1 .67.

03:34 Now we're gonna do a x .js.

03:39 So x .j's, this is a similar calculation but we're gonna use the column of the adjusted tables.

03:48 X .1 this is equal to the sum of the sum of the first row, no first column, and we're going to divide it by 25 times 2, because again, each entry entails a 25 people, and there are two entries.

04:14 So, this gives 28 .25 plus 1 -2 over 25 times 2.

04:25 This gives 0 .805 and x bar .2 again the same thing but we're gonna use the second column here of the adjusted table and this gives 39 plus 42 over 25 times 2 which equals 1 .62 x bar .3, same thing, but with the third column, 50 plus 71 .5 over 25 times 2.

05:19 This gives 2 .43.

05:24 Okay.

05:27 Now, the next thing we need to calculate is the means, and for the means, this is provided in the original table.

05:37 So we're just going to use the original table here.

05:44 So the original table recall is this one, this table.

05:49 This is the means.

05:54 Okay, now we're going to calculate the overall means.

05:59 This is going to be the sum of the adjusted table, the numbers in the adjusted table, over nt.

06:09 So we're going to sum the entire table.

06:14 And then divided by n t which we found to be 150 so x bar bar this is equal to 28 .25 plus 39 plus and other numbers and 42 plus 71 .5 over 150 and this yields and this yields a 1 .618.

06:54 Now we're going to calculate ssa and the other numbers for sum of squares.

07:07 Okay, so ssa, by the way, the sst is given in the question.

07:18 So sst has given is 327 .5 and ssa this is given by the formula b and sum of x bar square so this is the formula we found the x i dot in here so these are the numbers that we're going to fill in into the equations.

08:10 And then x bar bar, we just found it in the previous page.

08:14 So this gives a 0 .454 and ssb.

08:26 Basically the same thing, but a little bit different formula.

08:32 So this is a r, a times r, and j goes from 1 to be x bar .j minus x bar bar square.

08:49 And again, we found a and r in here, and then x.

08:57 Is calculated here.

09:00 And then sample means is this one.

09:02 So, when we calculate this number, we get 66 .016 and ssab.

09:27 Let me insert a new slide here.

09:35 Ssab.

09:37 This is given by r times i -1 through a.

09:44 J 1 through b x bar ij minus x i dot x bar dot j plus x bar bar bar square so all these numbers are found previously for example for x bar i j we are going to use the original table so for example this entry corresponds to x bar 1 -1 and then this table or this entry corresponds to x bar 2 -2.

10:29 So these are the numbers that we're going to use in order to calculate ssab.

10:39 And then x -i dot, x bar i dot and x bar .j was found in here and here.

10:50 Right and the total sample mean is found here so when we put it in the equation we get s s sab as 14 .253 and lastly we're gonna find a ssee so sse this is the shti minus ssa minus s s s b minus ssab minus ssab.

11:37 So we found these ssa, ssa, s s b, and ssa a b.

11:42 We found these numbers in here and here.

11:46 And ssd, this is given as 327 .5.

11:52 And when we put it in the equation, we get sse as 246 .7 7, 8...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace