# 统计：如何解读结果

Rowntree D (1981). Statistics without tears. A primer for non-mathematicians. Penguin Books Ltd., London, England.

1.    在列举数据时，说明使用的是何种参数，如“均值±标准差”。
2.    说明数据分析所采用的统计检验方法。
3.    百分比给出分子分母，如“40% (100/250)”。
4.    正态分布数据用均值和标准差表示。
5.    非正态分布数据用中位数和 百分位数表示。
6.    给出具体的P 值, 如 写出 “P=0.0035”，而不要只写 “P<0.05”。
7.    “significant’ 这个词仅用于描述统计学上的显著差异。

Statistics: what can we say about our findings?

Today, few professional activities are untouched by statistical thinking, and most academic disciplines use it to a greater or lesser degree… Statistics has developed out of an aspect of our everyday thinking to be a ubiquitous tool of systematic research… Statistical thinking is a way of recognizing that our observations of the world can never be totally accurate; they are always somewhat uncertain.
Rowntree D (1981). Statistics without tears. A primer for non-mathematicians. Penguin Books Ltd., London, England.

The term ‘statistics’ refers to the methods used to collect, process and interpret data. Because these methods are so inherent in the process of scientific inquiry, there have been multiple references to statistics throughout our blog, namely, in the posts on study design, methods, results and display items. However, given the importance of statistics in most scientific studies, it is worthwhile having a separate post on how they should be used and presented.

Statistics should first be considered long before the commencement of any research, during the initial study design. First, consider what information you need to collect in order to test your hypothesis or address your research question. It is important to get this right from the outset because, while data can be reanalyzed relatively easily if the wrong tests were used, it is far more difficult and time-consuming to repeat data collection with a different sample group or obtain additional variables from the same sample. If you wish to test the efficacy of a treatment for use in the general population, then your sample needs to be representative of the general population. If you wish to test its efficacy in a given ethnicity or age group, then your sample needs to be representative of that group. If comparing two groups of subjects separated on the basis of a particular disease or behavior, then other variables, such as age, sex and ethnicity, need to be matched as closely as possible between the two groups. This aspect of statistics relates to the collection of data; get it wrong and you could face major problems, potentially the need to start the research all over again, at the peer review stage many months later.

Second, you need to consider what statistical tests should be applied so that you can make meaningful statements about your data. This depends on the type of data you have collected: do you have categorical data, perhaps describing the presence or absence of a particular marker, or quantitative data with numerical values? If your data is quantitative, is it continuous (that is, can it be measured) or discrete (counts)? For example, age, weight, time and temperature are all examples of continuous data because they are measured on continuous scales with units that are infinitely sub-divisible. By contrast, the number of people in a given group and the number of cells with apoptotic features are examples of discrete data that need to be counted and are not sub-divisible. You also need to know how your data is distributed: is it normally distributed (Gaussian) or skewed? This also affects the type of test that should be used. It is important that you know what type of data you are collecting so that you apply the appropriate statistical tests to analyze the data and so you present them in an appropriate manner. The following useful website provides a guide to choosing the appropriate statistical test: http://www.graphpad.com/www/Book/Choose.htm

Finally, you need to know how to interpret the results of the statistical tests you have selected. What exactly does the p (or t or χ2 or other) value mean? That, after all is the point of statistical analysis: to determine what you can say about your findings; what they really mean. Statistics enable us to determine the central tendency (for example, mean and median) and dispersion (for example, standard deviation, standard error, and interpercentile range) of a dataset, giving us an idea of its distribution.
Also using statistics, values from two or more different sample groups can be compared (for example, by t-test, analysis of variance, or χ2 test) to determine if a difference between or among groups could have arisen by chance. If this hypothesis, known as the null hypothesis, can be shown to be highly unlikely (usually less than 5% chance), then the difference is said to be significant. It is important to keep in mind that there are two risks associated with reducing a decision about the ‘reality’ of a difference to probabilities, and both depend on the threshold set to determine significance: the first, known as type I error, is the possibility that a difference is accepted as significant when it is not; the opposite risk, known as type II error, refers to the possibility that a significant difference is considered not to be significant because we demand a larger difference between groups to be certain. Reducing the risk of type I errors increases the risk of type II errors, but this is infinitely more preferable than reaching a conclusion that isn’t justified. Statistics also provides a measure of the strengths of correlations and enables inferences about a much larger population to be drawn on the basis of findings in a sample group. In this way, statistics puts meaning into findings that would otherwise be of limited value, and allows us to draw conclusions based on probabilities, even when the possibility of error remains.

Example

Extracts from The Journal of Clinical Investigation (doi:10.1172/JCI38289; reproduced with permission).

Checklist
1.    Indicate what parameters are described when listing data; for example, “means±S.D.”
2.    Indicate the statistical tests used to analyze data
3.    Give the numerator and denominator with percentages; for example “40% (100/250)”
4.    Use means and standard deviations to report normally distributed data
5.    Use medians and interpercentile ranges to report data with a skewed distribution
6.    Report p values; for example, use “p=0.0035” rather than “p<0.05”
7.    Only use the word “significant’ when describing statistically significant differences.

Dr Daniel McGowan

http://blog.sciencenet.cn/blog-288924-665338.html

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