Statistics
| Data structure | Type of test | Power [CIs] | |
|---|---|---|---|
| aFigure 9A | N/APermutation test does not make assumptions about distribution of the data | Type of test: permutation test | p = 0.030 [0.0269–0.0334] |
| b Figure 9A | Description: test of whether there is a significant difference in the proportion of significant AUC cells in the glob vs interglob population (where significant AUC cells are those cells with AUCs significantly different than 0.5, or chance) for a given discrimination problem (e.g., low luminance/equiluminant)Type of test: Fisher’s exact test of proportions, two-tailedMethods used to compute 95% CIs: For each of 200 bootstrap samples of the cells (N = 300 for the globs, N = 181 for the interglobs), we determined the proportions of cells with significant AUCs and computed the test statistic described above. From the distribution of p values, we computed 95% CIs by the percentile method | Equiluminant/Low-luminance: p = 0.00002 [95% CIs: 3.95 × 10−10 to 0.006]High-luminance/Equiluminant: p = 2.6 × 10−13 [1.03 × 10−21 to 1.75 × 10−8] | |
| c Figure 9B | Normally distributed after Fisher’s z transform | Description: Test of whether the Pearson’s r values quantifying the correlation between peak tuning angles at two luminance levels is significantly different for the glob and interglob populations. We performed 200 bootstraps to define a distribution of r values for each luminance population combinationType of test: Student’s t test (two-tailed) applied to the z transform of a bootstrapped distribution of r values.Methods used to compute 95% CIs: We performed 200 bootstraps 1000 times in order to get 1000 p values for each comparison. From the distribution of p values, we computed 95% CIs by the percentile method. | Significance of glob cell vs interglob cell luminance peak correlationEquilum vs Low Lum: p = 1.27 × 10−155 [6.32 × 10−168 to 1.50 × 10−144]High Lum vs Equilum: p = 4.70 × 10−130 [3.67 × 10−141 to 2.92 × 10−118] |
| d Figure 9C | N/AMann–Whitney U rank-sum test does not assume a normal distribution | Description: test for peak shifting between luminance levels for eight evenly sized color categoriesType of test: Mann–Whitney U rank-sum test (MATLAB ranksum)Methods used to compute 95% CIs: We performed the rank-sum test on 2000 bootstraps containing 90% of the cells in each population in order to get a distribution of 1000 p values for each comparison. From the distribution of p values, we computed 95% CIs by the percentile method | GlobEquilum vs Low Lum (in same order as in panel C, top to bottom): p = 0.1267 [0.1193–0.1342];0.4726 [0.4596–0.4857];0.3052 [0.2923–0.3182];0.2256 [0.2143–0.2369];0.2731 [0.261–0.2853];0.3197 [0.307–0.3324];0.009168 [0.007482–0.01085];0.3883 [0.3748–0.4018];High Lum vs Equilum: p =0.592 [0.5808–0.6031];0.4484 [0.4354–0.4614];0.1211 [0.1125–0.1296];0.4631 [0.4495–0.4766];0.4176 [0.4041–0.4311];0.5271 [0.5149–0.5394];0.02754 [0.02441–0.03067];0.4146 [0.4013–0.428]InterglobsEquilum vs Low Lum (in same order as panel C, bottom to top): p = 0.3541 [0.3409–0.3673];0.3396 [0.3259–0.3533];0.07011 [0.06317–0.07704];0.1924 [0.1805–0.2044];0.4253 [0.4117–0.439];0.312 [0.2988–0.3252];0.4446 [0.4312–0.458];0.152 [0.1417–0.1623];High Lum vs Equilum: p =0.4467 [0.4335–0.4599];0.1771, [0.166–0.1882];0.07582, [0.069–0.08263];0.4654, [0.4517–0.4791];0.1828 [0.172–0.1936];0.009795 [0.007742–0.01185];0.02961, [0.02585–0.03336];0.457 [0.4438–0.4702] |
| e Figure 11A | Normally distributed after Fisher’s z transform | Description: Test of whether a Pearson’s r quantifying the correlation between a CIELUV RDM and a neural RDM is significantly different from zeroType of test: Student’s t test (two-tailed) applied to the z transform of r Methods used to compute 95% CIs: For each of 200 bootstrap samples of the cells, we created an RDM, computed the correlation between this bootstrap RDM and the CIELUV RDM, and computed the test statistic described above. From the distribution of p values, we computed 95% CIs | Significance of Glob and CIELUV RDM Correlation High Lum set: p = 4.31 × 10−296 [95% CIs: 2.11 × 10−316, 6.63 × 10−259]Equilum set: p = 1.62 × 10−271 [2.82 × 10−293 to 3.76 × 10−236]Low Lum set: p = 3.71 × 10−321 [0 to 2.44 × 10−276]Significance of Interglob and CIELUV RDM CorrelationHigh Lum set: p = 3.33 × 10−157 [1.08 × 10−171 to 1.40 × 10−114]Equilum set: p = 5.16 × 10−166 [1.70 × 10−174 to 6.68 × 10−115]Low Lum set: p = 4.80 × 10−93 [2.03 × 10−100 to 3.31 × 10−65]Significance of Model LGN and CIELUV RDM CorrelationAll values are highly significant, with p < 2.23 × 10−308 (upper bound on 95% CI 0, equivalent to 2.23 × 10−308 in MATLAB 2015b) |
| f Figure 11A | Normally distributed after Fisher’s z-transform | Description: Test of significance of difference between glob and interglob Pearson’s r correlation coefficientsType of test: Paired t test (two-tailed) applied to z-transforms of r’sMethods used to compute 95% CIs: As described in d above, we computed correlations between bootstrap RDMs and the CIELUV RDM, but here, subsequently performed the test statistic described above. | High Lum set: p = 2.05 × 10−8 [95% CIs, 6.15 × 10−5 to 4.00 × 10−15]Equilum set: p = 1.70 × 10−5 [2.20 × 10−3 to 6.17 × 10−11]Low Lum set: p < 2.0 × 10−16 [2.22 × 10−16, < 2.0 × 10−16] |
| g Figure 11B | Classification accuracies; permutation test does not make assumptions about distribution of the data | Description: Test of whether classification accuracy is significantly above chance (50%)Type of test: Permutation testMethods used to compute 95% CIs: For each of 200 bootstrap samples, we determined a classification accuracy given the bootstrap sample, and performed a permutation test to obtain a p value. Since our null distribution contained 200 points, p was bound at 0.005, permitting calculation of only an upper 95% confidence bound.Because the glob and interglob populations were of different sizes, we subsampled the glob population to N = 181 for each of 200 subsample runs, and consider the ps for all subsamples | Hue decodingGlobsGeneralizing to High Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any subsample of any bootstrap sample.]Generalizing to Equilum: p < 0.005. [No null points lay above the observed decoding accuracy for any subsample of any bootstrap sample.]Generalizing to Low Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any subsample of any bootstrap sample.]InterglobsGeneralizing to High Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any bootstrap sample.]Generalizing to equiluminant: p < 0.005 [upper 95% confidence bound = 0.08]Generalizing to Low Lum: p < 0.005 [upper 95% confidence bound = 0.315]Luminance decodingGlobsLow Lum/High Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any bootstrap sample.]Low Lum/Equilum: p < 0.005 [No null points lay above the observed decoding accuracy for any bootstrap sample.]Equilum/High Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any bootstrap sample.]InterglobsLow Lum/High Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any bootstrap sample.]Low Lum/Equilum: p < 0.005. [No null points lay above the observed decoding accuracy for any bootstrap sample.]Equilum/High Lum: p < 0.005. [No null points lay above the observed decoding accuracy for any bootstrap sample.] |
| h Figure 11B | Binomial distribution | Description: Significance of difference between classification accuracies for the glob versus interglob populationsType of test: McNemar’s exact test, two-tailed on paired binomial data, with α = 0.05Methods used to compute 95% CIs: For each of 200 bootstrap samples, we obtained a p value by taking the average of 200 p values derived by comparing the results for the interglob population and the results for one subsampling run of the glob population using McNemar’s extact test, two-tailed (for paired binomial data). | Hue decodingGeneralizing to High Lum: p = 5.29 × 10−7 [95% CIs: 1.05 × 10−10 to 0.003]Generalizing to Equilum: p = 6.27 × 10−12 [1.88 × 10−15 to 1.12 × 10−6]Generalizing to Low Lum: p = 1.69 × 10−5 [1.88 × 10−15 to 0.006]Luminance decodingLow Lum/High Lum: p = 0.213 [95% CIs: 0.005–0.939]Low Lum/Equilum: p = 0.463 [0.003–0.570]Equiluminant/High-luminance: p = 0.074 [2.6 × 10−6, 0.375] |
| iDiscussion | N/A, permutation test does not assume a normal distribution | Description: significance of difference between proportion of warm tuned and cool tuned cellsType of test: permutation test. For 2000 permutations, each cell was randomly assigned one of the 45 stimulus angles to be tuned to. A null distribution of warm-tuned-to-cool-tuned cell ratios was calculated from this permutation.Methods used to compute 95% CIs: We ran 2000 bootstraps using 90% of each population. For each bootstrap, we calculated a p value as the proportion of permuted populations with a higher warm-tuned-to-cool-tuned cell ratio than the warm-tuned-to-cool-tuned cell ratio of the bootstrap population. The 95% CIs are calculated from the bootstrap populations. Because we had 2000 bootstrap permutations, the lowest bound of the p value possible is p < 5 × 10−4 | GlobsHigh Lum: p = 0.001 [5 × 10−4 to 0.14]Equi Lum: 5 × 10−4 [5 × 10−4 to 0.001]Low Lum: p < 5 × 10−4 5 × 10−4 to 5 × 10−4] (globs had higher warm-tuned-to-cool-tuned cell ratio than all permutations on all bootstraps)InterglobsHigh Lum: p = 0.0035 [5 × 10−4 to 0.15]Equi Lum: p = .51 [0.06–0.95]Low Lum: p = p < 5 × 10−4 5 × 10−4 to 5 × 10−4] |
Equilum, Equiluminant; High Lum, high-luminance; Low Lum, low-luminance; N/A, not applicable.