**Medical Mathematical Statistics Teaching Practice and Exploration in the New Situation**
In the new situation, medical mathematical statistics teaching practice requires deep thinking. Through a large number of investigations, it is known that the average pulse rate of healthy adult men living on plains is generally 72 beats per minute. A doctor examined the pulse rate of a group of healthy adult men living in the mountains and reported a significant difference compared to the pulse rate of healthy adult men living on the plains. The doctor aims to determine the overall pulse rate of all healthy adult men living in the mountains. However, this is unrealistic due to the impracticality of measuring every individual. Therefore, only a partial determination of the pulse rate of some individuals (sample) can be conducted.
To achieve this, a random sample of 25 adult men (sample size) from the mountain was taken, and their average pulse rate was found to be 74.2 beats per minute (sample mean). Based on this, the question arises: Can the difference between 74.2 beats per minute and 72 beats per minute be used to judge whether there is a significant difference between the pulse rates of healthy adult men living in the mountains and those living on the plains?
To answer this question, we first analyze the reasons for this difference:
1. Differences derived from individual variations (sampling error).
2. Differences caused by environmental factors, such as the difference between the mountain environment and the plain environment (overall difference).
If the observed difference is due to reason (1), we cannot conclude that there is a significant difference between the pulse rates of healthy adult men living in the mountains and those on the plains. If the observed difference is due to reason (2), we can conclude that there is a significant difference between the two groups.
Where does this difference come from? We can analyze the possibility that the difference in sample indices is caused by sampling error through a series of analyses. This process elaborates on one of the most important statistical inferences—hypothesis testing.
Next, using statistical knowledge-based testing methods, we calculate the probability that the difference in sample indices may be entirely due to sampling error. If P ≤ 0.05, we infer that the difference between the sample index and the overall population is not due to sampling error but reflects a significant difference. This is referred to as a "significant difference."
Through this example, students not only easily understand abstract statistical terms and basic principles but also cultivate their ability to think logically. More importantly, they learn that sampling error in medical research is inevitable, but we can try to reduce it and use statistical analysis to assess the size of the sampling error. Modern audio-visual media should be fully utilized to conduct computer-aided teaching, achieving the purpose of integrating theory with practice. Reforming the teaching content and methods of medical statistics involves optimizing teaching methods and modernizing teaching techniques.
Modern audio-visual equipment serves as an effective medium to visualize and simplify abstract knowledge. Computer-assisted instruction (CAI) has become an important symbol of modern teaching. To carry out computer-aided teaching in medical statistics, Excel97 under Windows95 can be used, as it is more familiar to students. Excel is a user-friendly spreadsheet software with powerful data management capabilities and the ability to generate charts.
Below, a simple example illustrates how to use Excel for statistical inference. For instance, consider the treatment of silicosis patients where hemoglobin levels before and after treatment are shown below:
| Before Treatment | After Treatment |
|------------------|-----------------|
| 14.0 | 13.8 |
| 13.5 | 13.5 |
| 14.0 | 14.0 |
| 13.5 | 13.5 |
| 12.8 | 12.0 |
| 10.0 | 14.7 |
| 11.0 | 13.8 |
| 12.0 | 12.0 |
Test whether there is a significant difference in hemoglobin levels before and after treatment for the same group of patients.
First, correctly analyze the statistical method that should be used in this case. Since paired relationships exist due to the observed values of the sample, a paired two-sample t-test should be used. Then, perform statistical inference on the computer as follows:
1. Enter the Excel interface and input the data to be processed into a line or column in a spreadsheet.
2. Click the "Data Analysis" command in the "Tools" menu to browse the existing analysis tools. Select the paired two-sample t-test for means.
3. Perform the test by entering the data in a single column or single row format. Click the input box to the right of the button and return to the first set of data in the spreadsheet.
By following these steps, statistical inferences can be made effectively, providing valuable insights into the differences observed in the data.