24. Rosalie Friend (2001), and educational psychologist, compared three methods of teaching writing. Students were randomly assigned to three different experimental conditions involving different methods of writing a summary. At the end of the two days of instructions, participants wrote a summary. One of the ways it was scored was the percentage of specific details of information it included from the original material. Here is a selection from her article describing one of the findings:
The effect of summarization method on inclusion of important information was significant F(2, 144) = 4.1032, p < .019. The mean scores (with standard deviations in parantheses) were as follows: Argument Repetition, 59.6% (17.9); Generalization, 59.8% (15.2); and Self-Reflection, 50.2% (18.0). (p.14)
a. Explain these results to a person who has never had a course in statistics.
b. Using the information in the preceding description, figure the effect size for the study.
a. These results are from a study comparing different methods of teaching writing. The researcher had three different groups of students, and each group was taught a different method of summarizing information. After two days of instructions, the students were asked to write a summary. One of the ways the summaries were evaluated was based on the percentage of specific details they included from the original material.
The researcher found that the method of summarization used had a significant effect on the inclusion of important information in the summaries. This means that the different teaching methods had different impacts on how well the students incorporated important details into their summaries.
To further explain, statistical analysis was performed on the data collected. The result of this analysis was represented by the numbers stated: F(2, 144) = 4.1032, p < .019. The F-value represents the significance of the effect, while the numbers in the parentheses indicate the mean scores and standard deviations for each group. The three groups had mean scores of 59.6% (with a standard deviation of 17.9) for the Argument Repetition method, 59.8% (with a standard deviation of 15.2) for the Generalization method, and 50.2% (with a standard deviation of 18.0) for the Self-Reflection method. These numbers provide insights into the differences in performance between the three groups.
b. To calculate the effect size for the study, additional information is required. Effect size is typically measured using Cohen's d, which compares the difference between two groups mean scores to the standard deviation of the overall distribution. In this case, we need the mean scores and standard deviations for each group, as well as the sample sizes.
Since the information provided doesn't include the sample sizes, it is not possible to calculate the effect size for the study.
a. To explain these results to someone without a background in statistics, we will break down the information step by step:
1. The first part of the statement displays the statistical analysis used in the study. The notation "F(2, 144) = 4.1032, p < .019" provides information about the statistical test used, the degrees of freedom, the test statistics (F-value), and the level of significance (p-value).
2. The F-value (4.1032 in this case) is a measure of how different the means of the three experimental conditions were. A larger F-value indicates a greater difference between the group means.
3. The p-value (< .019) represents the level of significance. It indicates the probability of obtaining these results by chance alone. In this case, the p-value is less than .05, suggesting that the differences observed between the experimental conditions are unlikely to have occurred randomly.
4. The second part of the statement provides the mean scores (percentage of specific details included in the summary) for each experimental condition. It also includes the standard deviation for each mean, which represents the variability of scores within each condition.
In summary, the results indicate that there was a significant difference in the inclusion of important information among the three methods of summarization. Specifically, the Argument Repetition and Generalization methods had higher mean scores (59.6% and 59.8%) compared to the Self-Reflection method (50.2%). The standard deviations show the variability within each condition, suggesting that some participants within each group may have performed better or worse than the mean score.
b. To calculate the effect size for the study, we can use the mean scores provided in the results. Effect size is a measure of the strength or magnitude of a statistical relationship or difference.
In this case, we can use the formula for Cohen's d, which is one commonly used effect size measure:
Effect Size (d) = (mean1 - mean2) / pooled standard deviation
Let's use the mean scores from the results:
Mean1 = 59.6
Mean2 = 50.2
We also need the pooled standard deviation. The formula for calculating pooled standard deviation is:
pooled standard deviation = sqrt((SD1^2 + SD2^2) / 2)
Using the standard deviations from the results:
SD1 = 17.9
SD2 = 18.0
Now we can calculate the pooled standard deviation:
pooled standard deviation = sqrt((17.9^2 + 18.0^2) / 2)
pooled standard deviation = sqrt((320.41 + 324.00) / 2)
pooled standard deviation = sqrt(644.41 / 2)
pooled standard deviation = sqrt(322.205)
pooled standard deviation ≈ 17.95
Now, we can substitute the values into the formula for effect size:
Effect Size (d) = (59.6 - 50.2) / 17.95
Effect Size (d) ≈ 0.524
Therefore, the effect size for this study is approximately 0.524. This indicates a moderate effect size, suggesting a reasonably meaningful difference between the experimental conditions in terms of the inclusion of important information in the summaries.