Question

4. Matthew collected the following data: Table 4.1 Effect of Diazinon Exposure on Tadpole Length Tadpole lenth (cm) 1.0 ppb 3.5 3.1 2.8 3.3 2.6 3.06 0.4 0.0002 0.5 ppb 0.25 ppb 4.4 3.5 3.8 4.2 4.1 4.0 0.4 0.122 Control Tadpole 1 Tadpole 2 Tadpole 3 Tadpole 4 Tadpole 5 Mean (cm) 4.4 4.6 4.2 3.8 4.3 4.26 0.3 3.1 3.4 3.7 4.0 3.3 3.5 0.4 0.003 Std Dev(cm) t-test probability NA (p-value) Based on the data presented in the table above, are any of the treatment groups significantly different from the control group? If so which groups are different and how do you know they are different?

Answer 1

Answer

We have one control group and three tadpole length groups for 0.25 ppb, 0.50 ppb and 1.0 ppb

For comparing the treatment groups with control group, we have to compare the respective p value with standard significance level 0.05

P value for treatment group 1(0.25ppb) is 0.122

P value for treatment group 2(0.50ppb) is 0.003

P value for treatment group 3(1.0ppb) is 0.0002

We know that when the p value is less than significance level, then we reject the null hypothesis and conclude that there is a significant difference between the groups

and when the p value is greater than significance level, then we fail to reject the null hypothesis and conclude that there is no significant difference between the groups.

So, it is clear that p value for group 1 is greater than 0.05, i.e. p value of 0.122 is greater than 0.05 level. So, there is no significant difference between treatment group 1 and control group

p value for group 2 is less than 0.05, i.e. p value of 0.003 is less than 0.05 level. So, there is a significant difference between treatment group 2 and control group

p value for group 3 is less than 0.05, i.e. p value of 0.0002 is less than 0.05 level. So, there is a significant difference between treatment group 3 and control group

So, group 2 (0.50 ppb) and group 3 (1.0 ppb) are different from the control group because the p value is less than significance level and thus, we have a significant difference.

p value for group 2 and 3 are significant for alpha level 0.01, 0.05 and 0.10.