This analysis is looking at the relationship between ethnicity/race and freshman year science scores. Use the tables and graph included below to answer the following questions:
1. What are the null and alternative hypotheses for this analysis?
2. In a few sentences, describe the descriptive data for each ethnicity/race group (include N, mean, standard deviation, minimum, & maximum).
3. Did we violate the assumption of homogeneity in this analysis? Include evidence for your answer (i.e. how do you know?).
4. Were there significant differences in science scores between the different ethnicities?
5. Based on the results of your analysis, should you analyze the post hoc tests?
a. If yes, which groups are significantly different from each other? (List all).
b. Explain what the post hoc tests tell us about the relationship between ethnicity and science scores.
6. Complete Step 4 of hypothesis testing. Include your decision about the null hypothesis, a sentence describing the results (including post hoc tests), and the APA-style string of statistics.
7. In your own words , what is the relationship between ethnicity and science scores?
Descriptives | ||||||||
freshman yr science score | ||||||||
N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum | ||
Lower Bound | Upper Bound | |||||||
hispanic | 24 | 45.3750 | 8.21881 | 1.67766 | 41.9045 | 48.8455 | 26.00 | 63.00 |
asian | 11 | 51.4545 | 9.49067 | 2.86154 | 45.0786 | 57.8305 | 34.00 | 66.00 |
african-amer | 20 | 42.8000 | 9.44569 | 2.11212 | 38.3793 | 47.2207 | 29.00 | 61.00 |
white | 145 | 54.2000 | 9.09487 | .75529 | 52.7071 | 55.6929 | 33.00 | 74.00 |
Total | 200 | 51.8500 | 9.90089 | .70010 | 50.4694 | 53.2306 | 26.00 | 74.00 |
Test of Homogeneity of Variances | |||
freshman yr science score | |||
Levene Statistic | df1 | df2 | Sig. |
.565 | 3 | 196 | .639 |
ANOVA | |||||
freshman yr science score | |||||
Sum of Squares | df | Mean Square | F | Sig. | |
Between Groups | 3446.748 | 3 | 1148.916 | 14.021 | .000 |
Within Groups | 16060.752 | 196 | 81.943 | ||
Total | 19507.500 | 199 |
Post Hoc Tests
Multiple Comparisons | ||||||
Dependent Variable: freshman yr science score | ||||||
LSD | ||||||
(I) Ethinicy/Race | (J) Ethinicy/Race | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |
Lower Bound | Upper Bound | |||||
hispanic | asian | -6.07955 | 3.29600 | .067 | -12.5797 | .4206 |
african-amer | 2.57500 | 2.74069 | .349 | -2.8300 | 7.9800 | |
white | -8.82500* | 1.99484 | .000 | -12.7591 | -4.8909 | |
asian | hispanic | 6.07955 | 3.29600 | .067 | -.4206 | 12.5797 |
african-amer | 8.65455* | 3.39801 | .012 | 1.9532 | 15.3559 | |
white | -2.74545 | 2.83098 | .333 | -8.3285 | 2.8376 | |
african-amer | hispanic | -2.57500 | 2.74069 | .349 | -7.9800 | 2.8300 |
asian | -8.65455* | 3.39801 | .012 | -15.3559 | -1.9532 | |
white | -11.40000* | 2.15922 | .000 | -15.6583 | -7.1417 | |
white | hispanic | 8.82500* | 1.99484 | .000 | 4.8909 | 12.7591 |
asian | 2.74545 | 2.83098 | .333 | -2.8376 | 8.3285 | |
african-amer | 11.40000* | 2.15922 | .000 | 7.1417 | 15.6583 | |
*. The mean difference is significant at the 0.05 level. |
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