Which test should be used one samples t test, independent samples t test or dependent samples t test and how to set up the hypothesis
An educational psychologist was interested in whether using a student’s own name in a story affected children’s attention span while reading. Six children were randomly assigned to read a story under ordinary conditions (using names like and Jane). Five other children read versions of the same story, but with each child’s own name substituted for one of the children in the story. The researcher kept a careful measure of how long it took each child to read the story. Results are shown below with longer times indicative of shorter attention spans. Using a two-tailed test, determine whether including the child’s name made a difference in attention span.
You can see that you have two samples here so you will do either an indep or dep. test.
We usually use a dependent test if we are using twins or triples, married couples or if we repeat the test with the same students and using a different criteria. That did not happen here.
So this one I will run and independent test and my hypothesis will be set as what
It depends on your book
It can be set up as
Ho: mu1 = mu 2
Ha: mu1 does not equal mu2
or other books write it as:
Ho: mu1 - mu2 = 0
Ha: mu1 - mu2 does not = 0
In this scenario, the appropriate test to use would be an independent samples t-test. The reason for this is that you have two groups of participants - one group reading the story under ordinary conditions and another group reading the story with their own name included. These two groups are independent of each other because the participants in one group do not overlap with the participants in the other group.
To set up the hypothesis for the independent samples t-test, you can use the following steps:
1. State the null hypothesis (H0): In this case, the null hypothesis would be that there is no difference in attention span between the two groups. So, you could state it as "There is no difference in attention span between children reading the story under ordinary conditions and children reading the story with their own name included."
2. State the alternative hypothesis (Ha): The alternative hypothesis would be that there is a difference in attention span between the two groups. So, you could state it as "There is a difference in attention span between children reading the story under ordinary conditions and children reading the story with their own name included."
3. Determine the level of significance (α): The level of significance, denoted as α, is the probability of rejecting the null hypothesis when it is true. Commonly used values for α are 0.05 (5%) or 0.01 (1%). Choose a level of significance that is appropriate for your study.
4. Collect data and calculate the t-test statistic: In your case, you have the times taken to read the story for both groups. Calculate the mean and standard deviation for each group and then use these values to calculate the t-test statistic.
5. Determine the critical value or p-value: Compare the calculated t-test statistic to the critical value from the t-distribution table, or use statistical software to obtain the p-value associated with the calculated t-test statistic.
6. Make a decision: If the calculated t-test statistic is greater than the critical value from the table, or if the p-value is less than the chosen level of significance (α), then you can reject the null hypothesis and conclude that there is a significant difference in attention span between the two groups. If the calculated t-test statistic is smaller than the critical value or the p-value is greater than α, then you fail to reject the null hypothesis and conclude that there is no significant difference in attention span between the two groups.
Remember to interpret your results in the context of the study and consider any limitations or factors that may have influenced the results.