面板数据模型入门：Stata, SAS, SPSS实战指南

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"这篇文档是关于面板数据(panel data)的应用，特别关注了使用STATA、SAS和SPSS进行统计分析，包括t检验和单因素方差分析(ANOVA)。文档介绍了这些方法，适用于入门级学习者，旨在帮助他们理解和运用这些工具比较组间均值。" 面板数据，也称为截面时间序列数据，是一种包含多个观测单位（如个人、公司或国家）在不同时间点上数据的数据集。这种数据类型提供了更丰富的信息，因为它允许我们研究个体之间的差异和随时间的变化，使得分析师能够识别固定效应和随机效应，从而更好地理解模型中的变量关系。文档首先引入了t检验和ANOVA，这两种都是比较组间均值的经典方法。t检验通常用于检验两个独立或配对样本之间的均值差异，而当需要比较三个或更多组的均值时，单因素方差分析(ANOVA)就显得更为合适。t检验分为独立样本t检验（两组数据相互独立）和配对样本t检验（同一组数据在不同条件下的两次观测），而ANOVA则可以扩展到更复杂的多组比较。文档接下来详细阐述了以下内容： 2. 单变量样本：这部分可能涵盖了如何基于单一变量进行t检验和ANOVA的基本步骤。 3. 配对样本：讨论了如何处理相关样本，比如在实验前后对比的情况。 4. 独立样本与相等方差：解释了在假设各组方差相等的情况下进行t检验的条件。 5. 独立样本与不等方差：当各组方差不相等时，如何调整t检验或使用其他方法，如Welch's t检验。 6. 一元方差分析，广义线性模型和回归：介绍了一元ANOVA的原理，以及如何将其与GLM和回归分析结合，用于多组间的复杂比较。 7. 结论：总结了关键点，并可能提出进一步学习和应用的建议。通过这些方法，研究者能够测试假设，例如性别、种族或其他分类变量对连续变量（如工资或收入）的影响。t检验和ANOVA是统计学中的基本工具，对于理解面板数据中的差异性和趋势至关重要，特别是在社会科学、经济学和商科研究中。使用STATA、SAS和SPSS等统计软件，可以方便地执行这些分析并生成结果，帮助研究人员快速解读数据并做出决策。

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http://www.indiana.edu/~statmath

lung Folded F 21 21 1.17 0.7273

The F test for equal variance does not reject the null hypothesis of equal variances. Thus, the t-

test labeled as “Pooled” should be referred to in order to get the t -5.37 and its p-value .0001. If

the equal variance assumption is violated, the statistics of “Satterthwaite” and “Cochran”

should be read.

If you have a summary data set with the values of variables (

lung) and their frequency (count),

specify the count variable in the FREQ statement.

PROC TTEST DATA=masil.smoking;

CLASS smoke;

VAR lung;

FREQ count;

RUN;

Now, let us compare the death rates from leukemia and kidney in the second data arrangement

type of Figure 1. As mentioned before, you need to rearrange the data set to stack up two

variables into one and generate a grouping variable (first type in Figure 1).

DATA masil.smoking2;

SET masil.smoking;

death = leukemia; leu_kid ='Leukemia'; OUTPUT;

death = kidney; leu_kid ='Kidney'; OUTPUT;

KEEP leu_kid death;

RUN;

PROC TTEST COCHRAN DATA=masil.smoking2; CLASS leu_kid; VAR death; RUN;

The TTEST Procedure

Statistics

Lower CL Upper CL Lower CL Upper CL

Variable leu_kid N Mean Mean Mean Std Dev Std Dev Std Dev Std Err

death Kidney 44 2.6367 2.7945 2.9524 0.4289 0.5191 0.6577 0.0783

death Leukemia 44 6.6357 6.8298 7.0238 0.5273 0.6383 0.8087 0.0962

death Diff (1-2) -4.282 -4.035 -3.789 0.5063 0.5817 0.6838 0.124

T-Tests

Variable Method Variances DF t Value Pr > |t|

death Pooled Equal 86 -32.54 <.0001

death Satterthwaite Unequal 82.6 -32.54 <.0001

death Cochran Unequal 43 -32.54 <.0001

Equality of Variances

Variable Method Num DF Den DF F Value Pr > F

http://www.indiana.edu/~statmath

5. Independent Samples with Unequal Variances

If the assumption of equal variances is violated, we have to compute the adjusted t statistic

using individual sample standard deviations rather than a pooled standard deviation. It is also

necessary to use the Satterthwaite, Cochran-Cox (SAS), or Welch (STATA) approximations of

the degrees of freedom. In this chapter, you compare mean death rates from kidney cancer

between the west (south) and east (north).

5.1 T-test in STATA

As discussed earlier, let us check equality of variances using the

.oneway command. The

tabulate option produces a table of summary statistics for the groups.

. oneway kidney west, tabulate

| Summary of kidney

west | Mean Std. Dev. Freq.

------------+------------------------------------

0 | 3.006 .3001298 20

1 | 2.6183333 .59837219 24

------------+------------------------------------

Total | 2.7945455 .51907993 44

Analysis of Variance

Source SS df MS F Prob > F

------------------------------------------------------------------------

Between groups 1.63947758 1 1.63947758 6.92 0.0118

Within groups 9.94661333 42 .236824127

------------------------------------------------------------------------

Total 11.5860909 43 .269443975

Bartlett's test for equal variances: chi2(1) = 8.6506 Prob>chi2 = 0.003

Bartlett’s chi-squared statistic rejects the null hypothesis of equal variance at the .01 level. It is

appropriate to use the

unequal option in the .ttest command, which calculates

Satterthwaite’s approximation for the degrees of freedom.

Unlike the SAS TTEST procedure, the

.ttest command cannot specify the mean difference

other than zero. Thus, the null hypothesis is that the mean difference is zero.

. ttest kidney, by(west) unequal level(95)

Two-sample t test with unequal variances

------------------------------------------------------------------------------

Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]

---------+--------------------------------------------------------------------

0 | 20 3.006 .0671111 .3001298 2.865535 3.146465

1 | 24 2.618333 .1221422 .5983722 2.365663 2.871004

---------+--------------------------------------------------------------------

combined | 44 2.794545 .0782542 .5190799 2.636731 2.95236

---------+--------------------------------------------------------------------

diff | .3876667 .139365 .1047722 .6705611

------------------------------------------------------------------------------

http://www.indiana.edu/~statmath

diff = mean(0) - mean(1) t = 2.7817

Ho: diff = 0 Satterthwaite's degrees of freedom = 35.1098

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0

Pr(T < t) = 0.9957 Pr(|T| > |t|) = 0.0086 Pr(T > t) = 0.0043

See Satterthwaite’s approximation of 35.110 in the middle of the output. If you want to get

Welch’s approximation, use the

welch as well as unequal options; without the unequal option,

the

welch is ignored.

. ttest kidney, by(west) unequal welch

Two-sample t test with unequal variances

------------------------------------------------------------------------------

Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]

---------+--------------------------------------------------------------------

0 | 20 3.006 .0671111 .3001298 2.865535 3.146465

1 | 24 2.618333 .1221422 .5983722 2.365663 2.871004

---------+--------------------------------------------------------------------

combined | 44 2.794545 .0782542 .5190799 2.636731 2.95236

---------+--------------------------------------------------------------------

diff | .3876667 .139365 .1050824 .6702509

------------------------------------------------------------------------------

diff = mean(0) - mean(1) t = 2.7817

Ho: diff = 0 Welch's degrees of freedom = 36.2258

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0

Pr(T < t) = 0.9957 Pr(|T| > |t|) = 0.0085 Pr(T > t) = 0.0043

Satterthwaite’s approximation is slightly smaller than Welch’s 36.2258. Again, keep in mind

that these approximations are not integers, but real numbers. The t statistic 2.7817 and its p-

value .0086 reject the null hypothesis of equal population means. The north and east have

larger death rates from kidney cancer per 100 thousand people than the south and west.

For aggregate data, use the

.ttesti command with the necessary options.

. ttesti 20 3.006 .3001298 24 2.618333 .5983722, unequal welch

As mentioned earlier, the

unpaired option of the .ttest command directly compares two

variables without data manipulation. The option treats the two variables as independent of each

other. The following is an example of the unpaired and unequal options.

. ttest bladder=kidney, unpaired unequal welch

Two-sample t test with unequal variances

------------------------------------------------------------------------------

Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]

---------+--------------------------------------------------------------------

bladder | 44 4.121136 .1454679 .9649249 3.827772 4.4145

kidney | 44 2.794545 .0782542 .5190799 2.636731 2.95236

---------+--------------------------------------------------------------------

combined | 88 3.457841 .1086268 1.019009 3.241933 3.673748

---------+--------------------------------------------------------------------

diff | 1.326591 .1651806 .9968919 1.65629

------------------------------------------------------------------------------

diff = mean(bladder) - mean(kidney) t = 8.0312

Ho: diff = 0 Welch's degrees of freedom = 67.0324

http://www.indiana.edu/~statmath

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0

Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000

The F 3.4556 = (.9649249^2)/(.5190799^2) rejects the null hypothesis of equal variance

(p<0001). If the

welch option is omitted, Satterthwaite's degree of freedom 65.9643 will be

produced instead.

For aggregate data, again, use the

.ttesti command without the unpaired option.

. ttesti 44 4.121136 .9649249 44 2.794545 .5190799, unequal welch level(95)

5.2 T-test in SAS

The TTEST procedure reports statistics for cases of both equal and unequal variance. You may

add the

COCHRAN option to compute Cochran-Cox approximations for the degree of freedom.

PROC TTEST COCHRAN DATA=masil.smoking;

CLASS west;

VAR kidney;

RUN;

The TTEST Procedure

Statistics

Lower CL Upper CL Lower CL Upper CL

Variable s_west N Mean Mean Mean Std Dev Std Dev Std Dev

kidney 0 20 2.8655 3.006 3.1465 0.2282 0.3001 0.4384

kidney 1 24 2.3657 2.6183 2.871 0.4651 0.5984 0.8394

kidney Diff (1-2) 0.0903 0.3877 0.685 0.4013 0.4866 0.6185

Statistics

Variable west Std Err Minimum Maximum

kidney 0 0.0671 2.34 3.62

kidney 1 0.1221 1.59 4.32

kidney Diff (1-2) 0.1473

T-Tests

Variable Method Variances DF t Value Pr > |t|

kidney Pooled Equal 42 2.63 0.0118

kidney Satterthwaite Unequal 35.1 2.78 0.0086

kidney Cochran Unequal . 2.78 0.0109

Equality of Variances

Variable Method Num DF Den DF F Value Pr > F

kidney Folded F 23 19 3.97 0.0034

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