Practical Connection Assignment
Kishan@1529
ANOVAnewlessonFall20161.pptxReview:
t-tests
Practice #1: Independent samples t-test
Does wind or solar energy cost less for factories?
Practice #1 Answer
Wind energy (M= 474.53) was significantly less expensive than solar energy (M= 654.55) to run a factory, (t [20] = 1.9, p < .05).
Practice #2: Paired Samples t-test
Practice #2: Answer
There was a significant difference in employee participation after the seminar (M = 39.8) when compared to the participation pre seminar (M = 38.4), (t [9] = 2.50, p < .05).
ANOVA
(Analysis of Variance)
Statistical Tests:
In general, it is always important to remember the questions that are asked in any study you perform. Virtually everything you do from writing the research design to writing the study’s implications is dictated by the research questions. In our previous lesson, we looked at differences between two groups, but what if you have more than two groups? The ANOVA will tell us if there is a significant difference between three or more groups-however it will not tell us where. We will use post-hoc testing to determine where the significant difference occurs.
7
Analysis of Variance
The ANOVA
We are going to focus on chapter 11, one-way classification (one way means one independent variable).
Null hypothesis= all populations are the same. If p < .05, we can reject the null and need further analysis. This means there is a difference, we can use an independent sample t-test to determine the differences.
Excel: ANOVA Single Factor
Spatz: Table F = F Distribution
UC Handbook: p. 23-24
An example from a dissertation:
Small Group Reading Results for Ability Groups
An ANOVA test was used to compare changes in MAP scores among low, average, and high achieving students in the experimental group. Data in Table 3 indicated that there was a significant difference between academic achievements among the groups. The results of the ANOVA show that small group reading instruction produced higher academic outcomes in low achieving students (M = 23.27) when compared to average achieving students (M = 17.88), and high achieving students (M=16.15), (F [2, 109] = 3.89, p < .05).
Her data in excel:
See p < .05
(F [2, 109] = 3.89, p < .05)
F Distribution Table
(F [2, 109] = 3.89, p < .05)
Even though, the excel stats pack gives you the significance, you can also check in the Spatz book, table F. The F statistic is larger than the top value (.05), but not the bold value (.01). The same as we saw in our excel data.
Note on the dissertation results:
Since the results indicated there was a difference in scores, the researcher completed three independent sample t-tests to see where the differences occurred.
FYI: Statistically significant differences were revealed between the low and average achieving students (t [92] = 1.98, p < 0.05), and between the low and high achieving students (t [35] = 2.03, p < 0.05).
Let’s try an ANOVA
A UC doctorate student wanted to determine if there were differences in knowledge of dyslexia among Kentucky Educators. She piloted a survey, and then once reliability was determined, administered the survey to four groups.
Select an ANOVA
Enter Data in columns.
2. Select Data tab.
Select Data analysis.
Select Anova: Single Factor.
Click OK.
Next steps:
6. Input Range: Highlight all data.
7. Grouped by: select columns.
8. Click “Labels in first row.”
9. Leave alpha at 0.05.
10.Select an area for Output Range.
11. Click OK.
The results:
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| Elementary | 43 | 2563 | 59.60465 | 307.1495 | ||
| Middle | 40 | 2538 | 63.45 | 149.0231 | ||
| Special Education | 32 | 2237 | 69.90625 | 132.6038 | ||
| Guidance | 31 | 1865 | 60.16129 | 219.7398 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 2279.737 | 3 | 759.9125 | 3.668442 | 0.013862 | 2.668337 |
| Within Groups | 29415.09 | 142 | 207.1485 | |||
| Total | 31694.83 | 145 |
(f [3, 142] = 3.67= p < .05)
How many post-hoc tests are needed?
ANOVA:
Post-hoc testing
ANOVA: Post-hoc tests
The ANOVA is used to determine a difference in groups, but when examining three or more groups, it does not indicate where the differences occur.
Always defer to your dissertation advisor or editor on selection of post-hoc tests.
Let’s look at an example.
Post-hoc test examples:
Independent samples t-test
Tukey’s HSD
Bonferroni
Scheffe
Example:
ANOVA results
There was a significant difference between training and degree (M=91.8), training only (M = 74.67), and degree only (M=71) employee performance, (f [2,23] = 13.22, p < .001). Post-hoc tests are needed.
Excel: Independent Samples t-tests
Step 1: Select the independent samples t-test (two sample assuming equal variances). Examine columns A and B.
Step 2
Step 2: Select the independent samples t-test (two sample assuming equal variances). Examine columns A and C.
Step 3
Step 3: Select the independent samples t-test (two sample assuming equal variances). Examine columns B and C.
Post-hoc results:
There was a significant difference between training and degree (M = 91.8) and training only employees (M = 74.67), (t [17] = 5.84, p < .001).
There was a significant difference between training and degree (M = 91.8) and degree only employees (M = 71), (t [15] = 4.31, p < .001).
There was no significant difference between training only (M = 74.67) and degree only employees (M = 71), (t [14] = 0.66, p > .05).
SPSS
The Tukey HSD, Scheffe, and Bonferroni all indicate the same differences (significant differences between training and degree-training only, and training and degree-degree only.
