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Independent Sample t Test (~SPSS),
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Goal(s): Increased experience with the independent sample t test. Gain expertise with how to handle interpreting Levene's Test of Equality of Variances. Interpret the "Sig. (2-tailed)," depending upon whether it is a one-tail or two-tail hypothesis test. Recognize that if the result is considered "statistically significant," then the null hypothesis is rejected.
How: For each scenario presented, evaluate Levene's Test of Equality of Variances. Take into consideration whether it is a one-tail or two-tail hypothesis test. Evaluate the "Sig. (2-tailed)" result, and decide whether to reject the null hypothesis. Make 30 quick decisions, with immediate feedback.
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About
About
For this activity, the terms "Null Hypothesis Distribution" and "Ho: Null Distribution" are both used to indicate a distribution of sample means as specified by the null hypothesis.
Independent Sample t Test (~SPSS): The Purpose
Independent Sample t Test (~SPSS): The Purpose
In grade school many of us conducted the classic experiment, where there is a treatment group and a control group. After applying the treatment, we then evaluated whether a difference could be found between the treatment and control groups. The control group was our comparison, and nothing special was done with it.
To reject the null hypothesis, we want the difference between the two groups to be clear. Ideally, there would be a large difference between the treatment and control group. Within each group, the less variability the better. In this way, it would be obvious to all that a true difference exists between the two groups.
In order to use the "standard" Independent Samples t Test, the amount of variability in both groups (e.g., treatment and control) must be similar.
Levene's Test for Equality, t test and p value
Levene's Test for Equality, t test and p value
An assumption of the Independent Samples t Test is for equality of variances. That is to say, the expectation is that both groups (e.g., the experiment and control group) have roughly the same amount of variability. Levene's test for equality of variance actually assesses that assumption. Finally, the Independent Samples t Test results are provided for both possibilities - that the two groups are:
Similar in their variability
Different in their variability
If Levene's Test is not significant (i.e., the Sig. is greater than .05), then "Equal variances is assumed." Alternatively, if Levene's Test is significant (i.e., the Sig is less than or equal to .05), then "Equal variances not assumed." Read the results directly below the specified assumption.
Retain the Null Hypothesis. In this example, the two means are fairly similar. Levene's Test Sig. is 0.139, which is greater than .05, so equal variances is assumed. That row reads, "t: 0.4, df: 59, Sig. (2-tailed): 0.692". The t test is small, and the Sig. (2-tailed) is large.
A t test statistic that is close to zero indicates that the difference found between the two means is fairly common. When the t test is close to zero, you will see a corresponding large p value. This indicates that there is a high probability of getting this outcome when the null hypothesis is true. Given that the result was consistent with the null hypothesis, we retain the null hypothesis.
Reject the Null Hypothesis. In this example, the two mains are fairly different from one another. Levene's Test Sig. is 0.006, which is smaller than .05, so equal variances are not assumed. That row reads, "t: 2.7, df: 30.89, Sig. (2-tailed): 0.011". The t test is large, and the Sig. (2-tailed) is small.
The clearer the difference between the two groups (e.g., a large difference in means and/or little variability within each group), the further the t test statistic is from zero. When the t test statistic is further from zero, the reported p value will be smaller. A low p value indicates that getting this outcome is unusual when the null hypothesis is true. For a two-tailed test, if the p value is equal to or less than the alpha level, then the null hypothesis is rejected.
Alpha Level & Hypothesis Testing
Alpha Level & Hypothesis Testing
For this game, you will always be given the results as if for a two-tail test. What does it mean? You, the end user, must take into consideration whether it is a one-tailed or two-tailed hypothesis test.
After determining whether or not equal variances can be assumed...
If a two-tailed test:
Reject the null hypothesis when the 'Sig. (2-tailed)' ≤ .05
If a one-tailed test (e.g., "Mean1 >= Mean2"):
Retain the null hypothesis if the results are consistent with the null hypothesis
Otherwise, reject the null hypothesis:
If 'Sig. (2-tailed)' ≤ (2 x alpha level).
For a one-tailed test, with the sample mean in the direction opposite of that predicted by the null hypothesis, with a p-value (2-tailed) of .09, and an alpha level of .05, we would reject the null hypothesis.Which can also be stated as: reject the null if ('Sig. (2-tailed)' / 2) ≤ .05.
In the above example, it is a one-tailed hypothesis test. The null hypothesis states that the mean for group one will be equal to or larger than that of group two. Since the results are not consistent with the null hypothesis, the next step is to consider the Sig. (2-tailed). Levene's Test for Equality of Variance is a Sig. of 0.000, which is smaller than or equal to .05, so we will go with "Equal variances not assumed." The results for that approach are, "t: -1.93, df: 60.42, Sig. (2-tailed): 0.058". We can compare the 'Sig. (2-tailed)' of .058 to .10 (a value that is double the alpha level); we reject the null hypothesis. Alternatively, one could halve the 'Sig. (2-tailed)' of 0.058 to 0.029 and compare it to the alpha level of .05; . Mathematically, these two methods will give the same result, so pick whichever approach you find easier to apply.
Game
Optional: Earning Class Credit
To earn credit for this activity:
Click the 'Accommodations' button on the game menu.
Using the number pad (in the Accommodation dialog box), type the passcode provided by your instructor.
Click the 'Continue' button. Doing so will return you back to the game menu.
Then click 'Start' to begin the game.
When you complete the task with a score of 85% or greater, you will be given a completion code. To view this completion code, click on the 'Completion Code' button.
To get credit for having completed the activity, provide the completion code as your answer (e.g., to a quiz question). If the completion code is not yet available (e.g., performance was less than 85%), then click the 'Continue' button to re-do the activity.
Accommodations include:
Screen Reader (click the 'Screen Reader' button)
Unlimited decision time (e.g., Click the 'Accommodations' button, then type #17 by itself or at the end of a passcode. Click 'Continue').
Please notify your instructor if requesting these accommodations.
Instructors can modify games and set up quizzes rather easily. Check out game modifications.
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