You think that the best sampling strategy is stratified sampling. Youd like to list the characteristics of schools in this district, then randomly select 80 schools who roughly match the demographic characteristics of the entire population of schools in this district. 40 of these would come from schools that had the experimental curriculum and 40 would come from schools that kept the old curriculum.
However, people from the school board have made the following statements regarding sampling. One well meaning school board member has argued that ""because we are interested in how successful the curriculum is, we should randomly sample 80 schools with the experimental curriculum."" The school board member who represents a middle class neighborhood has said that ""These sorts of exercises always focus on improving schools in poor areas, but what is most important is how these reforms affect the typical middle class kid at the typical middle class school. You should only sample schools whose average family income is close to the overall district-wide average."" Finally, one school board member represents a district where a number of textbook publishers are located. This member has told you ""if the new curriculum is adopted then the textbook producers in the city will benefit by getting tons of orders for new books. You need to think about the greater good here; adopting the new curriculum would be a boon to the city in these hard financial times. You should sample the best performing schools with the new curriculum and the worst performing schools with the old curriculum in the sample...the bigger we can make the impact look, the greater the support will be to adopt the new curriculum district wide.""
Describe what is wrong methodologically with each of the three suggestions you received from the various school board members. You will want to focus on issues such as sampling error, the sorts of biases that will be introduced from such sampling methods, how you might expect to see those biases manifested in the data/data analysis, and how these issues will affect your ability to comment on the district's original question as to whether or not it would be a good idea to roll out the new curriculum to all schools in the district.
1. Randomly sampling 80 schools with the experimental curriculum: The problem with this suggestion is that it ignores the representation of schools with the old curriculum. By only focusing on schools with the experimental curriculum, there will be no comparison group to assess the impact of the new curriculum. This will lead to biased results and will not provide an accurate assessment of the effectiveness of the new curriculum compared to the old curriculum.
2. Sampling schools with an average family income close to the overall district-wide average: While it is important to consider the impact of the reforms on middle-class students, limiting the sample only to schools with a similar average family income will introduce a bias. The sample will not represent the full diversity of schools in the district, and the results will not be generalizable to the entire population. This approach also ignores the potential impact of the curriculum on schools with different socioeconomic backgrounds.
3. Sampling the best performing schools with the new curriculum and the worst performing schools with the old curriculum: This suggestion introduces a biased sampling method by selectively choosing schools based on their performance. By only including the best performing schools with the new curriculum and the worst performing schools with the old curriculum, the results will be skewed and will not provide a balanced assessment of the curricular effectiveness. It will only highlight extreme cases and may not accurately represent the overall impact of the new curriculum.
These methodological issues will compromise the validity and reliability of the study's findings. The biased sampling methods will introduce selection biases, leading to an unrepresentative sample. This, in turn, will impact the generalizability of the results and limit the ability to make accurate conclusions regarding the district's question of whether to adopt the new curriculum district-wide. To ensure accurate and unbiased results, it is crucial to employ a stratified sampling strategy that considers the characteristics of all schools in the district and randomly selects a representative sample from each stratum.
1. Randomly sampling only schools with the experimental curriculum:
The well-meaning school board member argues for randomly sampling only schools with the experimental curriculum. While random sampling is generally a good practice, this method would introduce a bias in the sample. By excluding schools with the old curriculum, we are not accounting for the comparison between the two curricula. Consequently, we would not be able to assess the effectiveness of the new curriculum relative to the old one. This bias would hinder our ability to determine whether it would be a good idea to roll out the new curriculum district-wide.
2. Sampling schools based on average family income:
The school board member representing the middle-class neighborhood suggests sampling schools whose average family income is close to the overall district-wide average. This approach introduces a bias towards middle-class schools, neglecting the impact of the new curriculum on schools with different income levels. It is essential to consider the variation in socioeconomic backgrounds within the district to evaluate the effectiveness of the curriculum for all students, regardless of their family income. By focusing only on middle-class schools, the analysis would not capture the full range of effects and could lead to inaccurate conclusions about the benefits of the new curriculum.
3. Sampling the best performing schools with the new curriculum and the worst performing schools with the old curriculum:
The school board member representing the district with textbook publishers proposes sampling the best performing schools with the new curriculum and the worst performing schools with the old curriculum. This approach introduces selection bias. By only including the best-performing schools with the new curriculum, we are likely to overestimate the impact of the new curriculum on student outcomes. Similarly, by only including the worst-performing schools with the old curriculum, we are likely to underestimate the effectiveness of the old curriculum. This biased sampling would distort the comparison between the two curricula, making it difficult to draw accurate conclusions about the relative merits of each. It would also fail to represent the entire population of schools, making it challenging to generalize the findings to the district as a whole.
To effectively assess the benefits and drawbacks of rolling out the new curriculum district-wide, it is crucial to use a stratified sampling strategy that ensures representation of schools with different demographic characteristics. By randomly selecting a sample of 80 schools, with 40 from schools with the experimental curriculum and 40 from schools with the old curriculum, we can minimize bias and gather comprehensive data on the curriculum's impact. This approach will provide a more accurate basis for evaluating the new curriculum's effectiveness and inform the decision on whether to adopt it throughout the district.