Group 2
Jim
Iris
Gina
Ruby
Joyce
Candy
Donna
1. French and O’Brien(2008) also performed paired-samples t-tests to see
whether the participants in the study improved on receptive vocabulary
(RVOACB), productive vocabulary (PVOCAB), and grammar measures
(GRAM).
Maximum points were 60 on both vocabulary measures and 45 on the
grammar measure.
Perform three t-tests to investigate whether the schoolchildren made
progress on these measures over the course of their English immersion.
First comment on the distribution of the data by using boxplots; then
report on the t-tests no matter whether distributions are normal or not .
Use the French and O’Brien grammar.sav file.
Case Processing Summary
Cases
Valid
N
Missing
Percent
N
Total
Percent
N
Percent
gram_1
104
100.0%
0
.0%
104
100.0%
gram_2
104
100.0%
0
.0%
104
100.0%
pvocab_1
104
100.0%
0
.0%
104
100.0%
pvocab_2
104
100.0%
0
.0%
104
100.0%
rvocab_1
104
100.0%
0
.0%
104
100.0%
rvocab_2
104
100.0%
0
.0%
104
100.0%
Answers:
1. From the boxplots, we can find the grammar participants made a lot of progress at
Time2. Because the medians increased from 16.58 to 27.24. We can also see that
there are many outliers at Time1. However, they are not very symmetrical. The
boxplot of grammar1 is a skewed distribution (positively skewed), but the boxplot
of grammar 2 shows a negatively skewed distribution.
2.The distribution for the productive vocabulary looks exactly normal because
the boxplots look very symmetrical. The participants in this group made a lot
of progress at Time2 as well. The medians increased from 30.61 to 43.
3.The boxplot of the receptive vocabulary at Time2 looks more symmetrical than at
Time1. The participants in this group made a lot of progress at Time2,too.
The medians increased from 32.81 to 38.13. We also can see that there is an outlier
at Time2.
Paired Samples Statistics
Mean
Pair 1
Pair 2
Pair 3
N
Std. Deviation
Std. Error Mean
gram_1
16.58
104
4.480
.439
gram_2
27.24
104
4.602
.451
rvocab_1
32.81
104
5.809
.570
rvocab_2
38.13
104
6.383
.626
pvocab_1
30.61
104
5.871
.576
pvocab_2
43.00
104
6.515
.639
4.From the mean scores we can say that the participants improved on
all three measures over the course of their study.
Because all the mean scores at Time2 are higher than at Time1.
Pair 1 (16.58;27.24)
Pair 2 (32.81;38.13)
Pair 3 (30.61;43.00)
Paired Samples Correlations
Correlation
N
Sig.
Pair 1
gram_1 & gram_2
104
.550
.000
Pair 2
rvocab_1 & rvocab_2
104
.851
.000
Pair 3
pvocab_1 & pvocab_2
104
.932
.000
5.We can see the correlation between the grammar is relatively large (r=0.55)
but not nearly as strong as the correlations between the vocabulary tests.
The r of the receptive vocabulary equals 0.851 and the r of the productive
vocabulary is 0.932.
Paired Samples Test
Paired Differences
Mean
Pair 1
gram_1 - gram_2
Pair 2
rvocab_1 - rvocab_2
Pair 3
pvocab_1 - pvocab_2
Std. Deviation
Std. Error Mean
-10.663
4.308
.422
-5.327
3.372
.331
-12.394
2.367
.232
Paired Samples Test
Paired Differences
95% Confidence Interval of the
Difference
Lower
Pair 1
gram_1 - gram_2
Pair 2
rvocab_1 - rvocab_2
Pair 3
pvocab_1 - pvocab_2
Upper
t
df
-11.501
-9.826
-25.245
103
-5.983
-4.671
-16.112
103
-12.854
-11.934
-53.411
103
Paired Samples Test
Sig. (2-tailed)
Pair 1
gram_1 - gram_2
.000
Pair 2
rvocab_1 - rvocab_2
.000
Pair 3
pvocab_1 - pvocab_2
.000
6. The improvement in grammar was the largest, with an average of 10.663 out
of 45 total. And the participants on average improved least on the receptive
vocabulary measure, with an average change of 5.327 points out of 60.
7. Because the p-value is zero, we can say that it is statistically significant.