UNISTAT - the ultimate Excel statistics add-in

Cross-Tabulation in Excel with UNISTAT

The UNISTAT statistics add-in extends Excel with Cross-Tabulation capabilities.

For further information visit UNISTAT User's Guide section 6.6.2. Cross-Tabulation.

Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.

Cross-Tabulation

Treatment (2 Rows) x Response (2 Columns)

Subsample selected by: Gender = female

Frequency

Treatment \ ResponseBetterSameRow Sum
Active 16.0000 11.0000 27.0000
Placebo 5.0000 20.0000 25.0000
Column Sum 21.0000 31.0000 52.0000

Expected

Treatment \ ResponseBetterSame
Active 10.9038 16.0962
Placebo 10.0962 14.9038

Chi-Square

Treatment \ ResponseBetterSame
Active 2.3818 1.6135
Placebo 2.5723 1.7426

Total %

Treatment \ ResponseBetterSameRow Sum
Active 30.77% 21.15% 51.92%
Placebo 9.62% 38.46% 48.08%
Column Sum 40.38% 59.62% 100.00%

Column %

Treatment \ ResponseBetterSame
Active 76.19% 35.48%
Placebo 23.81% 64.52%

Row %

Treatment \ ResponseBetterSame
Active 59.26% 40.74%
Placebo 20.00% 80.00%

Residuals

Treatment \ ResponseBetterSame
Active 5.0962-5.0962
Placebo-5.0962 5.0962

Standardised Residuals

Treatment \ ResponseBetterSame
Active 1.5433-1.2702
Placebo-1.6039 1.3201

Adjusted Residuals

Treatment \ ResponseBetterSame
Active 2.8827-2.8827
Placebo-2.8827 2.8827

Chi-square Tests

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Pearson 8.3102 1 0.0039
Likelihood-Ratio 8.6334 1 0.0033
Yates Correction 6.7595 1 0.0093
# Linear-by-linear 8.1504 1 0.0043
~ McNemar-Bowker

# Table scores
~ Reported for 3 x 3 or larger square tables.
Cells with expected count < 5 = 0 ( 0.00%)
Minimum expected count = 10.0962

Phi 0.3998
Contingency Coefficient 0.3712
Cramer’s V 0.3998

Fisher’s Exact Test

Two-Tail ProbabilityTable Probability
Fisher’s Exact 0.0052 0.0036

For an extended output see Fisher’s exact test for 2 x 2 tables.

Measures of Association

ValueStandard ErrorLower 95%Upper 95%
Goodman-Kruskal’s gamma 0.7067 0.1590 0.3951 1.0183
Kendall’s tau b 0.3998 0.1247 0.1554 0.6441
Kendall’s tau c 0.3920 0.1237 0.1495 0.6346
# Pearson Correlation 0.3998 0.1247 0.1554 0.6441
Spearman Rank Correlation 0.3998 0.1247 0.1554 0.6441
# Eta (col) 0.3998
# Eta (row) 0.3998
Somer’s delta (col) 0.3926 0.1239 0.1498 0.6354
Somer’s delta (row) 0.4071 0.1266 0.1590 0.6552
Somer’s delta symmetric 0.3997 0.1246 0.1554 0.6440
Lambda (col) 0.2381 0.2160-0.1852 0.6614
Lambda (row) 0.3600 0.1782 0.0108 0.7092
Lambda symmetric 0.3043 0.1729-0.0346 0.6433
Uncertainty coefficient (col) 0.1231 0.0793-0.0323 0.2784
Uncertainty coefficient (row) 0.1199 0.0775-0.0320 0.2718
Uncertainty coefficient symmetric 0.1215 0.0783-0.0321 0.2750

# Table scores

Cochran-Armitage Trend Test

Z-Statistic1-Tail Probability2-Tail Probability
# Cochran-Armitage Trend Test-2.8827 0.0020 0.0039

# Table scores
Binary variable is recoded to 0s and 1s.
Reported for 2 x K tables.

Expected Proportion 0.4963
Observed Proportion 0.6923

ValueStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Kappa 0.3891 0.1239 3.1404 0.0008 0.0017 0.1463 0.6320

Binomial Test

For Treatment
Subsample selected by: Gender = female

Expected Proportion 0.5000
Observed Proportion 0.5192

Proportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Wald 0.5192 0.0693 0.3834 0.6550
H0 0.5000 0.0693 0.2774 0.3908 0.7815
Wald with CC 0.5192 0.0693 0.3738 0.6646
H0 0.5000 0.0693 0.1387 0.4449 0.8897
Wilson (score) 0.3869 0.6490
Wilson with CC 0.3778 0.6578
Agresti-Coull 0.5179 0.0669 0.3869 0.6490
Agresti-Coull (+2) 0.5179 0.0668 0.3870 0.6487
Jeffreys 0.3855 0.6509
Clopper-Pearson (exact) 0.4449 0.8899 0.3763 0.6599

Binomial Test

For Response
Subsample selected by: Gender = female

Expected Proportion 0.5000
Observed Proportion 0.4038

Proportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Wald 0.4038 0.0680 0.2705 0.5372
H0 0.5000 0.0693-1.3868 0.0828 0.1655
Wald with CC 0.4038 0.0680 0.2609 0.5468
H0 0.5000 0.0693-1.2481 0.1060 0.2120
Wilson (score) 0.2816 0.5393
Wilson with CC 0.2731 0.5487
Agresti-Coull 0.4105 0.0658 0.2814 0.5395
Agresti-Coull (+2) 0.4107 0.0657 0.2819 0.5396
Jeffreys 0.2786 0.5394
Clopper-Pearson (exact) 0.1058 0.2116 0.2701 0.5490

Equivalence Test

For Treatment
Subsample selected by: Gender = female

Expected Proportion 0.5000
Observed Proportion 0.5192
Lower Equivalence Margin-0.2000

Lower EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.5192 0.0693 3.1641 0.0008 0.4053
H0 0.3000
Wald with CC 0.5192 0.0693 3.0254 0.0012 0.3956
H0 0.3000
Clopper-Pearson (exact) 0.0008 0.3972

Upper Equivalence Margin 0.2000

Upper EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.5192 0.0693-2.6090 0.0045 0.6332
H0 0.7000
Wald with CC 0.5192 0.0693-2.4702 0.0068 0.6428
H0 0.7000
Clopper-Pearson (exact) 0.0046 0.6396

Overall1-Tail ProbabilityLower 90%Upper 90%
Wald 0.0045 0.4053 0.6332
Wald with CC 0.0068 0.3956 0.6428
Clopper-Pearson (exact) 0.0046 0.3972 0.6396

Equivalence Test

For Response
Subsample selected by: Gender = female

Expected Proportion 0.5000
Observed Proportion 0.4038
Lower Equivalence Margin-0.2000

Lower EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.4038 0.0680 1.5262 0.0635 0.2919
H0 0.3000
Wald with CC 0.4038 0.0680 1.3849 0.0830 0.2823
H0 0.3000
Clopper-Pearson (exact) 0.0717 0.2889

Upper Equivalence Margin 0.2000

Upper EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.4038 0.0680-4.3524 0.0000 0.5158
H0 0.7000
Wald with CC 0.4038 0.0680-4.2111 0.0000 0.5254
H0 0.7000
Clopper-Pearson (exact) 0.0000 0.5273

Overall1-Tail ProbabilityLower 90%Upper 90%
Wald 0.0635 0.2919 0.5158
Wald with CC 0.0830 0.2823 0.5254
Clopper-Pearson (exact) 0.0717 0.2889 0.5273

Difference Between Unpaired Proportions

Proportion 1 0.7619
Proportion 2 0.3548

DifferenceStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Pooled Variance 0.4071 0.1412 2.8827 0.0020 0.0039 0.1303 0.6838
Separate Variance 0.1266 3.2158 0.0007 0.0013 0.1590 0.6552

Risk Ratio

ValueLower 95%Upper 95%
Risk Ratio 2.1472 1.2620 3.6533

Odds Ratio and Relative Risks

ValueLower 95%Upper 95%
Odds Ratio 5.8182 1.6755 20.2034
Exact 1.4609 25.2654
Relative Risk (Cohort 1) 2.9630 1.2740 6.8913
Relative Risk (Cohort 2) 0.5093 0.3103 0.8357

Difference Between Paired Proportions

Proportion 1 0.0962
Proportion 2 0.2115

DifferenceStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Asymptotic-0.1154 0.0752-1.5000 0.0668 0.1336-0.2629 0.0321
Exact Binomial 0.1051 0.2101-0.2399 0.0533

Fisher’s Exact Test

Left-Tail ProbabilityRight-Tail ProbabilityTwo-Tail ProbabilityTable Probability
Fisher’s Exact 0.9994 0.0042 0.0052 0.0036

McNemar’s Test

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Asymptotic 2.2500 1 0.1336
Asymptotic with CC 1.5625 1 0.2113

2-Tail ProbabilityLower 95%Upper 95%
Exact Binomial 1.0000 0.7047 8.0769

Odds Ratio (Paired)

ValueLower 95%Upper 95%
Odds Ratio (Paired) 0.4545 0.7047 8.0769

Tetrachoric Correlation

RatioTetrachoric Correlation
5.8182 0.6052

Statistics for Diagnostic Tests

Smaller factor level represents the positive outcome.
Confidence Intervals: Row 1: Asymptotic Normal, Row 2: Exact Binomial

ValueStandard ErrorLower 95%Upper 95%
Sensitivity 0.7619 0.0929 0.5797 0.9441
0.5283 0.9178
Specificity 0.6452 0.0859 0.4767 0.8136
0.4537 0.8077
Accuracy 0.6923 0.0640 0.5669 0.8178
0.5490 0.8128
Prevalence 0.4038 0.0680 0.2705 0.5372
0.2701 0.5490
Apparent Prevalence 0.5192 0.0693 0.3834 0.6550
0.3763 0.6599
Youden’s Index 0.4071
-0.0180 0.7256
Positive Predictive Value 0.5926 0.0946 0.4073 0.7779
0.3880 0.7761
Negative Predictive Value 0.8000 0.0800 0.6432 0.9568
0.5930 0.9317
Positive Likelihood Ratio 2.1472 1.2620 3.6533
Negative Likelihood Ratio 0.3690 0.1658 0.8212
Diagnostic Odds Ratio 5.8182 1.6755 20.2034
Weighted Positive Likelihood Ratio 1.4545 0.8375 2.5263
Weighted Negative Likelihood Ratio 0.2500 0.1119 0.5584

Treatment (2 Rows) x Response (2 Columns)

Subsample selected by: Gender = male

Frequency

Treatment \ ResponseBetterSameRow Sum
Active 12.0000 16.0000 28.0000
Placebo 7.0000 19.0000 26.0000
Column Sum 19.0000 35.0000 54.0000

Expected

Treatment \ ResponseBetterSame
Active 9.8519 18.1481
Placebo 9.1481 16.8519

Chi-Square

Treatment \ ResponseBetterSame
Active 0.4684 0.2543
Placebo 0.5044 0.2738

Total %

Treatment \ ResponseBetterSameRow Sum
Active 22.22% 29.63% 51.85%
Placebo 12.96% 35.19% 48.15%
Column Sum 35.19% 64.81% 100.00%

Column %

Treatment \ ResponseBetterSame
Active 63.16% 45.71%
Placebo 36.84% 54.29%

Row %

Treatment \ ResponseBetterSame
Active 42.86% 57.14%
Placebo 26.92% 73.08%

Residuals

Treatment \ ResponseBetterSame
Active 2.1481-2.1481
Placebo-2.1481 2.1481

Standardised Residuals

Treatment \ ResponseBetterSame
Active 0.6844-0.5043
Placebo-0.7102 0.5233

Adjusted Residuals

Treatment \ ResponseBetterSame
Active 1.2251-1.2251
Placebo-1.2251 1.2251

Chi-square Tests

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Pearson 1.5009 1 0.2205
Likelihood-Ratio 1.5148 1 0.2184
Yates Correction 0.8835 1 0.3472
# Linear-by-linear 1.4731 1 0.2249
~ McNemar-Bowker

# Table scores
~ Reported for 3 x 3 or larger square tables.
Cells with expected count < 5 = 0 ( 0.00%)
Minimum expected count = 9.1481

Phi 0.1667
Contingency Coefficient 0.1644
Cramer’s V 0.1667

Fisher’s Exact Test

Two-Tail ProbabilityTable Probability
Fisher’s Exact 0.2635 0.1090

For an extended output see Fisher’s exact test for 2 x 2 tables.

Measures of Association

ValueStandard ErrorLower 95%Upper 95%
Goodman-Kruskal’s gamma 0.3412 0.2581-0.1647 0.8471
Kendall’s tau b 0.1667 0.1331-0.0941 0.4275
Kendall’s tau c 0.1591 0.1276-0.0909 0.4091
# Pearson Correlation 0.1667 0.1331-0.0941 0.4275
Spearman Rank Correlation 0.1667 0.1331-0.0941 0.4275
# Eta (col) 0.1667
# Eta (row) 0.1667
Somer’s delta (col) 0.1593 0.1277-0.0910 0.4097
Somer’s delta (row) 0.1744 0.1391-0.0981 0.4470
Somer’s delta symmetric 0.1665 0.1329-0.0940 0.4271
Lambda (col) 0.0000 0.0000 0.0000 0.0000
Lambda (row) 0.1154 0.2140-0.3041 0.5348
Lambda symmetric 0.0667 0.1271-0.1825 0.3158
Uncertainty coefficient (col) 0.0216 0.0348-0.0465 0.0897
Uncertainty coefficient (row) 0.0203 0.0326-0.0436 0.0841
Uncertainty coefficient symmetric 0.0209 0.0336-0.0450 0.0868

# Table scores

Cochran-Armitage Trend Test

Z-Statistic1-Tail Probability2-Tail Probability
# Cochran-Armitage Trend Test-1.2251 0.1103 0.2205

# Table scores
Binary variable is recoded to 0s and 1s.
Reported for 2 x K tables.

Expected Proportion 0.4945
Observed Proportion 0.5741

ValueStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Kappa 0.1574 0.1265 1.2444 0.1067 0.2134-0.0905 0.4053

Binomial Test

For Treatment
Subsample selected by: Gender = male

Expected Proportion 0.5000
Observed Proportion 0.5185

Proportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Wald 0.5185 0.0680 0.3853 0.6518
H0 0.5000 0.0680 0.2722 0.3927 0.7855
Wald with CC 0.5185 0.0680 0.3760 0.6610
H0 0.5000 0.0680 0.1361 0.4459 0.8918
Wilson (score) 0.3885 0.6461
Wilson with CC 0.3798 0.6546
Agresti-Coull 0.5173 0.0657 0.3885 0.6461
Agresti-Coull (+2) 0.5172 0.0656 0.3886 0.6458
Jeffreys 0.3872 0.6479
Clopper-Pearson (exact) 0.4460 0.8919 0.3784 0.6566

Binomial Test

For Response
Subsample selected by: Gender = male

Expected Proportion 0.5000
Observed Proportion 0.3519

Proportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Wald 0.3519 0.0650 0.2245 0.4792
H0 0.5000 0.0680-2.1773 0.0147 0.0295
Wald with CC 0.3519 0.0650 0.2152 0.4885
H0 0.5000 0.0680-2.0412 0.0206 0.0412
Wilson (score) 0.2382 0.4852
Wilson with CC 0.2303 0.4945
Agresti-Coull 0.3617 0.0632 0.2379 0.4855
Agresti-Coull (+2) 0.3621 0.0631 0.2384 0.4858
Jeffreys 0.2348 0.4843
Clopper-Pearson (exact) 0.0201 0.0402 0.2268 0.4938

Equivalence Test

For Treatment
Subsample selected by: Gender = male

Expected Proportion 0.5000
Observed Proportion 0.5185
Lower Equivalence Margin-0.2000

Lower EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.5185 0.0680 3.2138 0.0007 0.4067
H0 0.3000
Wald with CC 0.5185 0.0680 3.0776 0.0010 0.3974
H0 0.3000
Clopper-Pearson (exact) 0.0006 0.3989

Upper Equivalence Margin 0.2000

Upper EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.5185 0.0680-2.6691 0.0038 0.6304
H0 0.7000
Wald with CC 0.5185 0.0680-2.5329 0.0057 0.6396
H0 0.7000
Clopper-Pearson (exact) 0.0038 0.6366

Overall1-Tail ProbabilityLower 90%Upper 90%
Wald 0.0038 0.4067 0.6304
Wald with CC 0.0057 0.3974 0.6396
Clopper-Pearson (exact) 0.0038 0.3989 0.6366

Equivalence Test

For Response
Subsample selected by: Gender = male

Expected Proportion 0.5000
Observed Proportion 0.3519
Lower Equivalence Margin-0.2000

Lower EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.3519 0.0650 0.7979 0.2125 0.2450
H0 0.3000
Wald with CC 0.3519 0.0650 0.6554 0.2561 0.2357
H0 0.3000
Clopper-Pearson (exact) 0.2441 0.2441

Upper Equivalence Margin 0.2000

Upper EquivalenceProportion used in SEStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 90%Upper 90%
Wald 0.3519 0.0650-5.3573 0.0000 0.4587
H0 0.7000
Wald with CC 0.3519 0.0650-5.2148 0.0000 0.4680
H0 0.7000
Clopper-Pearson (exact) 0.0000 0.4723

Overall1-Tail ProbabilityLower 90%Upper 90%
Wald 0.2125 0.2450 0.4587
Wald with CC 0.2561 0.2357 0.4680
Clopper-Pearson (exact) 0.2441 0.2441 0.4723

Difference Between Unpaired Proportions

Proportion 1 0.6316
Proportion 2 0.4571

DifferenceStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Pooled Variance 0.1744 0.1424 1.2251 0.1103 0.2205-0.1046 0.4535
Separate Variance 0.1391 1.2544 0.1048 0.2097-0.0981 0.4470

Risk Ratio

ValueLower 95%Upper 95%
Risk Ratio 1.3816 0.8394 2.2739

Odds Ratio and Relative Risks

ValueLower 95%Upper 95%
Odds Ratio 2.0357 0.6478 6.3975
Exact 0.5661 7.6071
Relative Risk (Cohort 1) 1.5918 0.7413 3.4180
Relative Risk (Cohort 2) 0.7820 0.5259 1.1626

Difference Between Paired Proportions

Proportion 1 0.1296
Proportion 2 0.2963

DifferenceStandard ErrorZ-Statistic1-Tail Probability2-Tail ProbabilityLower 95%Upper 95%
Asymptotic-0.1667 0.0859-1.8766 0.0303 0.0606-0.3350 0.0016
Exact Binomial 0.0466 0.0931-0.3134 0.0249

Fisher’s Exact Test

Left-Tail ProbabilityRight-Tail ProbabilityTwo-Tail ProbabilityTable Probability
Fisher’s Exact 0.9352 0.1738 0.2635 0.1090

McNemar’s Test

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Asymptotic 3.5217 1 0.0606
Asymptotic with CC 2.7826 1 0.0953

2-Tail ProbabilityLower 95%Upper 95%
Exact Binomial 1.0000 0.8897 6.5699

Odds Ratio (Paired)

ValueLower 95%Upper 95%
Odds Ratio (Paired) 0.4375 0.8897 6.5699

Tetrachoric Correlation

RatioTetrachoric Correlation
2.0357 0.2727

Statistics for Diagnostic Tests

Smaller factor level represents the positive outcome.
Confidence Intervals: Row 1: Asymptotic Normal, Row 2: Exact Binomial

ValueStandard ErrorLower 95%Upper 95%
Sensitivity 0.6316 0.1107 0.4147 0.8485
0.3836 0.8371
Specificity 0.5429 0.0842 0.3778 0.7079
0.3665 0.7117
Accuracy 0.5741 0.0673 0.4422 0.7060
0.4321 0.7077
Prevalence 0.3519 0.0650 0.2245 0.4792
0.2268 0.4938
Apparent Prevalence 0.5185 0.0680 0.3853 0.6518
0.3784 0.6566
Youden’s Index 0.1744
-0.2500 0.5488
Positive Predictive Value 0.4286 0.0935 0.2453 0.6119
0.2446 0.6282
Negative Predictive Value 0.7308 0.0870 0.5603 0.9013
0.5221 0.8843
Positive Likelihood Ratio 1.3816 0.8394 2.2739
Negative Likelihood Ratio 0.6787 0.3593 1.2818
Diagnostic Odds Ratio 2.0357 0.6478 6.3975
Weighted Positive Likelihood Ratio 0.7500 0.4394 1.2801
Weighted Negative Likelihood Ratio 0.3684 0.1902 0.7136

Conditional Independence

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Cochran 8.4650 1 0.0036
Mantel-Haenszel 7.1983 1 0.0073

Common Odds Ratio and Relative Risks

ValueStandard ErrorLower 95%Upper 95%
Common Odds Ratio 3.3132 0.4232 1.4456 7.5934
Relative Risk (Cohort 1) 2.1636 0.2867 1.2336 3.7948
Relative Risk (Cohort 2) 0.6420 0.1586 0.4705 0.8761
Logit(Odds Ratio) 3.2941 0.4300 1.4182 7.6515
Relative Risk (Cohort 1) 2.1059 0.2890 1.1951 3.7108
Relative Risk (Cohort 2) 0.6613 0.1580 0.4852 0.9013
Ln(Odds Ratio) 1.1979 0.4232 0.3685 2.0273

Homogeneity of Odds Ratio

Chi-Square StatisticDegrees of FreedomRight-Tail Probability
Breslow-Day 1.4929 1 0.2218
Tarone 1.4905 1 0.2221