Two T-Test Coursework Example

Two T-Test
Name
Institution
Two T-Test
Scenario 1

In the comparison of the pre to post test on measure one, the sample cases that were considered numbered 22, which fell under the recommended tests for T-Tests. The sample space had 21 degrees of freedom and resulted in a mean of 9.1364 for the pretest score, and 7.7727 for the posttest scores. The median scores were 8.5 and 7.0 for the pretest and posttest measures respectively. The descriptive statistics indicated that all the data input was valid with zero missing entities.

Statistics
Pretest score on first reading comprehension measure Posttest score on first reading comprehension measure
N Valid 22 22
Missing 0 0
Mean 9.1364 7.7727
Median 8.5000 7.0000
Mode 6.00a 4.00
Std. Deviation 3.34230 3.92710
Variance 11.171 15.422
Skewness .004 .260
Std. Error of Skewness .491 .491
Kurtosis -1.450 -.975
Std. Error of Kurtosis .953 .953
Range 10.00 14.00
Minimum 4.00 1.00
Maximum 14.00 15.00
Sum 201.00 171.00
Percentiles 25 6.0000 4.0000
50 8.5000 7.0000
75 12.2500 11.2500
a. Multiple modes exist. The smallest value is shown

The frequency distribution of the pre-tests and post-test scores were spread out, differently as shown in the histograms below. In the pretest scores, there were two distinct peaks, which did not follow the normal distribution curve but appeared to form two separate normal distribution curves. The posttest curve, on the other hand, appears to follow a normal distribution curve.

In regards to the improvement of scores, there was a lower score in the post-test, considering the average score of the students.

Accordingly, this suggested an overall improvement in the pre and post measure 1 assessment.

One-Sample Test
Test Value = 0
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
Pretest score on first reading comprehension measure 12.821 21 .000 9.13636 7.6545 10.6183
Posttest score on first reading comprehension measure 9.284 21 .000 7.77273 6.0316 9.5139

Considering the T-Test, the t-test values were 12.821 and 9.284 for the pretest and posttest scores. Whereas the p-value for both cases was p=0.00. The results suggest an improvement in the Strategy instructions, due to the lower scores posttest, with the distribution of the scores being normalized following the instructions. Based on the research, there appears to be no significant effect of the STRAT method of instructing, and since there is no other method to make the comparison with, there are only the scores from the students to consider. Which suggest that there is an improvement in the texts after the period of instruction.
Scenario 2
The second test case considers the differences in outcome for the STRAT and DRTA approaches of instruction. The STRAT approach is analyzed based on the number of errors, which suggests that lower error numbers translate to improvement, whereas the DRTA approach considers higher scores as a better outcome. Having selected both cases, as instructed, the results considered all scores and therefore means of 8.8182 and 7.5 for posttest measures one and two. Using this approach does not provide any information on the different teaching strategies.

Statistics
Posttest score on first reading comprehension measure Posttest score on second reading comprehension measure
N Valid 44 44
Missing 0 0
Mean 8.8182 7.5000
Median 9.0000 7.0000
Mode 11.00 6.00
Std. Deviation 3.39132 2.57447
Variance 11.501 6.628
Skewness -.207 -.141
Std. Error of Skewness .357 .357
Kurtosis -.601 .616
Std. Error of Kurtosis .702 .702
Range 14.00 13.00
Minimum 1.00 .00
Maximum 15.00 13.00
Sum 388.00 330.00

In considering the different approaches, STRAT, and DRTA, the posttest scores for both groups revealed a detailed result for both groups. For the STRAT group, moving from the first to the second reading comprehension, there was an increase of the scores from 7.7727 to 8.7727, which indicated more errors in the comprehension and no improvement, but rather a deterioration in the approach. Similarly, the results for the DRTA group indicated that there were no improvements from the first to the second reading comprehension test, with the mean score reducing from 9.8636 to 6.2273.

Group Statistics
Group Membership N Mean Std. Deviation Std. Error Mean
Posttest score on first reading comprehension measure STRAT 22 7.7727 3.92710 .83726
DRTA 22 9.8636 2.41613 .51512
Posttest score on second reading comprehension measure STRAT 22 8.7727 2.40895 .51359
DRTA 22 6.2273 2.09152 .44591

The resultant t-test scores indicated that the null hypothesis should be rejected with all the cases resulting in a score lower than 0.05-confidence level of 95%. In the assessment, the incorporation of groups resulted in the t-static tests being negative for the first posttest scores, t=-2.127, whereas for the second posttest were positive t=3.742. The p values for the first comprehension posttest according to the Levene test was p=0.011, while that of the second posttest was p=0.187, which meant that the null hypothesis could be adopted for the second posttest.

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
Posttest score on first reading comprehension measure Equal variances assumed 7.123 .011 -2.127 42 .039 -2.09091 .98303 -4.07475 -.10707
Equal variances not assumed -2.127 34.906 .041 -2.09091 .98303 -4.08676 -.09506
Posttest score on second reading comprehension measure Equal variances assumed 1.800 .187 3.742 42 .001 2.54545 .68016 1.17284 3.91807
Equal variances not assumed 3.742 41.188 .001 2.54545 .68016 1.17204 3.91887

Self-Reflection
The process of analyzing data using software is simpler to that of hand-written calculations, in addition to being time-saving, but it requires an understanding of statistics from the first principles. The data that was contained in the analysis was entered with no errors, from the 100% validity of the results, and one needed to understand the groupings that were incorporated in the data. The software may not be easily customizable as a personal notebook, but with the right approach to the data, it is possible to have all the information that one needs to be organized and produced in an easy-to-interpret manner.
The choices for analysis that were presented in the software were numerous, with each demanding a specific type of entity, from the variables to the groupings, and some errors were produced along the way. It was important to refer to past works and other notes on the use of the SPSS tool, to gain a better understanding of the processes that were running in the background, to get the data that one required. An assessment of the arguments and test that were being conducted in the test were necessary to make sense of the outputs from the t-test analysis since the software does not develop the hypotheses.