What does the bootstrap method mean?
The Bootstrap method is an important estimation of statistical variability in non-parametric statistics. It is also a statistical method that can estimate the interval of statistical quantities, also known as the bootstrap method.
The core ideas and basic steps are as follows:
(1) Use repeated sampling technology to extract a certain number of samples (can be given by yourself, generally the same as the original sample) from the original sample. This The process allows for repeated sampling.
(2) Calculate the statistic T to be estimated based on the extracted samples.
(3) Repeat the above N times (generally greater than 1000) to obtain N statistics T.
(4) Calculate the sample variance of the above N statistics T to estimate the variance of the statistic T.
It should be said that Bootstrap is a popular statistical method in modern statistics and works well in small samples. Confidence intervals can be constructed through the estimation of variance, and its application scope is further extended.
Example of specific sampling method: If you want to know the number of fish in the pond, you can first extract N fish, mark them, and put them back into the pond.
Carry out repeated sampling, draw M times, and draw N fish each time. Examine the proportion of marked fish among the fish drawn each time, and calculate the statistics based on the proportion of M times.
Reasons for applying bootstrap: In fact, when performing analysis, the first thing to do is to determine the type of random variable, and then to determine what distribution the data of the random variable obeys. What distribution is crucial, because it directly determines whether it can be analyzed. For example: If you perform variance analysis, you must first require a normal distribution. If it is not a normal distribution, you must take remedial measures. This remedial measure is bootstrap. Bootstrap also has another use, because classic statistics is relatively perfect for central tendency, but it is not perfect for interval estimation of some other distribution parameters, such as median, quartiles, standard deviation, coefficient of variation, etc., so bootstrap is needed. This method. Bootstrap is similar to the classic statistical method. Generally, the parametric method is more efficient than the non-parametric method. However, the biggest drawback of the parametric method is that it requires a distribution model in advance. If the model does not conform to the model, the analysis results may be wrong, which is a white analysis.
If there are obvious layers in the data, stratified sampling can be used to improve analysis efficiency. spss defaults to the non-parametric bootstrap method and uses completely random sampling. Therefore, if stratified sampling is required, you cannot rely on the default and need to set it yourself. .
There is also special attention to be paid to how many observations are needed to be the most scientific and reasonable. The answer is 1,000. If it is less than this number, the calculation result will be inaccurate because the confidence interval is calculated according to the percentile method, so it cannot be too small. If there are more than 1000, the accuracy improvement is very limited in most cases, and system resources and computing time are wasted.
Operation steps in bootstrap's spss analysis: "Analysis" ~ "Compare Means" ~ "Means" ~ Select the independent variable and dependent variable ~ "Options" sub-dialog ~ "Cell Statistics" ~ bootstrap sub-dialog box ~ Execute bootstrap check box
One more point, if the dependent variable conforms to or approximately conforms to the normal distribution, the bootstrap method does not need to be used.
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