diff --git a/docs/copying.html b/docs/copying.html index 6313ec4..c9a4d0d 100644 --- a/docs/copying.html +++ b/docs/copying.html @@ -3,7 +3,7 @@ - + diff --git a/docs/description.json b/docs/description.json index 35fd1d9..b2458fb 100644 --- a/docs/description.json +++ b/docs/description.json @@ -1,14 +1,14 @@ { "generator": "generate_html", "generator_version": "0.3.3", - "date_generated": "2024-05-07", + "date_generated": "2024-05-13", "package": { "name": "statistics-resampling", - "version": "5.5.10", + "version": "5.5.11", "description": "The statistics-resampling package is an Octave package and Matlab toolbox that can be used to perform a wide variety of statistics tasks using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, and calculate p-values for null hypothesis significance tests. Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures.", "shortdescription": "The statistics-resampling package is an Octave package and Matlab toolbox that can be used to perform a wide variety of statistics tasks using non-parametric resampling methods", - "date": "2024-04-27", + "date": "2024-05-13", "title": "A statistics package with a variety of resampling tools", "author": "Andrew Penn ", "maintainer": "Andrew Penn ", diff --git a/docs/function/boot.html b/docs/function/boot.html index 7899ec4..eaae0f6 100644 --- a/docs/function/boot.html +++ b/docs/function/boot.html @@ -3,7 +3,7 @@ - + @@ -118,15 +118,15 @@

Demonstration 1

Columns 1 through 13: - 1 2 1 1 3 3 3 2 1 3 1 2 3 - 2 1 3 1 3 2 3 3 3 2 3 2 2 - 2 2 1 2 2 2 2 1 1 3 1 3 1 + 2 3 3 2 2 2 1 1 3 1 3 3 2 + 3 1 3 1 2 3 2 2 2 1 2 1 2 + 2 1 3 3 2 1 2 3 1 2 1 2 3 Columns 14 through 20: - 2 1 3 2 3 1 2 - 2 2 1 3 1 1 2 - 1 3 1 3 3 3 1 + 1 2 2 3 3 1 1 + 2 3 3 1 1 3 3 + 1 1 1 2 3 3 1

Demonstration 2

@@ -141,15 +141,15 @@

Demonstration 2

Columns 1 through 13: - 2 3 2 3 3 1 2 1 1 2 3 2 3 - 3 3 2 3 3 2 2 1 1 2 1 2 2 - 2 3 1 2 3 2 3 1 1 3 3 2 3 + 2 3 2 2 3 1 3 1 2 2 1 2 2 + 2 1 1 2 3 2 2 1 1 3 3 1 3 + 3 3 1 2 3 1 3 1 2 2 3 2 3 Columns 14 through 20: - 3 2 2 1 1 1 3 - 1 1 3 1 2 2 3 - 1 1 2 1 1 1 3 + 3 1 2 1 2 3 3 + 3 1 2 1 1 1 2 + 1 1 3 3 1 3 2

Demonstration 3

diff --git a/docs/function/boot1way.html b/docs/function/boot1way.html index 5990489..dd68502 100644 --- a/docs/function/boot1way.html +++ b/docs/function/boot1way.html @@ -3,7 +3,7 @@ - + @@ -529,7 +529,7 @@

Demonstration 7

----------------------------------------------------------------------------- | Comparison | Test # | Ref # | Difference | t | p | |------------|------------|------------|------------|------------|----------| -| 1 | 2 | 1 | -0.1147 | -0.26 | .760 | +| 1 | 2 | 1 | -0.3684 | -0.63 | .564 | ----------------------------------------------------------------------------- | GROUP # | GROUP label | N | @@ -574,7 +574,7 @@

Demonstration 8

----------------------------------------------------------------------------- | Comparison | Test # | Ref # | Difference | t | p | |------------|------------|------------|------------|------------|----------| -| 1 | 2 | 1 | +1.340 | +2.51 | .019 |* +| 1 | 2 | 1 | +0.3039 | +0.44 | .600 | ----------------------------------------------------------------------------- | GROUP # | GROUP label | N | diff --git a/docs/function/bootbayes.html b/docs/function/bootbayes.html index 1d49530..13c5ee3 100644 --- a/docs/function/bootbayes.html +++ b/docs/function/bootbayes.html @@ -3,7 +3,7 @@ - + @@ -191,7 +191,7 @@

Demonstration 1

Posterior Statistics: original bias median stdev CI_lower CI_upper - +184.5 +0.04987 +184.5 1.286 +182.1 +187.1 + +184.5 +0.01529 +184.5 1.351 +181.7 +187.2

Demonstration 2

@@ -228,8 +228,8 @@

Demonstration 2

Posterior Statistics: original bias median stdev CI_lower CI_upper - +175.5 -0.1213 +175.3 2.401 +171.0 +180.2 - +0.1904 +0.003674 +0.1961 0.07964 +0.03563 +0.3449 + +175.5 -0.07775 +175.4 2.287 +171.1 +179.9 + +0.1904 +0.002169 +0.1929 0.07622 +0.03454 +0.3340

Package: statistics-resampling

diff --git a/docs/function/bootcdf.html b/docs/function/bootcdf.html index d8014b1..f6a7df4 100644 --- a/docs/function/bootcdf.html +++ b/docs/function/bootcdf.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/bootci.html b/docs/function/bootci.html index f441f9a..84aed2c 100644 --- a/docs/function/bootci.html +++ b/docs/function/bootci.html @@ -3,7 +3,7 @@ - + @@ -269,8 +269,8 @@

Demonstration 5

Produces the following output

ci =
 
-       114.34
-       257.98
+ 114.49 + 258.48

Demonstration 6

@@ -333,8 +333,8 @@

Demonstration 8

Produces the following output

ci =
 
-      0.50486
-       0.8608
+ 0.50615 + 0.86244

Demonstration 9

@@ -441,13 +441,13 @@

Demonstration 9

Produces the following output

ans =
 
-       -16.69      -20.563       -12.28
-      -11.721      -15.162      -7.7424
-      -8.0606       -11.43       -4.392
-      0.10476    -0.079726      0.28251
-     0.010336    -0.002213     0.023716
-      0.06452     0.032564     0.095997
-    0.0016638   0.00011273    0.0030787
+ -16.69 -20.554 -12.276 + -11.721 -15.155 -7.7419 + -8.0606 -11.428 -4.3915 + 0.10476 -0.079726 0.28245 + 0.010336 -0.0022151 0.023716 + 0.06452 0.032552 0.09599 + 0.0016638 0.00011268 0.0030786

Demonstration 10

@@ -468,8 +468,8 @@

Demonstration 10

Produces the following output

ci =
 
-     -0.61473     -0.41387
-      0.57767        0.869
+ -0.13896 -0.72921 + 0.7127 0.31607

Demonstration 11

@@ -595,9 +595,9 @@

Demonstration 11

% normal | 81.5% | 3.0% | 15.5% | 0.77 | 1.21 | % percentile | 81.5% | 0.9% | 17.6% | 0.76 | 0.91 | % basic | 81.1% | 2.5% | 16.4% | 0.78 | 1.09 | - % BCa | 84.2% | 5.4% | 10.4% | 0.86 | 1.82 | + % BCa | 83.9% | 5.2% | 10.9% | 0.83 | 1.84 | % bootstrap-t | 89.2% | 4.3% | 6.5% | 0.99 | 2.15 | - % calibrated | 87.4% | 4.2% | 8.4% | 0.91 | 2.03 | + % calibrated | 88.9% | 3.7% | 7.4% | 0.89 | 2.04 | % ---------------------|----------|--------|--------|--------|-------| % parametric - exact | 90.8% | 3.7% | 5.5% | 0.99 | 2.52 |

gives an example of how 'bootci' is used.

diff --git a/docs/function/bootclust.html b/docs/function/bootclust.html index 00f22e6..b980555 100644 --- a/docs/function/bootclust.html +++ b/docs/function/bootclust.html @@ -3,7 +3,7 @@ - + @@ -223,7 +223,7 @@

Demonstration 2

Bootstrap Statistics: original bias std_error CI_lower CI_upper - +29.65 -0.02581 +2.950 +22.83 +36.03 + +29.65 -0.02581 +2.950 +22.84 +36.04

Demonstration 3

@@ -312,11 +312,11 @@

Demonstration 5

Number of resamples: 1999 Number of data rows in each block: 1 Confidence interval (CI) type: Bias-corrected and accelerated (BCa) - Nominal coverage (and the percentiles used): 90% (11.6%, 98.6%) + Nominal coverage (and the percentiles used): 90% (11.7%, 98.6%) Bootstrap Statistics: original bias std_error CI_lower CI_upper - +171.5 -6.634 +42.13 +113.9 +258.2 + +171.5 -6.634 +42.13 +114.1 +258.7

Demonstration 6

@@ -343,11 +343,11 @@

Demonstration 6

Resampling method: Balanced, cluster bootstrap resampling Number of resamples: 1999 Confidence interval (CI) type: Bias-corrected and accelerated (BCa) - Nominal coverage (and the percentiles used): 90% (14.7%, 99.0%) + Nominal coverage (and the percentiles used): 90% (15.1%, 99.1%) Bootstrap Statistics: original bias std_error CI_lower CI_upper - +171.5 -10.30 +34.38 +124.4 +234.5 + +171.5 -10.30 +34.38 +125.0 +235.8

Demonstration 7

@@ -376,8 +376,8 @@

Demonstration 7

Bootstrap Statistics: original bias std_error CI_lower CI_upper - +0.1347 -0.0002717 +0.2395 -0.2643 +0.5321 - -0.02530 -0.01070 +0.1898 -0.3179 +0.2850 + +0.3052 -0.01557 +0.2059 -0.007480 +0.6725 + -0.1663 +0.02261 +0.1710 -0.4057 +0.1247

Demonstration 8

@@ -406,8 +406,8 @@

Demonstration 8

Bootstrap Statistics: original bias std_error CI_lower CI_upper - +0.2430 +0.006715 +0.3419 -0.2821 +0.8430 - +0.6460 -0.05234 +0.2541 +0.3552 +1.233 + +0.1401 +0.006113 +0.2929 -0.4786 +0.5297 + +0.04985 +0.009865 +0.1333 -0.1655 +0.2615

Demonstration 9

@@ -434,11 +434,11 @@

Demonstration 9

Resampling method: Balanced, cluster bootstrap resampling Number of resamples: 1999 Confidence interval (CI) type: Bias-corrected and accelerated (BCa) - Nominal coverage (and the percentiles used): 95% (1.9%, 96.9%) + Nominal coverage (and the percentiles used): 95% (2.8%, 97.8%) Bootstrap Statistics: original bias std_error CI_lower CI_upper - +0.7764 -0.02442 +0.1446 +0.3970 +0.9968 + +0.7764 -0.02442 +0.1446 +0.4355 +1.014

Demonstration 10

@@ -481,11 +481,11 @@

Demonstration 10

Number of resamples: 1999 Number of data rows in each block: 3 Confidence interval (CI) type: Bias-corrected and accelerated (BCa) - Nominal coverage (and the percentiles used): 95% (73.4%, 100.0%) + Nominal coverage (and the percentiles used): 95% (73.8%, 100.0%) Bootstrap Statistics: original bias std_error CI_lower CI_upper - +0.5858 -0.1686 +0.1319 +0.5009 +0.8686 + +0.5858 -0.1686 +0.1319 +0.5024 +0.8876

Package: statistics-resampling

diff --git a/docs/function/bootint.html b/docs/function/bootint.html index e6f3df7..ac7a8e9 100644 --- a/docs/function/bootint.html +++ b/docs/function/bootint.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/bootknife.html b/docs/function/bootknife.html index 524c0c1..b032f1d 100644 --- a/docs/function/bootknife.html +++ b/docs/function/bootknife.html @@ -3,7 +3,7 @@ - + @@ -345,11 +345,11 @@

Demonstration 5

Number of resamples (outer): 1999 Number of resamples (inner): 0 Confidence interval (CI) type: Bias-corrected and accelerated (BCa) - Nominal coverage (and the percentiles used): 90% (12.4%, 98.8%) + Nominal coverage (and the percentiles used): 90% (12.5%, 98.8%) Bootstrap Statistics: original bias std_error CI_lower CI_upper - +171.5 -7.008 +42.73 +115.6 +262.8 + +171.5 -7.008 +42.73 +115.8 +263.4

Demonstration 6

@@ -442,8 +442,8 @@

Demonstration 8

Bootstrap Statistics: original bias std_error CI_lower CI_upper - -0.06366 -0.003129 +0.2305 -0.4772 +0.2909 - -0.2389 +0.01182 +0.1885 -0.5011 +0.1103 + +0.1034 -0.001186 +0.1974 -0.1832 +0.4674 + -0.04645 +0.004099 +0.2699 -0.3929 +0.5239

Demonstration 9

@@ -470,11 +470,11 @@

Demonstration 9

Number of resamples (outer): 1999 Number of resamples (inner): 0 Confidence interval (CI) type: Bias-corrected and accelerated (BCa) - Nominal coverage (and the percentiles used): 95% (0.3%, 91.9%) + Nominal coverage (and the percentiles used): 95% (0.3%, 92.0%) Bootstrap Statistics: original bias std_error CI_lower CI_upper - +0.7764 -0.005773 +0.1423 +0.2271 +0.9389 + +0.7764 -0.005773 +0.1423 +0.2298 +0.9392

Demonstration 10

@@ -589,12 +589,12 @@

Demonstration 10

Bootstrap Statistics: original bias std_error CI_lower CI_upper -16.69 -0.5205 +2.058 -20.17 -12.46 - -11.72 -0.3644 +1.819 -14.92 -8.061 - -8.061 -0.2589 +1.722 -11.13 -4.497 - +0.1048 +0.005361 +0.09151 -0.07758 +0.2785 - +0.01034 +0.0006530 +0.006532 -0.003002 +0.02332 - +0.06452 +0.002386 +0.01657 +0.03330 +0.09536 - +0.001664 +8.603e-06 +0.0007476 +0.0001655 +0.003172 + -11.72 -0.3644 +1.819 -14.92 -8.059 + -8.061 -0.2589 +1.722 -11.13 -4.496 + +0.1048 +0.005361 +0.09151 -0.07761 +0.2784 + +0.01034 +0.0006530 +0.006532 -0.003006 +0.02331 + +0.06452 +0.002386 +0.01657 +0.03328 +0.09535 + +0.001664 +8.603e-06 +0.0007476 +0.0001654 +0.003172

Demonstration 11

@@ -790,7 +790,7 @@

Demonstration 12

% method | 0.05 | 0.95 | length | shape | % --------------------------------------|--------|--------|--------|-------| % ci2 - percentile (equal-tailed) | 96.2 | 237.2 | 141.0 | 0.87 | - % ci4 - BCa | 115.3 | 263.8 | 148.5 | 1.64 | + % ci4 - BCa | 116.1 | 265.1 | 149.0 | 1.69 | % ci6a - calibrated (equal-tailed) | 83.0 | 252.9 | 169.9 | 0.92 | % ci6b - calibrated | 113.2 | 282.4 | 169.2 | 1.90 | % --------------------------------------|--------|--------|--------|-------| @@ -805,13 +805,14 @@

Demonstration 12

% method | coverage | lower | upper | length | shape | % ---------------------------|----------|--------|--------|--------|-------| % percentile (equal-tailed) | 81.9% | 1.3% | 16.8% | 0.78 | 0.91 | - % BCa | 85.6% | 5.2% | 9.2% | 0.87 | 1.84 | + % BCa | 85.0% | 4.6% | 10.4% | 0.85 | 1.82 | % calibrated (equal-tailed) | 90.0% | 0.1% | 9.9% | 1.01 | 1.04 | % calibrated | 90.3% | 4.5% | 5.2% | 0.99 | 2.21 | % ---------------------------|----------|--------|--------|--------|-------| % parametric - exact | 90.8% | 3.7% | 5.5% | 0.99 | 2.52 | - % Summary of bias statistics from 'boot' package in R + % Summary of bias statistics computed using the 'statistics-resampling' + % package for Octave/Matlab % % method | original | bias | bias-corrected | % -----------------------------------|----------|---------|----------------| diff --git a/docs/function/bootlm.html b/docs/function/bootlm.html index 9a23862..e1a7140 100644 --- a/docs/function/bootlm.html +++ b/docs/function/bootlm.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/bootmode.html b/docs/function/bootmode.html index b0bb8b2..8f153d3 100644 --- a/docs/function/bootmode.html +++ b/docs/function/bootmode.html @@ -3,7 +3,7 @@ - + @@ -149,9 +149,9 @@

Demonstration 1

Produces the following output

ans = Summary of results:
 
-ans = H1 is 1 with p = 0 so reject the null hypothesisthat there is 1 mode
+ans = H1 is 1 with p = 0.001 so reject the null hypothesisthat there is 1 mode
 
-ans = H2 is 0 with p = 0.325 so accept the null hypothesis that there are 2 modes
+ans = H2 is 0 with p = 0.314 so accept the null hypothesis that there are 2 modes

Package: statistics-resampling

diff --git a/docs/function/bootstrp.html b/docs/function/bootstrp.html index 89d5df0..c06d38a 100644 --- a/docs/function/bootstrp.html +++ b/docs/function/bootstrp.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/bootwild.html b/docs/function/bootwild.html index ac6c2c2..0caacb1 100644 --- a/docs/function/bootwild.html +++ b/docs/function/bootwild.html @@ -3,7 +3,7 @@ - + @@ -218,8 +218,8 @@

Demonstration 2

Test Statistics: original std_err CI_lower CI_upper t-stat p-val FPR - +175.5 +2.502 +170.0 +181.0 +70.1 <.001 .010 - +0.1904 +0.08261 +0.009462 +0.3714 +2.31 .040 .259 + +175.5 +2.502 +169.8 +181.2 +70.1 <.001 .010 + +0.1904 +0.08261 +0.003534 +0.3773 +2.31 .047 .280

Package: statistics-resampling

diff --git a/docs/function/cor.html b/docs/function/cor.html index 225b7ac..0a91802 100644 --- a/docs/function/cor.html +++ b/docs/function/cor.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/credint.html b/docs/function/credint.html index 2a81311..939d91d 100644 --- a/docs/function/credint.html +++ b/docs/function/credint.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/deffcalc.html b/docs/function/deffcalc.html index 5a116de..03d60b8 100644 --- a/docs/function/deffcalc.html +++ b/docs/function/deffcalc.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/images/boot1way_701.png b/docs/function/images/boot1way_701.png index 68fd9c0..7f2fdbf 100644 Binary files a/docs/function/images/boot1way_701.png and b/docs/function/images/boot1way_701.png differ diff --git a/docs/function/images/boot1way_801.png b/docs/function/images/boot1way_801.png index 36a8710..4f5e5b2 100644 Binary files a/docs/function/images/boot1way_801.png and b/docs/function/images/boot1way_801.png differ diff --git a/docs/function/randtest.html b/docs/function/randtest.html index 35e6e1e..8a8d555 100644 --- a/docs/function/randtest.html +++ b/docs/function/randtest.html @@ -3,7 +3,7 @@ - + @@ -146,8 +146,8 @@

Demonstration 2

Produces the following output

pval =
 
-      0.53905
-   0.00035035
+      0.53148
+   0.00049014
 
 stat =
 
diff --git a/docs/function/randtest1.html b/docs/function/randtest1.html
index 79337b4..7713957 100644
--- a/docs/function/randtest1.html
+++ b/docs/function/randtest1.html
@@ -3,7 +3,7 @@
 
   
   
-  
+  
   
   
   
diff --git a/docs/function/randtest2.html b/docs/function/randtest2.html
index 38ef3cb..f04a664 100644
--- a/docs/function/randtest2.html
+++ b/docs/function/randtest2.html
@@ -3,7 +3,7 @@
 
   
   
-  
+  
   
   
   
@@ -162,9 +162,9 @@ 
Demonstration 1

                            @(A, B) log (var (A) ./ var (B)))

Produces the following output

-
pval = 0.3546
-pval = 0.2802
-pval = 0.317
+
pval = 0.3668
+pval = 0.2698
+pval = 0.30905

Demonstration 2

diff --git a/docs/function/sampszcalc.html b/docs/function/sampszcalc.html index e9f812b..ffea6c7 100644 --- a/docs/function/sampszcalc.html +++ b/docs/function/sampszcalc.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/smoothmad.html b/docs/function/smoothmad.html index ec4d580..903e20a 100644 --- a/docs/function/smoothmad.html +++ b/docs/function/smoothmad.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function/smoothmedian.html b/docs/function/smoothmedian.html index 6105c8d..e9be7ea 100644 --- a/docs/function/smoothmedian.html +++ b/docs/function/smoothmedian.html @@ -3,7 +3,7 @@ - + diff --git a/docs/function_reference.html b/docs/function_reference.html index cf955c8..65fc2f1 100644 --- a/docs/function_reference.html +++ b/docs/function_reference.html @@ -3,7 +3,7 @@ - + diff --git a/docs/index.html b/docs/index.html index ace1b61..2432f1f 100644 --- a/docs/index.html +++ b/docs/index.html @@ -3,7 +3,7 @@ - + @@ -27,8 +27,8 @@

About this package

- - + + diff --git a/matlab/statistics-resampling.mltbx b/matlab/statistics-resampling.mltbx index 902626c..10ab54f 100644 Binary files a/matlab/statistics-resampling.mltbx and b/matlab/statistics-resampling.mltbx differ diff --git a/matlab/statistics-resampling.prj b/matlab/statistics-resampling.prj index 12d5b5b..6a0e256 100644 --- a/matlab/statistics-resampling.prj +++ b/matlab/statistics-resampling.prj @@ -1,5 +1,5 @@ - + statistics-resampling Andrew Penn andy.c.penn@gmail.com @@ -7,7 +7,7 @@ Statistical analysis using resampling methods The statistics-resampling package is an Octave package and Matlab toolbox that can be used to perform a wide variety of statistics tasks using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, and calculate p-values for null hypothesis significance tests. Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures. Y:\Documents\GitHub\statistics-resampling\doc\icon.png - 5.5.10 + 5.5.11 ${PROJECT_ROOT}\statistics-resampling.mltbx @@ -53,6 +53,11 @@ Y:\Documents\GitHub\statistics-resampling\inst\boot.m + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexa64 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexmaca64 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexmaci64 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexw32 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexw64 Y:\Documents\GitHub\statistics-resampling\inst\boot1way.m Y:\Documents\GitHub\statistics-resampling\inst\bootbayes.m Y:\Documents\GitHub\statistics-resampling\inst\bootcdf.m @@ -74,6 +79,11 @@ Y:\Documents\GitHub\statistics-resampling\inst\sampszcalc.m Y:\Documents\GitHub\statistics-resampling\inst\smoothmad.m Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.m + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexa64 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexmaca64 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexmaci64 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexw32 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexw64
Package Version:5.5.10
Last Release Date:2024-04-27
Package Version:5.5.11
Last Release Date:2024-05-13
Package Author:Andrew Penn <andy.c.penn@gmail.com>
Package Maintainer:Andrew Penn <andy.c.penn@gmail.com>
License:GPLv3+