Simply reporting measures of central tendency or measures of variability will not tell the whole story. Using the following information, what else does a psychologist need to know or think about when interpreting this information?
A school psychologist decided to separate some classes by gender to see if learning improved. She looked at student scores on the final exam and obtained the following information: Students in boy-girl classrooms obtained an average of 71.4 on their final exams with a standard deviation of 10.8 whereas students in single-gendered classrooms obtained an average of 75.9 on their final exams with a standard deviation of 8.2. She concludes that the single-gendered classrooms lead to better learning.
I would be curious if one single-gendered classes did better than the other too. I would want to separate into all-boy and all-girl data. The difference between combined and separated data might be due solely to one gender or the other.
When interpreting the information provided, there are several important factors that a psychologist should consider:
1. Sample Size: The psychologist should consider the number of students in each group. A larger sample size generally leads to more reliable results, whereas smaller sample sizes may be more susceptible to outliers or chance variations. Without knowing the sample sizes of each group, it is challenging to draw definitive conclusions.
2. Statistical Significance: It is important to determine whether the observed differences in exam scores between the two classroom types are statistically significant. This can be assessed by conducting a statistical test, such as a t-test or an analysis of variance (ANOVA). These tests determine the probability that the observed differences are due to chance or if they represent a true difference. Without conducting a statistical test, one cannot confidently claim that single-gendered classrooms lead to better learning.
3. Other Factors: Different factors might contribute to the differences observed in exam scores. For example, the quality of instruction, teacher effectiveness, student motivation, and prior academic performance can all influence learning outcomes. It is crucial to consider if any other factors might be influencing the results and to control for them if possible. A controlled experiment with random assignment of students to different classroom types would help address these potential confounding variables.
4. External Validity: The psychologist should also consider the generalizability of the findings. The study focused on a specific school or set of classes, so it is essential to consider whether the results can be applied to other settings or populations. It is possible that the effects observed in this specific context may not hold true in different educational settings.
In summary, simply reporting the measures of central tendency (average) and variability (standard deviation) does not provide enough information to draw definitive conclusions. To interpret the information correctly, a psychologist should consider sample size, statistical significance, other influencing factors, and the external validity of the results.