State the null and alternative hypothesis and state the critical t* value ( = .0
ID: 3218404 • Letter: S
Question
State the null and alternative hypothesis and state the critical t* value ( = .05; two-tail test).
According to Levene’s test for Equality of Variances – can you assume the treatment vs. control group have equal variances for the postlet scores? Explain why or why not. Discuss which row you should look at for the correct test statistics in the output.
Write an APA style conclusion including the t-statistic, df, and 95% confidence interval.
Group Statistics
regular
N
Mean
Std. Deviation
Std. Error Mean
postlet
control
54
16.91
9.481
1.290
treatment
186
29.60
12.997
.953
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
postlet
Equal variances assumed
32.696
.000
-6.673
238
.000
-12.689
1.902
-16.435
-8.943
Equal variances not assumed
-7.911
116.658
.000
-12.689
1.604
-15.866
-9.513
Group Statistics
regular
N
Mean
Std. Deviation
Std. Error Mean
postlet
control
54
16.91
9.481
1.290
treatment
186
29.60
12.997
.953
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
postlet
Equal variances assumed
32.696
.000
-6.673
238
.000
-12.689
1.902
-16.435
-8.943
Equal variances not assumed
-7.911
116.658
.000
-12.689
1.604
-15.866
-9.513
Explanation / Answer
This gives the descriptive statistics for each of the two groups (as defined by the grouping variable.) there are 54 controls(N), and they have, on average, 16.91 controls, with a standard deviation of 9.481 controls.
There are 186 treatments (N) ,and they have, on average, 29.60 treatments, with a standard deviation of 12.997 treatments. The last column gives the standard error of the mean for each of the two groups.
The second part of the output gives the inferential statistics of the independent sample test.
The columns labeled "Levene's Test for Equality of Variances" tell us whether an assumption of the t-test has been met. The t-test assumes that the variability of each group is approximately equal. If that assumption isn't met, then a special form of the t-test should be used. Look at the column labeled "Sig." under the heading "Levene's Test for Equality of Variances". the significance (p value) of Levene's test is .000. If this value is less than or equal to your level for the test (usually .05), then you can reject the null hypothesis that the variability of the two groups is equal, implying that the variances are unequal. If the p value is less than or equal to the level, then you should use the bottom row of the output (the row labeled "Equal variances not assumed.") If the p value is greater than your level, then you should use the middle row of the output (the row labeled "Equal variances assumed.") here .000 is lesser than , so we will assume that the variances are unequal and we will use the middle row of the output.
The column labeled "t" gives the observed or calculate t value. In this example, assuming equal variances, the t value is -6.673. (We can ignore the sign of t for a two tailed t-test.) The column labeled "df" gives the degrees of freedom associated with the t test. In this example, there are 238 degrees of freedom.
The column labeled "Sig. (2-tailed)" gives the two-tailed p value associated with the test. the p value is .000. If this had been a one-tailed test, we would need to look up the critical t in a table.
so finally we reject the null hypothesis.
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