The Excel output is:
Mean | n | Std. Dev | ||||
11.8 | 5 | 4.15 | 15 mg | |||
15.0 | 5 | 3.74 | 20 mg | |||
18.4 | 5 | 2.51 | 25 mg | |||
21.0 | 5 | 4.30 | 30 mg | |||
11.6 | 5 | 2.70 | 35 mg | |||
15.6 | 25 | 4.97 | Total | |||
ANOVA table | ||||||
Source | SS | df | MS | F | p-value | |
Treatment | 338.96 | 4 | 84.740 | 6.69 | .0014 | |
Error | 253.20 | 20 | 12.660 | |||
Total | 592.16 | 24 | ||||
Post hoc analysis | ||||||
p-values for pairwise t-tests | ||||||
35 mg | 15 mg | 20 mg | 25 mg | 30 mg | ||
11.6 | 11.8 | 15.0 | 18.4 | 21.0 | ||
35 mg | 11.6 | |||||
15 mg | 11.8 | .9301 | ||||
20 mg | 15.0 | .1465 | .1704 | |||
25 mg | 18.4 | .0067 | .0082 | .1465 | ||
30 mg | 21.0 | .0005 | .0006 | .0148 | .2616 | |
Tukey simultaneous comparison t-values (d.f. = 20) | ||||||
35 mg | 15 mg | 20 mg | 25 mg | 30 mg | ||
11.6 | 11.8 | 15.0 | 18.4 | 21.0 | ||
35 mg | 11.6 | |||||
15 mg | 11.8 | 0.09 | ||||
20 mg | 15.0 | 1.51 | 1.42 | |||
25 mg | 18.4 | 3.02 | 2.93 | 1.51 | ||
30 mg | 21.0 | 4.18 | 4.09 | 2.67 | 1.16 | |
critical values for experimentwise error rate: | ||||||
0.05 | 2.99 | |||||
0.01 | 3.74 |
The plot is:
Yes, there is a significant difference.
Since the p-value (0.0014) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we have sufficient evidence to conclude that there is a significant difference.
The post-hoc analysis shows that 25 mg and 35 mg is significant.
Therefore, food additives have different effects.
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please answer all the questions and explain and write clearly what do you mean this is...
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