c:ms:2017:schedule:week03
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c:ms:2017:schedule:week03 [2017/04/05 07:47] – hkimscil | c:ms:2017:schedule:week03 [2022/05/15 11:25] – hkimscil | ||
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- | ====== Week 3 내용 ====== | + | ㄹ====== Week 3 내용 ====== |
===== SPSS ===== | ===== SPSS ===== | ||
< | < | ||
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* Data file: [[http:// | * Data file: [[http:// | ||
* [[:range]] | * [[:range]] | ||
- | * [[:outlier]] | + | * [[:outliers]]: It is beyond our scope. Please just refer to it. Won't be appearing in tests. |
* 평균편차 | * 평균편차 | ||
* [[: | * [[: | ||
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< | < | ||
- | SET Statistic Std. Error | + | SET Statistic Std. Error |
- | ATTRACT 4 Mean 2.6445 .14651 | + | ATTRACT 4 Mean 2.6445 .14651 |
- | 95% Confidence | + | 95% Confidence Lower Bound 2.3379 |
- | Upper Bound 2.9511 | + | Interval for Upper Bound 2.9511 |
- | 5% Trimmed Mean 2.6483 | + | Mean |
- | Median 2.5950 | + | 5% Trimmed Mean 2.6483 |
- | Variance .429 | + | Median 2.5950 |
- | Std. Deviation .65520 | + | Variance .429 |
- | Minimum 1.20 | + | Std. Deviation .65520 |
- | Maximum 4.02 | + | Minimum 1.20 |
- | Range 2.82 | + | Maximum 4.02 |
+ | Range 2.82 | ||
Interquartile Range .82 | Interquartile Range .82 | ||
- | Skewness -.001 .512 | + | Skewness -.001 .512 |
- | Kurtosis .438 .992 | + | Kurtosis .438 .992 |
- | 32 Mean 3.2615 .01541 | + | 32 Mean 3.2615 .01541 |
95% Confidence Interval for Mean Lower Bound 3.2292 | 95% Confidence Interval for Mean Lower Bound 3.2292 | ||
- | Upper Bound 3.2938 | + | Upper Bound 3.2938 |
5% Trimmed Mean 3.2622 | 5% Trimmed Mean 3.2622 | ||
- | Median 3.2650 | + | Median 3.2650 |
Variance .005 | Variance .005 | ||
Std. Deviation .06892 | Std. Deviation .06892 | ||
- | Minimum 3.13 | + | Minimum 3.13 |
- | Maximum 3.38 | + | Maximum 3.38 |
- | Range .25 | + | Range .25 |
Interquartile Range .11 | Interquartile Range .11 | ||
Skewness -.075 .512 | Skewness -.075 .512 | ||
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* Variance calculation formula | * Variance calculation formula | ||
- | * {{anchor:variance_calculation_formula}} $\displaystyle S_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N-1} $ | + | * <wrap #variance_calculation_formula |
- | * $\displaystyle \sigma_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N} = \displaystyle \frac {\Sigma X^2}{N} - \frac {(\Sigma X)^2}{N^2} = \displaystyle \frac {\Sigma X^2}{N} - \bigg(\frac {\Sigma X}{N}\bigg)^2 = \displaystyle \frac {\Sigma X^2}{N} - \mu^2 | + | * $ \displaystyle \sigma_x^2 = \displaystyle \frac {\Sigma X^2 - \frac{(\Sigma X)^2}{N} } {N} = \displaystyle \frac {\Sigma X^2}{N} - \frac {(\Sigma X)^2}{N^2} = \displaystyle \frac {\Sigma X^2}{N} - \bigg(\frac {\Sigma X}{N}\bigg)^2 = \displaystyle \frac {\Sigma X^2}{N} - \mu^2 $ |
* [[:Degrees of Freedom]] N-1 | * [[:Degrees of Freedom]] N-1 | ||
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와 같다. | 와 같다. | ||
- | 이렇게 얻은 샘플들(k 개의)의 평균인 $A_k$ 는, | + | 이렇게 얻은 샘플들(k 개의)의 평균인 $ A_k $ 는, |
- | $$A_k = \displaystyle \frac{(X_1 + X_2 + . . . + X_k)}{k} = \frac{S_{k}}{k} $$ | + | $$ A_k = \displaystyle \frac{(X_1 + X_2 + . . . + X_k)}{k} = \frac{S_{k}}{k} $$ |
라고 할 수 있다. | 라고 할 수 있다. | ||
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이때, | 이때, | ||
- | $$ | + | $$ |
\begin{align*} | \begin{align*} | ||
E[S_k] & = E[X_1 + X_2 + . . . +X_k] \\ | E[S_k] & = E[X_1 + X_2 + . . . +X_k] \\ | ||
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$$ | $$ | ||
- | $$ | + | $$ |
\begin{align*} | \begin{align*} | ||
Var[S_k] & = Var[X_1 + X_2 + . . . +X_k] \\ | Var[S_k] & = Var[X_1 + X_2 + . . . +X_k] \\ | ||
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이다. | 이다. | ||
- | 그렇다면, | + | 그렇다면, |
- | $$ | + | $$ |
\begin{align*} | \begin{align*} | ||
E[A_k] & = E[\frac{S_k}{k}] \\ | E[A_k] & = E[\frac{S_k}{k}] \\ |
c/ms/2017/schedule/week03.txt · Last modified: 2022/05/15 11:25 by hkimscil