Reporting Statistical Outcomes
1. Reporting Results for One Sample t-test
If there are only one or two t-tests to report, text format may be appropriate, e.g.,
IQ scores for participants in this study demonstrated a statistically significant mean difference from the national average of 100 at the .05 level of significance (M = 92.80, SD = 9.65, 95% CI –14.10 to -0.30, n = 10, t = -2.36, df = 9, p = .043). Results show that study participants have an average IQ that is lower than the national average.
Data used for the above presentation:
IQ scores: 93, 101, 105, 85, 95, 96, 81, 75, 102, 95
SPSS results/output:
One-Sample Statistics
N / Mean / Std. Deviation / Std. Error MeanIQ / 10 / 92.8000 / 9.6471 / 3.0507
One-Sample Test
Test Value = 100t / df / Sig. (2-tailed) / Mean Difference / 95% Confidence Interval of the Difference
Lower / Upper
-2.360 / 9 / .043 / -7.2000 / -14.1011 / -.2989
2. Reporting Results for the Two-Independent Samples t-test
If there are only one or two t-tests to report, text format may be appropriate, e.g.,
Statistical analysis shows that levels of achievement in geography between the cooperative learning (M = 83.33, SD = 9.57, n = 9) and lecture groups (M = 84.89, SD = 8.85, n = 9) did not differ statistically at the .05 level of significance (t = -.36, df = 16, p = .73, 95% CI for mean difference –10.77 to 7.65). Results of this experiment indicate that both cooperative learning and lecture formats of instruction appear to be equally effective.
For more than a limited number of t-tests to report, use tabular format, e.g.,
Table 3: Results of t-tests and Descriptive Statistics SAT Verbal, SAT Math, and GPA by Sex
Outcome / Group / 95% CI for Mean DifferenceMale / Female
M / SD / n / M / SD / n / t / df
SAT-Verbal / 463.81 / 98.89 / 45 / 532.21 / 101.23 / 44 / -110.56, -26.24 / -3.22* / 87
SAT-Math / 515.43 / 99.56 / 44 / 483.31 / 98.97 / 44 / -9.95, 74.20 / 1.52 / 86
College GPA / 2.71 / 1.32 / 45 / 3.16 / 1.16 / 44 / -0.97, -0.07 / -1.71 / 87
* p < .05.
Information in this table may be reported as follows:
There are statistically significant differences, at the .05 level of significance, between male and female college students in SAT verbal scores, but not with SAT mathematics or college GPA. Results show that females had higher verbal scores, but no statistical difference exists between males and females in terms of GPA or SAT mathematics scores.
Data used for the analysis of achievement by type of instruction (presented in the paragraph):
Achievement / Group / For Group, note that 1 = cooperative learning and 2 = traditional instruction85 / 1.00
76 / 1.00
100 / 1.00
95 / 1.00
84 / 1.00
73 / 1.00
71 / 1.00
82 / 1.00
84 / 1.00
87 / 2.00
78 / 2.00
99 / 2.00
94 / 2.00
87 / 2.00
79 / 2.00
69 / 2.00
86 / 2.00
85 / 2.00
SPSS results/output:
Group Statistics
SAT / N / Mean / Std. Deviation / Std. Error MeanACHIEVEM / 1.00 / 9 / 83.33 / 9.57 / 3.19
2.00 / 9 / 84.89 / 8.85 / 2.95
Independent Samples Test
Levene's Test for Equality of Variances / t-test for Equality of MeansF / Sig. / t / df / Sig. (2-tailed) / Mean Difference / Std. Error Difference / 95% Confidence Interval of the Difference
Lower / Upper
ACHIEVE / Equal variances assumed / .045 / .834 / -.358 / 16 / .725 / -1.56 / 4.34 / -10.77 / 7.65
Equal variances not assumed / -.358 / 15.905 / .725 / -1.56 / 4.34 / -10.77 / 7.66
3. Reporting Results for the Matched Samples (correlated samples) t-test
Note that matched samples t-tests (correlated samples t-test) are used when one has data from one of the following conditions:
- Naturally occurring pairs
- Two measures taken from the sample subject
- Two subjects who have been matched or paired on some variable
Results from the correlated t-test are reported in the sample manner as for the independent samples t-test. If there are only one or two t-tests to report, text format may be appropriate, e.g.,
There was statistically no change in test anxiety (n = 9, t = 0.58, r = -.29, df = 8, p = .58, 95% CI for mean difference –1.66 to 2.77), at the .05 level of significance, from before the treatment was administered (M = 4.33, SD = 1.58) to after exposure to the treatment (M = 3.78, SD = 1.99). This finding suggests that the treatment has little effect on levels of test anxiety experienced by students.
For more than a limited number of t-tests to report, use tabular format, e.g.,
Table 2: Descriptive Statistics and t-test Results for Anxiety, Efficacy, and Persistence
Outcome / Group / 95% CI for Mean DifferencePretest / Posttest
M / SD / M / SD / n / r / t / df
Anxiety / 5.80 / 1.89 / 6.12 / 1.23 / 45 / -0.48, -0.16 / .75 / -2.59* / 44
Efficacy / 5.24 / 1.56 / 5.31 / 1.97 / 45 / -0.16, 0.02 / .86 / 1.98 / 43
Persistence / 6.13 / 1.89 / 5.56 / 1.21 / 45 / 0.55, 0.83 / .90 / 4.89* / 44
* p < .05.
(Background to research problem -- a counseling intervention was tested to determine whether differences in anxiety, efficacy, and persistence would occur. Counselors expect that the intervention would lower anxiety, and increase both efficacy and persistence.)
As displayed in Table 2, there are statistically significant differences, at the .05 significance level, in pretest to posttest scores for anxiety and persistence, but not for efficacy. Results show that anxiety increased, persistence decreased, and efficacy remained unchanged after exposure to the treatment. These results suggest that the treatment had, unexpectedly, opposite effects from those anticipated.
If you perform a correlated t-test in which two groups of people are involved, then use a table that reports sample sizes separately for both groups, e.g.,
Table 3: Descriptive Statistics and t-test Results Sex and GPA
Outcome / Sex / 95% CI for Mean DifferenceMale / Female
M / SD / n / M / SD / n / r / t / df
GPA / 2.99 / 0.99 / 18 / 3.21 / 1.01 / 18 / 0.55, 0.83 / .90 / 4.89* / 17
* p < .05.
Data used for the analysis of test anxiety (pre vs. post; presented in the paragraph):
Pre- Test Anxiety / Post- Test Anxiety5.00 / 4.00
7.00 / 2.00
6.00 / 5.00
4.00 / 6.00
2.00 / 7.00
3.00 / 1.00
5.00 / 2.00
4.00 / 4.00
3.00 / 3.00
SPSS results:
Paired Samples Statistics
Mean / N / Std. Deviation / Std. Error MeanPair 1 / PRE_TA / 4.3333 / 9 / 1.5811 / .5270
POST_TA / 3.7778 / 9 / 1.9861 / .6620
Paired Samples Correlations
N / Correlation / Sig.Pair 1 / PRE_TA & POST_TA / 9 / -.292 / .446
Paired Samples Test
Paired Differences / t / df / Sig. (2-tailed)Mean / Std. Deviation / Std. Error Mean / 95% Confidence Interval of the Difference
Lower / Upper
Pair 1 / PRE_TA - POST_TA / .5556 / 2.8771 / .9590 / -1.6560 / 2.7671 / .579 / 8 / .578
4. Reporting Correlations
*********
(a) Table of Correlations– For doctoral students, one may be interested in studying anxiety toward doctoral study, students’ level of efficacy concerning doctoral study, and how these two relate to graduate GPA and student sex. Table 2 below provides an example correlation matrix of results.
Table 2. Correlations and Descriptive Statistics for Anxiety and Efficacy toward Doctoral Study, Graduate GPA, and Sex of Student
1 / 2 / 3 / 41. Doctoral Anxiety / ---
2. Doctoral Efficacy / -.43* / ---
3. Graduate GPA / -.24* / .31* / ---
4. Sex / -.11 / .19* / -.02 / ---
M / 3.20 / 4.12 / 3.92 / 0.40
SD / 1.12 / 1.31 / 0.24 / 0.51
Range / 1 to 5 / 1 to 5 / 0 to 4 / 0, 1
Cronbach’s α / .83 / .76 / --- / ---
Note. Sex coded Male = 1, Female = 0; n = 235.
* p < .05.
(b) Interpretation of Results – For inferential statistical tests, one should provide discussion of inferential findings (was null hypothesis rejected; are results statistically significant), and follow this with interpretation of results. Below is a sample of written results. (Note that separation of results into Inferential and Interpretational components was done for instructional purposes and should not occur when writing results.)
Inferential component: The focus of this study was to determine whether anxiety and efficacy toward doctoral study was related, and whether any sex differences for doctoral students were present for anxiety and efficacy. Statistical analysis revealed that efficacy toward doctoral study was negatively and statistically related, at the .05 level of significance, to students’ reported level of anxiety toward doctoral study, and positively related with students’ sex. There was not a statistically significant relationship between student sex and doctoral study anxiety.
Interpretational component: These results indicate that students’ who have higher levels of anxiety about doctoral study also tended to demonstrate lower levels of efficacy toward doctoral work. The positive correlation between sex and efficacy must be interpreted within the context of the coding scheme adopted for the variable sex where 1 = males and 0 = females. Since the correlation is positive, this means that males held higher average efficacy scores than did females. Lastly, there was no evidence in this sample that anxiety toward doctoral study differed between males and females; both sexes appeared to display similar levels of anxiety when thinking about doctoral work.
(c) Additional Examples of Possible Correlational Studies –
- How does number of hours studied per week correlate with mathematics test scores?
- Do per pupil expenditure and average teacher salary associate with CRCT mathematics and CRCT reading scores?
- The more positive a student’s attitude toward their teacher, the higher their levels of academic motivation and the better grades their grades.
**************
If there is only one correlation to report, one may report the correlation in text form rather than table form, e.g.,
Test anxiety (M = 5.00, SD = 2.74) was negatively associated (r = -.857, p = .003, n = 9) with academic self-efficacy (M = 4.33, SD = 2.24) at the .05 significance level. This correlation indicates that students with less self-efficacy tend to have higher levels of test anxiety prior to taking examinations.
For more than one correlation, use table format to condense the information, e.g.,
Table 4. Correlations and Descriptive Statistics for SAT, GRE, and GPA
SAT / GRE / College GPASAT / ---
GRE / .33 / ---
College GPA / .53* / .59* / ---
M / 490 / 497 / 2.12
SD / 93 / 95 / 0.53
* p < .05.
n = 35
Information in this table may be reported as follows:
There are positive correlations among all three variables, but only the correlations between SAT and GPA, and between GRE and GPA are statistically significant at the .05 level. These results show that both SAT and GRE scores are strong predictors of academic performance in college, with students scoring higher on the SAT or GRE also showing higher GPA scores.
Data used for the correlation between test anxiety and academic self-efficacy:
Anxiety / Efficacy1.00 / 7.00
2.00 / 5.00
3.00 / 8.00
4.00 / 4.00
5.00 / 5.00
6.00 / 3.00
7.00 / 4.00
8.00 / 2.00
9.00 / 1.00
SPSS results:
Descriptive Statistics
Mean / Std. Deviation / NANXIETY / 5.0000 / 2.7386 / 9
EFFICACY / 4.3333 / 2.2361 / 9
Correlations
ANXIETY / EFFICACYANXIETY / Pearson Correlation / 1.000 / -.857
Sig. (2-tailed) / . / .003
EFFICACY / Pearson Correlation / -.857 / 1.000
Sig. (2-tailed) / .003 / .
** Correlation is significant at the 0.01 level (2-tailed).
1 Listwise N=9
5. Reporting Chi-square
Perhaps the best presentation for 2 is the use of tables in which the raw data counts are reported, e.g.,
Table 5: Results of Chi-square Tests and Descriptive Statistics for Sex and Dropout Status
Dropout Status / SexMale / Female
Persist / 4 (40%) / 8 (80%)
Dropout / 6 (60%) / 2 (20%)
Note. Numbers in parentheses indicate column percentages.
2 = 3.33, df = 1, p = .068
There was not a statistically significant difference in dropout rates between males and females. Males had the higher dropout rate at 60%, with females showing a dropout rate of only 20%, but this difference was not greater than what could be expected by chance given the small sample size. Based upon these data, it does not appear that dropout rates differ between males and females.
See p. 624 of Huck’s (3rd ed., 2000) text to learn how to report chi-square results with more than two groups present.
Data used for dropout by sex analysis presented in paragraph form:
Dropout / sex1.00 / 1.00
1.00 / 1.00
.00 / 1.00
.00 / 1.00
.00 / 1.00
.00 / 1.00
.00 / 1.00
.00 / 1.00
.00 / 1.00
.00 / 1.00
1.00 / 2.00
1.00 / 2.00
1.00 / 2.00
1.00 / 2.00
1.00 / 2.00
1.00 / 2.00
.00 / 2.00
.00 / 2.00
.00 / 2.00
.00 / 2.00
SPSS results:
DROPOUT * SEX Crosstabulation
SEX / Totalfemale / male
DROPOUT / stay-in / Count / 8 / 4 / 12
% within DROPOUT / 66.7% / 33.3% / 100.0%
% within SEX / 80.0% / 40.0% / 60.0%
dropout / Count / 2 / 6 / 8
% within DROPOUT / 25.0% / 75.0% / 100.0%
% within SEX / 20.0% / 60.0% / 40.0%
Total / Count / 10 / 10 / 20
% within DROPOUT / 50.0% / 50.0% / 100.0%
% within SEX / 100.0% / 100.0% / 100.0%
Chi-Square Tests
Value / df / Asymp. Sig. (2-sided) / Exact Sig. (2-sided) / Exact Sig. (1-sided)Pearson Chi-Square / 3.333 / 1 / .068
Continuity Correction / 1.875 / 1 / .171
Likelihood Ratio / 3.452 / 1 / .063
Fisher's Exact Test / .170 / .085
Linear-by-Linear Association / 3.167 / 1 / .075
N of Valid Cases / 20
a Computed only for a 2x2 table
b 2 cells (50.0%) have expected count less than 5. The minimum expected count is 4.00.
6. Reporting ANOVA and Multiple Comparisons in ANOVA
Data below will be used to illustrate ANOVA reporting. The independent variable is School Type (HS, Middle, Elementary) and the dependent variable is Familial Leadership Style. For leadership style, each score represents one principle, and higher scores indicate higher levels of familial leadership behavior, with scores ranging from 1 to 100.
Elementary / Middle / High85 / 100 / 65 / 41 / 45 / 85
73 / 87 / 50 / 60 / 55
65 / 79 / 95 / 33 / 43
50 / 93 / 12 / 9 / 37
96 / 46 / 25 / 26
31 / 35 / 69
45 / 40 / 75
Research question: Of interest is whether principals of differing school types show variability in leadership behavior. Specifically, does familial behavior among principals differ by school type?
Multiple Comparisons in one-way ANOVA
Since there are more than 2 groups, multiple comparisons are needed to determine precisely which groups differ significantly from other groups. As noted in your readings, there are two categories of multiple comparison, planned and post hoc. We will treat these two types as essentially the same. In addition, I will only cover two comparison procedures, Bonferroni and Scheffe. Bonferroni is typically used for planned comparisons, and Scheffe used for post hoc comparison. In this class, I recommend using Bonferroni when 7 or fewer comparisons are to be examined, and Scheffe when more than 7 are to be examined.
To illustrate multiple comparisons in one-way ANOVA, leadership style and school type data will be used. Since there are three groups in the current example (high, middle, and elementary), there are a total of three comparisons (high vs. middle; high vs. elementary; and middle vs. elementary). Results of the multiple comparisons will be presented in both Bonferroni and Scheffe formats. Since there are three comparisons, the Bonferroni adjusted alpha is .05/3 = .0167.
Table 1: ANOVA Results and Descriptive Statistics for Leadership Style by School Type
School Type / Mean / SD / nElementary / 73.09 / 22.75 / 11
Middle / 48.00 / 24.15 / 8
High / 46.83 / 22.62 / 12
Source / SS / df / MS / F
Group / 4727.10 / 2 / 2363.55 / 4.45*
Error / 14888.58 / 28 / 531.73
Note. R2 = .241, adj. R2 = .187.
* p < .05
Table 2: Mean Differences in Familial Leadership Style by School Type
Comparison / Mean Difference / s.e. / 95% CIHigh vs. Middle / -1.167 / 10.52 / -27.97, 25.64
High vs. Elementary / -26.26* / 9.62 / -50.77, -1.75
Middle vs. Elementary / -25.09 / 10.71 / -52.38, 2.19
* p < .05, where p-values are adjusted using the Bonferroni method.
Results of the ANOVA show that there are statistically significant group differences, at the .05 level, among the three school types regarding the principal’s leadership style. Results of multiple comparisons among each of the three school types shows that the only statistically significant difference occurs between high school and elementary school principals. Differences in leadership style between middle school principals and others are not statistically significant. Elementary school principals displayed the highest average level of familial leadership style, while high school principals displayed the lowest levels (although the difference in familial leadership styles between high school and middle school principals were not statistically distinguishable).
Data used for style by school type example above are entered into SPSS in a manner similar to data entered for an independent samples t-test: one column represents the dependent variable, and one column the grouping variable.
SPSS Results using ONEWAY command:
Descriptives
STYLE
N / Mean / Std. Deviation / Std. Error / 95% Confidence Interval for Mean / Minimum / MaximumLower Bound / Upper Bound
1.00 / 11 / 73.0909 / 22.7484 / 6.8589 / 57.8083 / 88.3735 / 31.00 / 100.00
2.00 / 8 / 48.0000 / 24.1543 / 8.5398 / 27.8065 / 68.1935 / 12.00 / 95.00
3.00 / 12 / 46.8333 / 22.6227 / 6.5306 / 32.4595 / 61.2071 / 9.00 / 85.00
Total / 31 / 56.4516 / 25.5706 / 4.5926 / 47.0722 / 65.8310 / 9.00 / 100.00
ANOVA
STYLE
Sum of Squares / df / Mean Square / F / Sig.Between Groups / 4727.102 / 2 / 2363.551 / 4.445 / .021
Within Groups / 14888.576 / 28 / 531.735
Total / 19615.677 / 30
SPSS Results using GENERAL LINEAR MODEL, UNIVARIATE command:
Between-Subjects Factors
NSCHOOL / 1.00 / 11
2.00 / 8
3.00 / 12
Descriptive Statistics
Dependent Variable: STYLE
SCHOOL / Mean / Std. Deviation / N1.00 / 73.0909 / 22.7484 / 11
2.00 / 48.0000 / 24.1543 / 8
3.00 / 46.8333 / 22.6227 / 12
Total / 56.4516 / 25.5706 / 31
Tests of Between-Subjects Effects
Dependent Variable: STYLE
Source / Type III Sum of Squares / df / Mean Square / F / Sig.Corrected Model / 4727.102 / 2 / 2363.551 / 4.445 / .021
Intercept / 94233.133 / 1 / 94233.133 / 177.218 / .000
SCHOOL / 4727.102 / 2 / 2363.551 / 4.445 / .021
Error / 14888.576 / 28 / 531.735
Total / 118406.000 / 31
Corrected Total / 19615.677 / 30
a R Squared = .241 (Adjusted R Squared = .187)
For the Scheffe procedure for multiple comparisons, the table is presented in the same format except for the footnote by the alpha level.
Table 2: Mean Differences in Familial Leadership Style by School Type
Comparison / Mean Difference / s.e. / 95% CIHigh vs. Middle / -1.167 / 10.52 / -28.37, 26.04
High vs. Elementary / -26.26* / 9.63 / -51.14, -1.38
Middle vs. Elementary / -25.09 / 10.72 / -52.79, 2.60
* p < .05, where p-values are adjusted using the Scheffe method.
SPSS Results using either ONEWAY or GENERAL LINEAR MODEL, UNIVARIATE:
Multiple Comparisons Dependent Variable: STYLE
Mean Difference (I-J) / Std. Error / Sig. / 95% Confidence Interval(I) TYPE / (J) TYPE / Lower Bound / Upper Bound
Scheffe / 1.00 / 2.00 / 25.0909 / 10.715 / .082 / -2.6038 / 52.7856
3.00 / 26.2576 / 9.626 / .037 / 1.3783 / 51.1369
2.00 / 1.00 / -25.0909 / 10.715 / .082 / -52.7856 / 2.6038
3.00 / 1.1667 / 10.525 / .994 / -26.0378 / 28.3711
3.00 / 1.00 / -26.2576 / 9.626 / .037 / -51.1369 / -1.3783
2.00 / -1.1667 / 10.525 / .994 / -28.3711 / 26.0378
Bonferroni / 1.00 / 2.00 / 25.0909 / 10.715 / .080 / -2.1939 / 52.3757
3.00 / 26.2576 / 9.626 / .033 / 1.7465 / 50.7686
2.00 / 1.00 / -25.0909 / 10.715 / .080 / -52.3757 / 2.1939
3.00 / 1.1667 / 10.525 / 1.000 / -25.6352 / 27.9685
3.00 / 1.00 / -26.2576 / 9.626 / .033 / -50.7686 / -1.7465
2.00 / -1.1667 / 10.525 / 1.000 / -27.9685 / 25.6352
* The mean difference is significant at the .05 level.
7. Analysis of Covariance (ANCOVA) with Multiple Comparisons
ANCOVA is appropriate for any situation in which one has one or more qualitative independent variables (e.g., sex, race) and a quantitative dependent variable (e.g., achievement, time to complete a task, various attitudinal scores). This description resembles that for one-way and two-way ANOVA. The difference is that ANCOVA can also add quantitative independent variables (e.g., IQ scores) to serve as covariates (control variables). In short, ANCOVA can have qualitative AND quantitative independent variables, and a quantitative dependent variable.
If more than two groups are compared with ANCOVA, then one must perform follow-up tests (multiple comparisons) to determine precisely where differences occur. A key difference between multiple comparisons for ANCOVA and that performed for ANOVA is that the comparisons within ANCOVA are made on the adjusted means rather than the observed means.
ANCOVA Data: The qualitative independent variable is type of instruction (cooperative, lecture, self-guided); the quantitative independent variable is prior achievement level as measured by a standardized achievement test taken in a prior grade (scores ranged from 1 to 100); and the dependent variable is reading achievement as measured by a final test in a class (scores range from 1 to 100).
Reading Achievement / Type of Instruction / Prior Reading Achievement83 / CL / 85
82 / CL / 77
74 / CL / 72
79 / CL / 80
93 / CL / 86
91 / Lec / 84
85 / Lec / 79
97 / Lec / 75
76 / Lec / 72
65 / SG / 68
76 / SG / 80
80 / SG / 75
69 / SG / 74
90 / SG / 92
Note. Types of instruction are: CL = cooperative learning, Lec = lecture, SG = self-guided.
Research question: Does reading achievement vary by type of instruction once prior reading is taken into account? Results are presented on next page.
Results of ANCOVA on next page.
Table 1: Descriptive Statistics for Prior Reading Achievement by Instruction Type Group
Type of Instruction / Prior Reading AchievementMean / SD / n
Cooperative Learning / 80.00 / 5.79 / 5
Lecture / 77.50 / 5.20 / 4
Self-guided / 77.80 / 9.01 / 5
Note. ANOVA F (2,11)= 0.18, MSE = 49.07, p = .837, ns.
Results of Table 1 show that the three groups did not differ statistically on prior reading achievement levels. Table 2 presents results of ANCOVA of reading achievement and Table 3 contains the multiple comparisons among the groups.
Table 2: ANCOVA Results and Descriptive Statistics for Reading Achievement by Instruction Type
Type of Instruction / Reading AchievementObserved Mean / Adjusted Mean / SD / n
Cooperative Learning / 82.20 / 80.77 / 6.98 / 5
Lecture / 87.25 / 88.21 / 8.96 / 4
Self-guided / 76.00 / 76.67 / 9.77 / 5
Source / SS / df / MS / F
Prior Achievement / 492.29 / 1 / 492.29 / 15.14*
Instruction / 298.73 / 2 / 149.37 / 4.59*
Error / 325.26 / 10 / 32.53
Note. R2 = .705, Adj. R2 = .617, adjustments based on prior achievement mean = 78.50. Interaction between prior achievement and instruction was not statistically significant at the .05 level (F = 0.07, p = .938) and was removed from the model. (Note EDUR 8131: The last statement here would normally be included, but we will not cover interactions, so the last statement will not be included in ANCOVA results for EDUR 8131. For students in EDUR 8132, interactions may be covered so this statement would be included if the interaction were dropped.)
* p < .05
Table 3: Multiple Comparisons of Reading Achievement by Instruction Type
Comparison / Mean Difference / s.e. / 95% CICL vs. Lec / -7.44 / 3.88 / -18.56, 3.68
CL vs. SG / 4.10 / 3.65 / -6.37, 14.57
Lec vs. SG / 11.54* / 3.83 / 0.55, 22.52
Note. Mean comparisons based upon ANCOVA adjusted means controlling for prior reading achievement. CL = cooperative learning, Lec = lecture, SG = self-guided.