1. Case introduction
A doctor measured the hemoglobin content of 36 male workers engaged in lead work, and calculated the mean to be 130.83g/L and the standard deviation to be 25.74g/L. Question: Is the average hemoglobin content of male workers engaged in lead work not equal to the average of 140g/L for normal males? Part of the data is shown in Figure 1:
figure 1
2. Problem Analysis
To test whether the sample mean is different from the known overall mean, that is, to judge whether the hemoglobin content of 36 male workers engaged in lead work is different from the known normal male mean of 140g/L, you can use the single-sample t test for analysis .
There are two prerequisites for the one-sample t-test:
Condition 1: Independence—the observations are independent of each other; for example, in this case, each test object is independent and there is no mutual interference.
Condition 2: Normality - the data needs to satisfy a normal distribution (or approximately normal); a normality test is required for judgment.
3. Software operation and result interpretation
(1) Normality test
1. Theoretical explanation
It is a simple and easy method to use the graphical method to test the normality. By visualizing the graph, you can roughly understand whether the observation data obey the normal distribution. Commonly used graphic methods mainly include PP diagram and QQ diagram. The principle of the PP diagram is that if the data is normal, then the cumulative proportion of the data is basically consistent with the cumulative proportion of the normal distribution. The principle of the QQ graph is that if the data is normal, then its assumed normal quantile will be basically consistent with the actual data.
If the scatter points in the above two graphs basically form a diagonal line, it can be roughly considered that the observation data obey the normal distribution.
2. Software operation
Use statistical software for normality test, upload the data to SPSSAU online data analysis software, in the [Visualization] module, select [PP graph/QQ graph], drag the "hemoglobin content" to the right analysis box, the operation is as follows figure 2:
figure 2
3. Interpretation of results
The PP diagram and QQ diagram of SPSSAU output hemoglobin content are shown in Figure 3 and Figure 4:
image 3
Figure 4
It can be seen from Figure 3 and Figure 4 that the scatter points of the PP diagram and QQ diagram of the hemoglobin content basically form a diagonal line, so it can be considered that the hemoglobin content basically obeys the normal distribution and satisfies the normality characteristics, and the single-sample t test.
Supplement: In addition to the graphical method, SPSSAU [normality test] can also be used for analysis, and the analysis results are as follows:
Figure 5
It can be seen from Figure 5 that none of the hemoglobin contents showed significance (p>0.05), which means that the null hypothesis (null hypothesis: normal distribution of data) was accepted, and all the hemoglobin contents had normal characteristics.
(2) One-sample t-test
1. Theoretical explanation
The one-sample t-test is applicable to the comparison between the sample mean and the known overall mean. The purpose is to test whether the unknown overall mean represented by the sample mean is different from the known overall mean.
H0: μ=μ0
H1：μ≠μ0
The formula for calculating the test statistic is as follows:
After obtaining the t value, look up the table to obtain the corresponding p value. If p>0.05, the null hypothesis is not rejected, and the difference between the two groups of data is considered to be not statistically significant; otherwise, the difference is considered to be statistically significant.
2. Software operation
Use SPSSAU to perform single-sample t-test, select [Single-sample t-test], put "hemoglobin content" into the analysis item (quantitative) box on the right, and enter the comparison number "140", the operation is as shown in Figure 6:
Figure 6
3. Interpretation of results
The analysis results of single-sample t-test output by SPSSAU are shown in Figure 7:
Figure 7
It can be seen from Figure 7 that p<0.05, so the null hypothesis is rejected and the alternative hypothesis is accepted, and the difference is statistically significant; that is, it can be considered that the average hemoglobin content of male workers engaged in lead work is not equal to that of normal adult males.
4. Conclusion
In this study, a one-sample t-test was used to test the difference between the average hemoglobin content of male workers engaged in lead work and normal male workers. Through professional knowledge, it is judged that each test object is independent and does not interfere with each other; by using PP diagram and QQ diagram to test the normality of data, it is known that the observed data obey the normal distribution. Analysis of differences can be performed using a one-sample t-test.
The research results show that the average hemoglobin content of male workers engaged in lead work is 130.8g/L, which is 140g/L lower than the average hemoglobin content of normal adult male workers. Male workers had lower average hemoglobin levels than normal adult males.
5. Knowledge Tips
What are the normality test methods?
There are mainly statistical test methods, graphic methods, and description methods. Statistical testing methods carry out normality testing through the method of hypothesis testing, and have the strictest requirements on data normality. The graphical method can include the use of histograms, PP diagrams, and QQ diagrams for normality testing. It is generally believed that when the histogram basically meets the bell-shaped distribution shape of "high in the middle and low at both ends", it can be considered that the data basically meets the normality characteristics ; When the scatter points of the PP graph and the QQ graph basically present a diagonal straight line, it can be considered that the data basically satisfy the normality characteristic. The descriptive method means that the statistical test method is difficult to meet the strict data requirements, so it is generally believed that when the absolute value of the kurtosis of the data is less than 10 and the absolute value of the skewness is less than 3, it means that although the data is not absolutely normal, it is basically Normal distribution is acceptable.
references:
[1] Sun Zhenqiu, Xu Yongyong. Medical Statistics. 4th Edition [M]. People's Health Publishing House, 2014
[2] Yan Hong, Xu Yongyong. Medical Statistics. 3rd Edition [M]. People's Health Publishing House, 2015