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1. Statistics Software Mac Correspondence Analysis Pdf
2. Analysis Software

Numbers does have the ability to make a histogram. I am not familiar with the analysis pack but reviewing the features listed on this web site:

Confidence Statistics for Column points. Includes standard deviation and correlations for all nonsupplementary column points. To Select Statistics in Correspondence Analysis. This feature requires the Categories option. From the menus choose: Analyze Dimension Reduction Correspondence Analysis.

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• Anova: Single Factor
• Anova: Two-Factor with Replication
• Anova: Two-Factor Without Replication
• Correlation
• Covariance
• Descriptive Statistics
• Exponential Smoothing
• F-Test Two Sample for Variance
• Fourier Analysis
• Histogram
• Moving Average
• Random Number Generation
• Rank and Percents
• Regression
• Sampling
• t-Test: Paired Two Sample for Means
• t-Test: Two-Sample Assuming Equal Variances
• t-Test: Two-Sample Assuming Unequal Variances
• Z-Test: Two-Samples for Mean

Are there specific features you want to use?

Correspondence analysis plays a role similar to factor analysis or principal component analysis for categorical data expressed as a contingency table (e.g. as described in the chi-square test of independence). For a 10 × 10, a complete description of the associations between row elements and column elements requires nine dimensions. Unfortunately, it is difficult for us to visualize such associations in more than two dimensions. In correspondence analysis, we project the row/column associations into two dimensions even if this requires that there is some loss in the accuracy of the representation.

Essentially, correspondence analysis decomposes the chi-square statistic of independence into orthogonal factors. This approach is valid even when the cell sizes in the contingency table are less than 5 (or even zero).

Example 1: 80 teenagers were asked to select which of 6 characteristics best describe 4 popular brands of smart phones. The teenagers were permitted to comment on multiple brands of smart phone and choose more than one characteristic for any of the brands.

The brands are Apple, Samsung, Nokia and Huawei. The characteristics are Screen Display, Price, Design, Battery, Software, and Camera. The raw data is shown in Figure 1.

Figure 1 – Survey data

Note that the chi-square statistic for this contingency table is 164.33, as calculated, for example, by the Real Statistics formula =CHI_STAT(B4:E9). The inertia statistic is now set to the chi-square statistic divided by the sample size, i.e. 164.33/657 = .2501.

We next create the proportional matrix P by dividing each of the elements in the contingency table by the sample size, as shown in range O3:S9 of Figure 2.

Figure 2 – Proportional matrix

Next we create the row totals in range T4:T9 and column totals in range P10:S10, and then the 6 × 6 array D_r (in range V4:AA9) using the array formula

=DIAGONAL(1/SQRT(T4:T9))

Here DIAGONAL(R1) is the Real Statistics array function which outputs a diagonal matrix whose diagonal consists of the elements in the row or column range R1, which in this case consists of the reciprocal of the square root of the elements in range T4:T9. Similarly, we create the 4 × 4 array D_c (located in range P13:S16) using the array formula =DIAGONAL(1/SQRT(P10:S10)).

We now create matrix A = D_rPD_c, as shown in range W13:Z18, using the array formula =MMULT(V4:AA9,MMULT(P4:S9,P13:S16)). Finally, we using the Matrix Operations data analysis tool to create a singular value decomposition of matrix A, as shown in Figure 3.

Figure 3 – Singular Value Decomposition

We now calculate the F and G coordinate matrices and DD^T matrix as shown in Figure 4. The coordinate matrices contain the factor coordinates and the DD^T matrix contains the eigenvalues that are used to decompose the chi-square statistic.

Figure 4 – Coordinate matrices and eigenvalues

From the DD^T matrix, we obtain the Eigenvalue table shown in Figure 5. This table corresponds to the table that produces a scree plot for factor analysis. In fact, we can use the table to create a scree plot for correspondence analysis. With just three potential factors, we won’t actually create the scree plot for this example.

Figure 5 – Eigenvalue decomposition

This table tells us that the first factor accounts for 87.57 % of the variation and the second factor accounts for 10.56% of the variation. Consequently, the first two factors account for 98.13% of the variation, and so we only lose 1.43% of the variation if we use only these two factors.

Statistics Software Mac Correspondence Analysis Pdf

Note that the sum of the eigenvalues (i.e. the trace), 0.2501, is equal to the inertia that we calculated earlier (just after Figure 1).

A rule of thumb is that a two-dimension correspondence analysis (i.e. one where we retain just two factors) is sufficient provided the first two eigenvalues account for at least 50% of the variation, ideally much more. If this rule of thumb is not met, then we need to make a trade-off between adding more factors and the difficulty of visualizing the information when more than two dimensions are used. For our purposes, we will assume that two factors are sufficient.

We next create the correspondence analysis plot detail reports for rows and columns, as shown in Figure 6.

Figure 6 – Plot Detail Reports

Since we retain two factors, we use two dimensions (or axes) in each report. Figure 7 describes the screen display profile entries in the Rows report (row 14).

Figure 7 – Detailed description for screen display profile

Analysis Software

The description of the axis 2 components of the screen display profile are similar to the axis 1 descriptions shown in Figure 7, except that now the next column of the F matrix is used (i.e. range AE12:AE17 of Figure 4).

Note that cell AN20 contains the total inertia, as calculated by the formula =SUMPRODUCT(AL25:AL28,AM25:AM28). Note that this value, .2501, agrees with the value that we calculated twice previously.

The values in the Column part of the report in Figure 6 are calculated as described in Figure 7, except that now we use the factors that result from the columns in the G matrix of Figure 4.

The row profile coordinates that are most important are characterized by COR > 1/k and CTR > 1/r where r = # of rows, c = # of columns and k = min(r, c) – 1. For Example 1 r = 6, c = 4 and k = 3, and so the most important row coordinates are characterized by COR > .3333 and CTR > .1667, which means that the most important row coordinates are for factor 1 of price and factor 2 of design and battery.

Similarly, the most important column profile coordinates are characterized by COR > 1/k and CTR > 1/c.