GraphPad Prism v5.0统计分析指南

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"GraphPad Prism v5.0.pdf" GraphPad Prism是一款广泛用于生物医学、生命科学以及社会科学领域的数据分析和图形制作软件。该软件的版本为5.0，由GraphPad Software, Inc.于2007年发布，并保留所有版权。GraphPad Prism以其易用性和强大的统计分析功能著称，特别适合非专业统计人员进行科学数据的处理和可视化。统计指南由GraphPad Software公司的创始人Harvey Motulsky撰写，旨在帮助用户理解统计测试的基本概念，以便选择合适的统计方法并正确解读结果。此指南不仅适用于使用GraphPad Prism的用户，即使使用其他统计软件的用户也能从中受益。 GraphPad Prism 5的功能包括： 1. 数据图形化：用户可以轻松创建各种类型的图表，如散点图、柱状图、线图、生存曲线等，以直观展示数据分布和趋势。 2. 统计分析：提供多种统计测试，如t检验、ANOVA、非参数检验、生存分析等，覆盖了一般科学研究中的常见分析需求。 3. 曲线拟合：配合配套的Regression Guide，用户可以学习如何使用Prism来拟合曲线，包括线性、非线性回归、剂量响应曲线等，便于研究变量间的关系。 4. 数据管理：方便地组织和管理实验数据，支持多列数据表，便于进行复杂的比较和分析。 5. 结果解释：通过清晰的报告模板，用户可以生成包含统计结果和图形的专业报告。 6. 自动化分析：Prism允许用户设置分析流程，自动执行一系列分析步骤，节省时间和精力。 7. 教程和帮助系统：提供的Statistics Guide和Regression Guide与软件内置的帮助系统同步，为用户提供详尽的使用指导。 GraphPad Prism 5是科学研究中一个强大而实用的工具，它简化了数据分析过程，使用户能够更加专注于科学研究本身，而不是复杂的统计计算。无论是初学者还是经验丰富的研究人员，都能通过这款软件提升数据分析的效率和准确性。

The Gaussian Distribution

Prism 5 Statistics Guide

www.graphpad.com

The distribution looks a lot like an ideal Gaussian distribution. Repeat the experiment 15,000 times

rather than 1,000 and you get even closer to a Gaussian distribution.

This simulation demonstrates a principle that can also be mathematically proven. Scatter will

approximate a Gaussian distribution if your experimental scatter has numerous sources that are

additive and of nearly equal weight, and the sample size is large.

The Gaussian distribution is a mathematical ideal. Few biological distributions, if any, really follow

the Gaussian distribution. The Gaussian distribution extends from negative infinity to positive

infinity. If the weights in the example above really were to follow a Gaussian distribution, there

would be some chance (albeit very small) that the weight is negative. Since weights can't be

negative, the distribution cannot be exactly Gaussian. But it is close enough to Gaussian to make it

OK to use statistical methods (like t tests and regression) that assume a Gaussian distribution.

Standard Deviation and Standard Error of the Mean

Prism 5 Statistics Guide

www.graphpad.com

Computing the SD

How is the SD calculated?

1. Compute the square of the difference between each value and the sample mean.

2. Add those values up.

3. Divide the sum by N-1. This is called the variance.

4. Take the square root to obtain the Standard Deviation.

Why N-1?

Why divide by N-1 rather than N in the third step above? In step 1, you compute the difference

between each value and the mean of those values. You don't know the true mean of the population;

all you know is the mean of your sample. Except for the rare cases where the sample mean happens

to equal the population mean, the data will be closer to the sample mean than it will be to the true

population mean. So the value you compute in step 2 will probably be a bit smaller (and can't be

larger) than what it would be if you used the true population mean in step 1. To make up for this, we

divide by N-1 rather than N.

But why N-1? If you knew the sample mean, and all but one of the values, you could calculate what

that last value must be. Statisticians say there are N-1 degrees of freedom.

But I've seen equations with N, not N-1, in the denominator!

The N-1 equation is used in the common situation where you are analyzing a sample of data and

wish to make more general conclusions. The SD computed this way (with N-1 in the denominator)

is your best guess for the value of the SD in the overall population.

If you simply want to quantify the variation in a particular set of data, and don't plan to extrapolate

to make wider conclusions, then you can compute the SD using N in the denominator. The resulting

SD is the SD of those particular values, but will most likely underestimate the SD of the population

from which those points were drawn.

How many values do you need to compute a SD?

The SD quantifies scatter, so clearly you need more than one value! Is two values enough? Many

people believe it is not possible to compute a SD from only two values. But that is wrong. The

equation that calculates the SD works just fine when you have only duplicate (N=2) data.

Are the results valid? There is no mathematical reason to think otherwise, but I answered the

question with simulations. I simulated ten thousand data sets with N=2 and each data point

randomly chosen from a Gaussian distribution. Since all statistical tests are actually based on the

variance (the square of the SD), I compared the variance computed from the duplicate values with

the true variance. The average of the 10,000 variances of simulated data was within 1% of the true

variance from which the data were simulated. This means that the SD computed from duplicate

data is a valid assessment of the scatter in your data. It is equally likely to be too high or too low, but

is likely to be pretty far from the true SD .

Calculating the SD with Excel

Excel can compute the SD from a range of values using the STDEV() function. For example, if you

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