Independent Worksheet # 1: A review of Introductory Statistics (including t-test and correlation)
Briefly, the study involves middle grade teachers. The schools where the data were collected are of two types: Type A schools use teaming as the instructional model. That is, content teachers (math, English, Science, etc.) work together in teams for instructional purposes. Type B schools do not use teaming. The core purpose of the study is to see if this difference in instructional format affects Self-Efficacy. The student collected data on two types of self-efficacy: Collective Self-Efficacy and Personal Self-Efficacy. Collective Self-Efficacy is the teacher's perception that the school and the teachers in the school are effective and competent. Personal Self-Efficacy is the teacher's perception of her or his own competence and effectiveness.
Descriptive statistics for Collective Self-Efficacy and Personal Self-Efficacy are presented in Table 1. For both scales the minimum score is 20 and the maximum score is 100.
Table 1a: Descriptive Statistics for Collective and Personal Self-Efficacy
|
|
Collective Self-Efficacy
|
Personal Self-Efficacy
|
|
N
|
|
110
|
110
|
|
Mean
|
56.5047
|
61.3818
|
|
Median
|
57.0000
|
61.5000
|
|
Mode
|
59.00
|
81.00
|
|
Std. Deviation
|
6.74659
|
12.61278
|
|
Variance
|
45.516
|
159.082
|
|
Skewness
|
-.854
|
.173
|
|
Kurtosis
|
.803
|
-.995
|
|
|
|
|
At-test comparing Collective Self-Efficacy and Personal Self-Efficacy was computed. For this analysis t = 4.25, p = .000, partial eta squared = .055.
Differences between male teachers and female teachers were computed. These results are presented in Table 2.
Table 2a: Means and Standard Deviations for Collective and Personal Self-Efficacy by Gender
|
|
Gender
|
N
|
Mean
|
Std. Deviation
|
|
Collective Self-Efficacy
|
Male
|
28
|
55.7500
|
7.59934
|
|
Female
|
82
|
56.8205
|
6.47622
|
|
Personal Self-Efficacy
|
Male
|
28
|
59.4643
|
10.08292
|
|
Female
|
82
|
63.8395
|
13.32240
|
Table 2b: Results of t-tests for Collective and Personal Self-Efficacy by Gender
|
|
t-test
|
df
|
Sig. (2-tailed)
|
Partial Eta Squared
|
|
Collective
Self-Efficacy
|
|
-.716
|
108
|
.476
|
.003
|
|
Personal
Self-Efficacy
|
|
-2.35
|
108
|
.015
|
.041
|
Results for teachers who do or do not work in teams are presented in Table 3:
Table 3a: Means and Standard Deviations for Collective and Personal Self-Efficacy by Team Membership
|
|
|
N
|
Mean
|
Std. Deviation
|
|
Collective Self-Efficacy
|
Team
|
86
|
56.5244
|
6.74624
|
|
Non-Team
|
24
|
56.8750
|
6.67450
|
|
Personal Self-Efficacy
|
Team
|
86
|
64.6353
|
12.39417
|
|
Non-Team
|
24
|
57.4167
|
12.84664
|
Table 3b: Results of t-tests for Team Membership
|
|
t-test
|
df
|
Sig. (2-tailed)
|
Partial eta squared
|
|
Collective
Self-Efficacy
|
|
-.224
|
108
|
.823
|
.001
|
|
Personal
Self-Efficacy
|
|
2.807
|
108
|
.004
|
.061
|
Correlations between various demographic variables and Collective and Personal Self-Efficacy are presented in Table 4:
Table 4: Correlations
|
|
|
|
Collective Self-Efficacy
|
Personal Self-Efficacy
|
|
Gender
|
Pearson Correlation
|
.070
|
.283*
|
|
Sig. (2-tailed)
|
.476
|
.015
|
|
N
|
106
|
109
|
|
Years
Teaching
|
Pearson Correlation
|
.248*
|
.216*
|
|
Sig. (2-tailed)
|
.014
|
.032
|
|
N
|
97
|
99
|
|
Degree
|
Pearson Correlation
|
.028
|
.117
|
|
Sig. (2-tailed)
|
.775
|
.225
|
|
N
|
107
|
110
|
|
Years in District
|
Pearson Correlation
|
.175
|
.140
|
|
Sig. (2-tailed)
|
.082
|
.162
|
|
N
|
99
|
101
|
|
Years in Building
|
Pearson Correlation
|
-.033
|
-.134
|
|
Sig. (2-tailed)
|
.751
|
.185
|
|
N
|
97
|
99
|
|
Years in Current Position
|
Pearson Correlation
|
-.036
|
-.135
|
|
Sig. (2-tailed)
|
.725
|
.184
|
|
N
|
97
|
99
|
|
*. Correlation is significant at the 0.05 level (2-tailed).
|
Note: Gender is scored where Males = 1 and Females = 2
Degree is scored where Bachelor's = 1; Master's = 2 and Doctorate = 3
Questions:
Q1: How would you describe this study in terms of its design? (That is, is this experimental research? If so, what kind of experiment? Is it correlational? Is it a mixed methods study? Etc.)
Q2: Does it appear that Collective Self-Efficacy and Personal Self-Efficacy are normally distributed?
Q3: Looking at the data in Table 1a, are there any issues you see that might warrant investigation in terms of the data?
Q4: What kind of t-test was used to compare Collective Self-Efficacy and Personal Self-Efficacy (the sentence after Table 1a). What does the result indicate?
Q5: What kind of t-test was used for the data in Table 2b? Interpret what these data show.
Q6: What kind of t-test was used for the data in Table 3b? Interpret what these data show.
Q7: Interpret the results of the correlations (Table 4).
Q8: Looking at the results presented, do you think the student will be happy? (That's a strange way of saying: do you think the data make any sense.)