Course Learning Outcomes for Unit VI
Upon completion of this unit, students should be able to:
- Differentiate between various research-based tools commonly used in businesses.
- Identify the most appropriate statistical procedure to use from among t tests or ANOVA to test hypotheses.
- Test data for a business research project.
- Determine whether to accept or reject null and alternative hypotheses by using t tests and ANOVA.
| Course/Unit Learning Outcomes | Learning Activity |
| 6.1 | Unit Lesson
Video: ANOVA with Excel Video: Performing an Independent Samples t test in Excel Video: How to do a Two Sample t test Paired Two Sample for Means in Excel 2013 Video: t-test in Microsoft Excel Article: “Encyclopedia of Research Design: Causal-Comparative Design” Unit VI Scholarly Activity |
| 7.1 | Unit Lesson
Unit VI Scholarly Activity |
Reading Assignment
In order to access the following resources, click the links below:
Badii, M. (2009, November 23). ANOVA with Excel [Video file]. Retrieved from https://www.youtube.com/watch?v=leHOBf_-9kM
Click here for a transcript of the video.
Blake, K. (2011, April 9). Performing an independent samples t test in Excel [Video file]. Retrieved from https://www.youtube.com/watch?v=norKDF0MH0M
Click here for a transcript of the video.
Brewer, E. W., & Kubn, J. (2010). Casual-comparative design. In N. J. Salkind (Ed.), Encyclopedia of research design: Causal-comparative design. Retrieved from
http://methods.sagepub.com.libraryresources.columbiasouthern.edu/reference/encyc-of-researchdesign/n42.xml
Glen, S. (2013, December 21). How to do a two sample t test paired two sample for means in Excel 2013
[Video file]. Retrieved from https://www.youtube.com/watch?v=RHBIQ2reACM&t=8s
Click here for a transcript of the video.
1 Grange, J. (2011, April 7). t-test in Microsoft Excel [Video file]. Retrieved from UNIT x STUDY GUIDE
https://www.youtube.com/watch?v=BlS11D2VL_U Title
Click here for a transcript of the video.
Unit Lesson
Data Analysis of t Test and ANOVA
Unit V focused on the use of parametric statistical procedures, correlation analysis and regression analysis, to test hypotheses. Unit VI focuses on two additional parametric statistical procedures used to test hypotheses. Those two additional procedures are the t test and ANOVA. Like correlation analysis and regression analysis, the t test and ANOVA are forms of inferential statistics. Predictions are stated in the form of hypotheses, sample data are collected and tested, and statistically significant results are used to make inferences about the population of interest (Zikmund, Babin, Carr, & Griffin, 2013).
As was pointed out several times throughout the course, hypothesis testing either looks for statistically significant relationships between variables or statistically significant differences between variables or groups. While correlation analysis and regression analysis look for relationships between variables, the t test and ANOVA look for differences between variables or groups. Consider these examples of research questions that may be answered using t tests and ANOVA.
- Are there differences in air quality between sites A, B, C, and D?
- Are there differences in employee safety training scores before and after completion of a training course?
- Are there differences in box weight for cereal coming off production Line 1, Line 2, Line 3, and Line 4?
- Are there differences in product satisfaction between male and female consumers?
On the surface, it would seem these questions could easily be answered by simply comparing means. If samples show that the mean weights of cereal boxes coming off production Line 1, Line 2, Line 3, and Line 4 are 18.2 oz., 18.4 oz., 17.8 oz., and 18 oz. respectively, it would appear the answer is “yes,” there are differences in box weights for products coming off Line 1, Line 2, Line 3, and Line 4. There is, however, one important point that prevents drawing any hasty conclusions about mean differences between variables or groups; mean averages must be tested to determine if statistically significant differences exist. Statistical procedures, like the t test and ANOVA, are interested in the mean, but they also analyze how the data points are dispersed around the means. The means from two samples may appear different, but because of the variance of each data set, there may, in fact, be no statistically significant differences in means.
The t test is used to compare two means (e.g., product satisfaction between male and female consumers) while ANOVA is used to compare more than two means (e.g., air quality between sites A, B, C, and D).
Experimental and quasi-experimental research designs often use t tests and ANOVA. These are extremely powerful and useful procedures since variables can be manipulated and controlled to make claims of causation. For this reason, these statistical procedures are the primary tools used to determine the efficacy of drugs. This could be seen in testing for the efficacy of a new cancer drug. For example, a control group will receive a placebo (independent variable1 [IV1]) while an experimental group receives a new drug (IV2). After the IV1 and IV2 are administered, the control group’s tumor size (dependent variable [DV]) will be compared to the experimental group’s tumor size. If the mean size of experimental group’s tumor is less than the mean size of the control group’s tumor and the differences are statistically significant, a claim can be made that the new drug (IV2) caused a reduction in tumor size (assuming all other variables were held constant).
In many business and social science settings, it is impractical, impossible, unethical, or cost-prohibitive to use experimental research designs. As an alternative, researchers use causal-comparative research designs (i.e., ex post facto designs) to similarly look for differences between groups by comparing means. Since causalcomparative designs are ex post facto, meaning events and variables are analyzed after the fact, it is not possible to manipulate and control variables. Since causal-comparative designs cannot control variables, as do experimental designs, causation cannot be claimed (even though the name causal-comparative would suggest otherwise). Nevertheless, causal-comparative designs are effective and frequently use the UNIT x STUDY GUIDEt test and ANOVA in business and social science research because they can make strong inferences about the effect Title the IV has on the DV (Brewer & Kubn, 2010).
The t Test (i.e., Student’s t Test)
The t test is the simplest form of a test of differences where only two means are compared. There are two types of t tests: independent test (i.e., between-groups) and dependent test (i.e., within group, paired, or repeated-measures test).
Independent sample t test (i.e., between groups): Using an independent t test, a DV is measured for two different groups of people or things that were exposed to different IVs. For example, Plant A employees were trained using a new safety program that the company is considering purchasing and rolling out to all of their plants across the United States (IV1). Plant B employees are trained using the same safety program the employer has used for the past five years (IV2). Lost-time-hours (DV) are then compared between the two plants to determine if a statistically significant difference exists. The hypotheses would be stated as below.
Ho1: There is no statistically significant difference in lost-time-hours (DV) between Plant A (IV1) and Plant B
(IV2).
Ha1: There is a statistically significant difference in lost-time-hours (DV) between Plant A (IV1) and Plant B
(IV2).
Interpreting the independent sample t test output results: If statistically significant differences exist and lost-time-hours are lower in Plant A, management can make an informed decision, with certainty, about whether to invest in the new training program for all plants.
The independent sample t test looked for a statistically significant difference in lost-time-hours between Plant A training (IV1) and Plant B training (IV2). The results below indicate that the mean lost-time-hours are indeed lower for Plant A (Variable 1); however, the results also indicate a p value of .37627 > .05. Therefore, the null hypothesis is accepted that there is no statistically significant difference in lost-time-hours (DV) between Plant A (IV1) and Plant B (IV2). Given these results, the company would not benefit from purchasing the new training program for all plants.
Accept Ho1: There is no statistically significant difference in lost-time-hours (DV) between Plant A (IV1) and Plant B (IV2).
Reject Ha1: There is a statistically significant difference in lost-time-hours (DV) between Plant A (IV1) and Plant B (IV2).
Dependent sample t test (i.e., within-group, paired, or repeated measure): In a dependent t test, a DV is measured for one group of people or thing both before and after exposure to an IV to determine if statistically significant differences exist. For example, assume a company has several years of data for the dependent UNIT x STUDY GUIDE variable (DV) of lost-time-hours. A year ago, they implemented a new safety training program Title (IV) that was purchased from a third party vendor. Management is now interested to know if there has been an improvement in safety. They compare the mean lost-time-hours before implementing the training to the mean lost-time-hours after implementing the training. The hypotheses would be stated as below.
Ho1: There is no statistically significant difference in lost-time-hours (DV) before and after safety training (IV).
Ha1: There is a statistically significant difference in lost-time-hours (DV) before and after safety training (IV).
Interpreting the dependent sample t test: If there is a statistically significant difference in mean lost-timehours, and the mean has declined after the training, the company can infer that the training (IV) was successful. Additionally, this information would be helpful in cost-justifying the expenditure for continued use of the safety program.
The dependent t test looked for a statistically significant difference in in lost-time-hours (DV) before and after safety training (IV). The results below indicate that the mean lost-time-hours are indeed lower post-training and, more importantly, the results also indicate a p value of .0445 < .05. Therefore, the null hypothesis is rejected, and the alternative hypothesis is accepted that there is a statistically significant difference in losttime-hours (DV) before and after safety training (IV). Given these results, the company would benefit from continuing the use of the new training program implemented last year.
Reject Ho1: There is no statistically significant difference in lost-time-hours (DV) before and after safety training (IV).
Accept Ha1: There is a statistically significant difference in lost-time-hours (DV) before and after safety training (IV).
The t test is both effective and easy to use when there are only two levels (or groups) of the independent variables (e.g., Plant A training and Plant B training). If, however, the business problem requires comparing the means at more than two levels of the independent variable (e.g., Plant A training, Plant B training, and Plant C training), the t test cannot be used. In this case, ANOVA would be used to compare the DV means for more than two groups of the IV (Field, 2005).
ANOVA (Analysis of Variance, i.e., One-Way ANOVA, Single-Factor ANOVA)UNIT x STUDY GUIDE
Title
Although the calculations are different, the purpose of using ANOVA and the t test is the same. The researcher is interested in determining if there are statistically significant differences in the mean scores for the dependent variable for different groups of people or things. The difference between the t test and ANOVA is that ANOVA must be used when there are more than two groups or more than two levels of the independent variable.
Interpreting ANOVA: Interpreting ANOVA output is very similar to how other parametric test results have been interpreted thus far in the course. Like correlation, regression, and the t test, the main interest interpreting ANOVA output is whether the p value is less than the .05 alpha level. This determines whether to accept or reject the null hypothesis. Consider the following example.
A sales organization has used four different lead generation programs (IV). In the table below, columns A, B, C, and D represent the different groups of the lead generation programs, and the data represent the number of leads produced each month (DV) for a ten-month period. The ANOVA output indicates that there is a statistically significant difference in leads (DV) between lead generation programs (IV) at a p value of .00091< .05. The null hypothesis would, therefore, be rejected, and the alternative hypothesis accepted.
| One-way ANOVA | |||||||||||
| Data Set: | Statistical Results: | ||||||||||
| Program 1 | Program 2 | Program 3 | Program 4 | Anova: Single Factor | |||||||
| 98 | 83 | 79 | 69 | ||||||||
| 68 | 110 | 78 | 68 | SUMMARY | |||||||
| 56 | 98 | 84 | 76 | Groups | Count | Sum | Average | Variance | |||
| 72 | 88 | 57 | 94 | Program 1 | 10 | 750 | 75 | 176.8889 | |||
| 76 | 103 | 85 | 63 | Program 2 | 10 | 951 | 95.1 | 77.87778 | |||
| 70 | 99 | 97 | 65 | Program 3 | 10 | 830 | 83 | 123.1111 | |||
| 85 | 89 | 96 | 102 | Program 4 | 10 | 737 | 73.7 | 187.1222 | |||
| 90 | 84 | 87 | 66 | ||||||||
| 58 | 96 | 82 | 73 | ||||||||
| 77 | 101 | 85 | 61 | ANOVA | |||||||
| Source of Variation | SS | df | MS | F | P-value | F crit | |||||
| Between Groups | 2901.4 | 3 | 967.1333 | 6.846962 | 0.00091 | 2.866266 | |||||
| Within Groups | 5085 | 36 | 141.25 | ||||||||
| Total | 7986.4 | 39 | |||||||||
At this stage, when using correlation, regression, and the t test, the results provide sufficient information to answer the research questions and inform decision-making regarding the business problem. This is not true for ANOVA. Although the ANOVA results provide enough information to accept or reject the null, they do not provide complete information for decision-making. Significant ANOVA results only inform the researcher that differences exist between means. While the above ANOVA results indicate that differences exist between means, the results do not indicate where the differences exist (Field, 2005). Therefore, it is unknown whether differences exist between mean leads produced for all of the methods or only some of the methods. Fortunately, there is a post-hoc test, Tukey’s HSD that can be conducted to determine exactly where the significant differences exist between means. Once these differences are known, the sales organization can eliminate the least effective lead generation method(s). Tukey’s will not be covered in this course, but it is important to be aware of this second stage in using ANOVA to be able to make a completely informed decision.
Old Navy Scenario Using t Test and ANOVA
To elucidate the differences between t test and ANOVA, consider the following scenario.
Assume Old Navy is interested in running a multimillion-dollar promotional campaign. Their business problem is how to best allocate the promotional dollars. Since their target market includes both males and females in a range of ages, they want to determine if statistically significant differences exist in the average expenditure UNIT x STUDY GUIDE made in their stores each year. If statistically significant differences exist, they can allocate their promTitle otional dollars to more heavily target the market that spends significantly more.
Thanks to their loyalty program, they have in-house data that have been collected at the point-of-purchase and at the time of purchase. The loyalty program database includes demographic data, such as gender, age, and expenditures.
The independent variable (IV) in this scenario is the target market. The target market can be segmented into groups by gender and age range. Old Navy’s researcher is also interested in mean scores of annual expenditures, which is the dependent variable (DV).
The t test is limited to using two groups, or two levels of the independent variable. In this scenario, assume that the independent variable that will be tested is gender, and the two levels are males (IV1) and females (IV2). Since Old Navy’s database contains data for both gender and expenditure, the DV is tested for statistically significant differences in mean expenditure between males and females. The research question and hypotheses for this t test would be as follows.
RQ1: Are there differences in expenditure by gender?
Ho1: There is no statistically significant difference in expenditure (DV) between males (IV1) and females (IV2).
Ha1: There is a statistically significant difference in expenditures (DV) between males (IV1) and females (IV2).
If the t test results indicate that there is a statistically significant difference in mean expenditure by gender, the null hypothesis can be rejected, and Old Navy can make an informed decision about how best to allocate promotional dollars.
The researcher could similarly use a t test to analyze the IV of age to determine if there are statistically significant differences in the DV of expenditure. However, the t test is limited to only two groups, or two levels of the independent variable. The researcher would have to select only two levels of the IV, such as below 34 and above 35, or 25–34 and 35–44, or any other combination of two levels of age ranges. This restriction limits value that can be gleaned from the data set. A solution that may seem intuitive would be to conduct multiple t tests, but there are problems with this approach. If only three levels of the independent variable were tested (e.g., 25–34, 35–44, 45–54), it would require three separate t tests to compare group means (e.g., t test 1: 25–34 and 35–44; t test 2: 25–34 and 45–54; and t test 3: 35–44 and 45–54). If the level of independent variable was increased from 3 to 5, the number of t tests that would need to be conducted would increase to 10. It should be evident that this is a very cumbersome and impractical approach to testing for mean differences when the number of groups of the independent variable exceeds two. Another more important problem with this approach is that the chance of committing a Type I error (rejecting the null when it should not be rejected) is magnified dramatically as the number of t tests increase (Field, 2005). The lesson here is that multiple t tests should not be used. Fortunately, ANOVA avoids the problem of both complexity and magnification of the chance of Type I errors.
ANOVA does not limit the number of groups of the independent variable that can be tested. In the same scenario, each of the groups of the IV variable can be analyzed at once to determine if there are statistically significant differences in mean expenditures (DV). The different groups of the IV would be described as follows:
IV1: Under 12 years old
IV2: 12–17 years old
IV3:18–24 years old
IV4: 25–34 years old
IV5: 35–44 years old
IV6: 45–54 years old
IV7: 55–64 years old
IV8: 65–74 years old
IV9: 75 years or older
The research question and hypotheses for the ANOVA analysis would be: UNIT x STUDY GUIDE
Title
RQ2: Are there differences in expenditure by age range?
Ho2: There is no statistically significant difference in expenditures (DV) among IV1, IV2, IV3, IV4, IV5, IV6, IV7,
IV8, or IV9.
Ha2: There is a statistically significant difference in expenditures (DV) among IV1, IV2, IV3, IV4, IV5, IV6, IV7,
IV8, or IV9.
If the ANOVA results indicate that there are statistically significant differences in mean expenditure by age group, the null hypothesis is rejected. As mentioned above, the Tukey’s post-hoc test would be required to determine exactly where those significant differences exist. When Old Navy has these results, they would be empowered to make an informed decision about how best to allocate promotion dollars by age group.
Food for Thought
This unit discusses the use of t test and ANOVA. Each example used only one independent variable and one dependent variable although different groups of the independent variable were used (e.g., male and female for the independent variable of gender, and Methods 1, 2, 3, and 4 for the independent variable of lead generation method). Similarly, the examples only used one dependent variable (e.g., lost-time-hours, leads produced, and expenditures). Business problems are not always this straight-forward. There are times when the researcher will need to analyze multiple independent variables and multiple groups of those independent variables to determine if mean differences exist for the dependent variable. For those instances, a different parametric procedure called factorial ANOVA would be used. Still, there are times when the research will need to analyze multiple independent and multiple dependent variables to determine if mean differences exist. For those instances, a parametric procedure called MANOVA (multivariate analysis of variance) would be used. These parametric tests are beyond the scope of this course, but it is important to know that there is a parametric or non-parametric test to answer any research question imaginable.
References
Brewer, E. W., & Kubn, J. (2010). Casual-comparative design. In N. J. Salkind (Ed.), Encyclopedia of research design: Causal-comparative design. Retrieved from
http://methods.sagepub.com.libraryresources.columbiasouthern.edu/reference/encyc-of-researchdesign/n42.xml
Field, A. (2005). Discovering stats using SPSS (2nd ed.). London, England: Sage.
Zikmund, W. G., Babin, B. J., Carr, J. C., & Griffin, M. (2013). Business research methods (9th ed.). Mason, OH: Cengage.
Suggested Reading
Review the following videos to learn about t tests.
StatisticalLab. (2011, December 6). t test paired two sample for means by using Excel [Video file]. Retrieved form https://www.youtube.com/watch?v=KQGlxG6cmcA
Click here for a transcript of the video.
Below is a practical example of using ANOVA. UNIT x STUDY GUIDE
Title
Annenberg Learner (Producer). (2013). One-way ANOVA: Against all odds—inside statistics [Video file]. Retrieved from
https://libraryresources.columbiasouthern.edu/login?auth=CAS&url=https://fod.infobase.com/PortalPl aylists.aspx?wID=273866&xtid=111550
The transcript for the video can be found by clicking the Transcript tab next to the video in the Films o
