Test for differences in direction means with pairwise comparisons
Source:R/test_direction.R
test_direction.Rdtest_direction() evaluates differences in mean direction across different tracks using a specified statistical test. It includes options for ANOVA, Kruskal-Wallis test, and Generalized Linear Models (GLM), and checks for assumptions such as normality and homogeneity of variances. For datasets with more than two tracks, it performs pairwise comparisons to identify specific differences between tracks.
Arguments
- data
A
trackR object, which is a list consisting of two elements:Trajectories: A list of interpolated trajectories, where each trajectory is a series of midpoints between consecutive footprints.Footprints: A list of data frames containing footprint coordinates, metadata (e.g., image reference, ID), and a marker indicating whether the footprint is actual or inferred.
- analysis
A character string specifying the type of analysis:
"ANOVA","Kruskal-Wallis", or"GLM". Default is"ANOVA".
Value
A list with the results of the statistical analysis and diagnostic tests:
normality_results: A matrix of test statistics and p-values from the Shapiro-Wilk test for each track, with rows for the test statistic and p-value, and columns for each track.homogeneity_test: The result of Levene's test, including the p-value for homogeneity of variances.ANOVA(Ifanalysisis"ANOVA"): A list containing the ANOVA table and Tukey HSD post-hoc test results.Kruskal_Wallis(Ifanalysisis"Kruskal-Wallis"): A list containing the Kruskal-Wallis test result and Dunn's test post-hoc results.GLM(Ifanalysisis"GLM"): A summary of the GLM fit and pairwise comparisons.
Details
The test_direction() function performs the following operations:
Condition Testing:
Normality: Shapiro-Wilk test for normality on step direction data within each track.
Homogeneity of Variances: Levene's test for equal variances across tracks.
Statistical Analysis:
ANOVA: Compares step mean directions across tracks, assuming normality and homogeneity of variances. Includes Tukey's HSD post-hoc test for pairwise comparisons.
Kruskal-Wallis Test: Non-parametric alternative to ANOVA for comparing step median directions across tracks when assumptions are violated. Includes Dunn's test for pairwise comparisons.
GLM: Generalized Linear Model with a Gaussian family for comparing step means if ANOVA assumptions are not met. Pairwise comparisons in the GLM are conducted using estimated marginal means (least-squares means) with the emmeans package, which computes differences between group means while adjusting for multiple comparisons using Tukey’s method.
Direction Measurement:
The direction is measured in degrees. The reference direction, or 0 degrees, is considered to be along the positive x-axis. Angles are measured counterclockwise from the positive x-axis, with 0 degrees pointing directly along this axis.
Author
Humberto G. Ferrón
humberto.ferron@uv.es
Macroevolution and Functional Morphology Research Group (www.macrofun.es)
Cavanilles Institute of Biodiversity and Evolutionary Biology
Calle Catedrático José Beltrán Martínez, nº 2
46980 Paterna - Valencia - Spain
Phone: +34 (9635) 44477
Examples
# Example 1: Test for Differences in Direction Means with Pairwise Comparisons in MountTom dataset
test_direction(MountTom, analysis = "ANOVA")
#> Warning: The following tracks were removed from the analysis due to having 3 or fewer footprints: Track 05, Track 06, Track 10, Track 11, Track 12, Track 14, Track 17, Track 19, Track 20, Track 21, Track 22, Track 23.
#> Warning: One or more tracks do not follow a normal distribution (p-value <= 0.05). Assumptions for ANOVA are not met. Consider using 'Kruskal-Wallis' or 'GLM'.
#> $normality_results
#> Track 01 Track 02 Track 03 Track 04 Track 07 Track 08
#> statistic.W 0.9651863 0.9159365 0.8835034 0.8785774 0.717041538 0.9574186
#> p_value 0.8507202 0.3596607 0.3254893 0.3029142 0.005672604 0.7996415
#> Track 09 Track 13 Track 15 Track 16 Track 18
#> statistic.W 0.78162330 0.8903881 0.8576212 0.9064091 0.9483026
#> p_value 0.05691451 0.3590583 0.2198329 0.3294686 0.7250578
#>
#> $homogeneity_test
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 10 1.8236 0.07643 .
#> 58
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> $ANOVA
#> $ANOVA$ANOVA
#> Df Sum Sq Mean Sq F value Pr(>F)
#> track 10 372424 37242 1081 <2e-16 ***
#> Residuals 58 1999 34
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> $ANOVA$Tukey
#> Tukey multiple comparisons of means
#> 95% family-wise confidence level
#>
#> Fit: aov(formula = dir ~ track, data = M_analysis)
#>
#> $track
#> diff lwr upr p adj
#> Track 02-Track 01 -8.0809326 -17.352515 1.1906495 0.1421812
#> Track 03-Track 01 -4.2235962 -15.193880 6.7466877 0.9669723
#> Track 04-Track 01 -8.9073199 -19.877604 2.0629641 0.2165280
#> Track 07-Track 01 -15.9377861 -25.849524 -6.0260479 0.0000688
#> Track 08-Track 01 -14.2962893 -24.662233 -3.9303453 0.0010286
#> Track 09-Track 01 -157.8393877 -168.809672 -146.8691037 0.0000000
#> Track 13-Track 01 -263.5986805 -274.568964 -252.6283965 0.0000000
#> Track 15-Track 01 -19.4449561 -30.415240 -8.4746721 0.0000090
#> Track 16-Track 01 -10.2244220 -19.781350 -0.6674939 0.0264453
#> Track 18-Track 01 -25.9444892 -36.914773 -14.9742053 0.0000000
#> Track 03-Track 02 3.8573364 -7.112948 14.8276203 0.9825136
#> Track 04-Track 02 -0.8263872 -11.796671 10.1438967 1.0000000
#> Track 07-Track 02 -7.8568535 -17.768592 2.0548847 0.2456248
#> Track 08-Track 02 -6.2153566 -16.581301 4.1505873 0.6437392
#> Track 09-Track 02 -149.7584550 -160.728739 -138.7881711 0.0000000
#> Track 13-Track 02 -255.5177478 -266.488032 -244.5474639 0.0000000
#> Track 15-Track 02 -11.3640234 -22.334307 -0.3937395 0.0362396
#> Track 16-Track 02 -2.1434894 -11.700418 7.4134387 0.9995411
#> Track 18-Track 02 -17.8635566 -28.833841 -6.8932727 0.0000536
#> Track 04-Track 03 -4.6837236 -17.122856 7.7554092 0.9716324
#> Track 07-Track 03 -11.7141899 -23.230589 -0.1977908 0.0429263
#> Track 08-Track 03 -10.0726930 -21.982256 1.8368699 0.1715168
#> Track 09-Track 03 -153.6157914 -166.054924 -141.1766587 0.0000000
#> Track 13-Track 03 -259.3750842 -271.814217 -246.9359515 0.0000000
#> Track 15-Track 03 -15.2213598 -27.660493 -2.7822271 0.0056705
#> Track 16-Track 03 -6.0008258 -17.213309 5.2116570 0.7791969
#> Track 18-Track 03 -21.7208930 -34.160026 -9.2817602 0.0000125
#> Track 07-Track 04 -7.0304663 -18.546865 4.4859329 0.6192299
#> Track 08-Track 04 -5.3889694 -17.298532 6.5205935 0.9084457
#> Track 09-Track 04 -148.9320678 -161.371201 -136.4929350 0.0000000
#> Track 13-Track 04 -254.6913606 -267.130493 -242.2522279 0.0000000
#> Track 15-Track 04 -10.5376362 -22.976769 1.9014966 0.1698520
#> Track 16-Track 04 -1.3171022 -12.529585 9.8953806 0.9999989
#> Track 18-Track 04 -17.0371694 -29.476302 -4.5980366 0.0011459
#> Track 08-Track 07 1.6414969 -9.300766 12.5837596 0.9999884
#> Track 09-Track 07 -141.9016015 -153.418001 -130.3852024 0.0000000
#> Track 13-Track 07 -247.6608943 -259.177293 -236.1444952 0.0000000
#> Track 15-Track 07 -3.5071699 -15.023569 8.0092292 0.9940963
#> Track 16-Track 07 5.7133641 -4.465791 15.8925190 0.7269309
#> Track 18-Track 07 -10.0067031 -21.523102 1.5096961 0.1450230
#> Track 09-Track 08 -143.5430984 -155.452661 -131.6335355 0.0000000
#> Track 13-Track 08 -249.3023912 -261.211954 -237.3928283 0.0000000
#> Track 15-Track 08 -5.1486668 -17.058230 6.7608961 0.9302534
#> Track 16-Track 08 4.0718672 -6.550065 14.6937990 0.9679259
#> Track 18-Track 08 -11.6482000 -23.557763 0.2613630 0.0605113
#> Track 13-Track 09 -105.7592928 -118.198426 -93.3201600 0.0000000
#> Track 15-Track 09 138.3944316 125.955299 150.8335644 0.0000000
#> Track 16-Track 09 147.6149656 136.402483 158.8274484 0.0000000
#> Track 18-Track 09 131.8948984 119.455766 144.3340312 0.0000000
#> Track 15-Track 13 244.1537244 231.714592 256.5928572 0.0000000
#> Track 16-Track 13 253.3742584 242.161776 264.5867412 0.0000000
#> Track 18-Track 13 237.6541912 225.215058 250.0933240 0.0000000
#> Track 16-Track 15 9.2205340 -1.991949 20.4330168 0.2018750
#> Track 18-Track 15 -6.4995332 -18.938666 5.9395996 0.8028891
#> Track 18-Track 16 -15.7200672 -26.932550 -4.5075844 0.0007922
#>
#>
#>
# Example 2: Test for Differences in Direction Means with Pairwise Comparisons in MountTom dataset
test_direction(MountTom, analysis = "Kruskal-Wallis")
#> Warning: The following tracks were removed from the analysis due to having 3 or fewer footprints: Track 05, Track 06, Track 10, Track 11, Track 12, Track 14, Track 17, Track 19, Track 20, Track 21, Track 22, Track 23.
#> Warning: One or more tracks do not follow a normal distribution (p-value <= 0.05). Assumptions for ANOVA are not met. Consider using 'Kruskal-Wallis' or 'GLM'.
#> Kruskal-Wallis rank sum test
#>
#> data: x and group
#> Kruskal-Wallis chi-squared = 53.6361, df = 10, p-value = 0
#>
#>
#> Comparison of x by group
#> (No adjustment)
#> Col Mean-|
#> Row Mean | Track 01 Track 02 Track 03 Track 04 Track 07 Track 08
#> ---------+------------------------------------------------------------------
#> Track 02 | 1.879941
#> | 0.0301
#> |
#> Track 03 | 0.844071 -0.744769
#> | 0.1993 0.2282
#> |
#> Track 04 | 1.809292 0.220451 0.851244
#> | 0.0352 0.4128 0.1973
#> |
#> Track 07 | 2.969080 1.210555 1.751332 0.831882
#> | 0.0015* 0.1130 0.0399 0.2027
#> |
#> Track 08 | 2.974102 1.292630 1.811121 0.922025 0.128001
#> | 0.0015* 0.0981 0.0351 0.1783 0.4491
#> |
#> Track 09 | 4.865825 3.276984 3.546853 2.695608 2.079707 1.893445
#> | 0.0000* 0.0005* 0.0002* 0.0035* 0.0188* 0.0291
#> |
#> Track 13 | 5.312686 3.723845 3.940948 3.089703 2.505378 2.305064
#> | 0.0000* 0.0001* 0.0000* 0.0010* 0.0061* 0.0106*
#> |
#> Track 15 | 3.668236 2.079395 2.490679 1.639434 0.938908 0.790307
#> | 0.0001* 0.0188* 0.0064* 0.0506 0.1739 0.2147
#> |
#> Track 16 | 2.238443 0.414632 1.082092 0.137720 -0.789466 -0.888419
#> | 0.0126* 0.3392 0.1396 0.4452 0.2149 0.1872
#> |
#> Track 18 | 4.240219 2.651378 2.995120 2.143875 1.483767 1.317179
#> | 0.0000* 0.0040* 0.0014* 0.0160* 0.0689 0.0939
#> Col Mean-|
#> Row Mean | Track 09 Track 13 Track 15 Track 16
#> ---------+--------------------------------------------
#> Track 13 | 0.394094
#> | 0.3468
#> |
#> Track 15 | -1.056174 -1.450268
#> | 0.1454 0.0735
#> |
#> Track 16 | -2.852788 -3.289997 -1.681068
#> | 0.0022* 0.0005* 0.0464
#> |
#> Track 18 | -0.551732 -0.945827 0.504441 2.240695
#> | 0.2906 0.1721 0.3070 0.0125*
#>
#> alpha = 0.05
#> Reject Ho if p <= alpha/2
#> $normality_results
#> Track 01 Track 02 Track 03 Track 04 Track 07 Track 08
#> statistic.W 0.9651863 0.9159365 0.8835034 0.8785774 0.717041538 0.9574186
#> p_value 0.8507202 0.3596607 0.3254893 0.3029142 0.005672604 0.7996415
#> Track 09 Track 13 Track 15 Track 16 Track 18
#> statistic.W 0.78162330 0.8903881 0.8576212 0.9064091 0.9483026
#> p_value 0.05691451 0.3590583 0.2198329 0.3294686 0.7250578
#>
#> $homogeneity_test
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 10 1.8236 0.07643 .
#> 58
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> $Kruskal_Wallis
#> $Kruskal_Wallis$Kruskal_Wallis
#>
#> Kruskal-Wallis rank sum test
#>
#> data: dir by track
#> Kruskal-Wallis chi-squared = 53.636, df = 10, p-value = 5.671e-08
#>
#>
#> $Kruskal_Wallis$Dunn
#> $Kruskal_Wallis$Dunn$chi2
#> [1] 53.63609
#>
#> $Kruskal_Wallis$Dunn$Z
#> [1] 1.8799419 0.8440717 -0.7447692 1.8092926 0.2204517 0.8512448
#> [7] 2.9690804 1.2105558 1.7513323 0.8318828 2.9741021 1.2926309
#> [13] 1.8111218 0.9220257 0.1280017 4.8658252 3.2769843 3.5468532
#> [19] 2.6956084 2.0797071 1.8934455 5.3126867 3.7238459 3.9409480
#> [25] 3.0897032 2.5053781 2.3050641 0.3940948 3.6682364 2.0793955
#> [31] 2.4906791 1.6394344 0.9389087 0.7903077 -1.0561741 -1.4502689
#> [37] 2.2384437 0.4146322 1.0820921 0.1377208 -0.7894666 -0.8884194
#> [43] -2.8527883 -3.2899972 -1.6810683 4.2402191 2.6513782 2.9951205
#> [49] 2.1438757 1.4837676 1.3171795 -0.5517327 -0.9458275 0.5044413
#> [55] 2.2406958
#>
#> $Kruskal_Wallis$Dunn$P
#> [1] 3.005800e-02 1.993147e-01 2.282056e-01 3.520278e-02 4.127597e-01
#> [6] 1.973167e-01 1.493462e-03 1.130328e-01 3.994435e-02 2.027375e-01
#> [11] 1.469236e-03 9.806936e-02 3.506100e-02 1.782576e-01 4.490738e-01
#> [16] 5.699010e-07 5.246109e-04 1.949309e-04 3.513010e-03 1.877620e-02
#> [21] 2.914932e-02 5.401032e-08 9.810538e-05 4.058011e-05 1.001783e-03
#> [26] 6.116028e-03 1.058149e-02 3.467555e-01 1.221146e-04 1.879051e-02
#> [31] 6.374960e-03 5.056141e-02 1.738888e-01 2.146740e-01 1.454443e-01
#> [36] 7.349178e-02 1.259607e-02 3.392056e-01 1.396058e-01 4.452305e-01
#> [41] 2.149197e-01 1.871576e-01 2.166874e-03 5.009419e-04 4.637482e-02
#> [46] 1.116508e-05 4.008200e-03 1.371682e-03 1.602142e-02 6.893529e-02
#> [51] 9.388923e-02 2.905657e-01 1.721183e-01 3.069756e-01 1.252289e-02
#>
#> $Kruskal_Wallis$Dunn$P.adjusted
#> [1] 3.005800e-02 1.993147e-01 2.282056e-01 3.520278e-02 4.127597e-01
#> [6] 1.973167e-01 1.493462e-03 1.130328e-01 3.994435e-02 2.027375e-01
#> [11] 1.469236e-03 9.806936e-02 3.506100e-02 1.782576e-01 4.490738e-01
#> [16] 5.699010e-07 5.246109e-04 1.949309e-04 3.513010e-03 1.877620e-02
#> [21] 2.914932e-02 5.401032e-08 9.810538e-05 4.058011e-05 1.001783e-03
#> [26] 6.116028e-03 1.058149e-02 3.467555e-01 1.221146e-04 1.879051e-02
#> [31] 6.374960e-03 5.056141e-02 1.738888e-01 2.146740e-01 1.454443e-01
#> [36] 7.349178e-02 1.259607e-02 3.392056e-01 1.396058e-01 4.452305e-01
#> [41] 2.149197e-01 1.871576e-01 2.166874e-03 5.009419e-04 4.637482e-02
#> [46] 1.116508e-05 4.008200e-03 1.371682e-03 1.602142e-02 6.893529e-02
#> [51] 9.388923e-02 2.905657e-01 1.721183e-01 3.069756e-01 1.252289e-02
#>
#> $Kruskal_Wallis$Dunn$comparisons
#> [1] "Track 01 - Track 02" "Track 01 - Track 03" "Track 02 - Track 03"
#> [4] "Track 01 - Track 04" "Track 02 - Track 04" "Track 03 - Track 04"
#> [7] "Track 01 - Track 07" "Track 02 - Track 07" "Track 03 - Track 07"
#> [10] "Track 04 - Track 07" "Track 01 - Track 08" "Track 02 - Track 08"
#> [13] "Track 03 - Track 08" "Track 04 - Track 08" "Track 07 - Track 08"
#> [16] "Track 01 - Track 09" "Track 02 - Track 09" "Track 03 - Track 09"
#> [19] "Track 04 - Track 09" "Track 07 - Track 09" "Track 08 - Track 09"
#> [22] "Track 01 - Track 13" "Track 02 - Track 13" "Track 03 - Track 13"
#> [25] "Track 04 - Track 13" "Track 07 - Track 13" "Track 08 - Track 13"
#> [28] "Track 09 - Track 13" "Track 01 - Track 15" "Track 02 - Track 15"
#> [31] "Track 03 - Track 15" "Track 04 - Track 15" "Track 07 - Track 15"
#> [34] "Track 08 - Track 15" "Track 09 - Track 15" "Track 13 - Track 15"
#> [37] "Track 01 - Track 16" "Track 02 - Track 16" "Track 03 - Track 16"
#> [40] "Track 04 - Track 16" "Track 07 - Track 16" "Track 08 - Track 16"
#> [43] "Track 09 - Track 16" "Track 13 - Track 16" "Track 15 - Track 16"
#> [46] "Track 01 - Track 18" "Track 02 - Track 18" "Track 03 - Track 18"
#> [49] "Track 04 - Track 18" "Track 07 - Track 18" "Track 08 - Track 18"
#> [52] "Track 09 - Track 18" "Track 13 - Track 18" "Track 15 - Track 18"
#> [55] "Track 16 - Track 18"
#>
#>
#>
# Example 3: Test for Differences in Direction Means with Pairwise Comparisons in MountTom dataset
test_direction(MountTom, analysis = "GLM")
#> Warning: The following tracks were removed from the analysis due to having 3 or fewer footprints: Track 05, Track 06, Track 10, Track 11, Track 12, Track 14, Track 17, Track 19, Track 20, Track 21, Track 22, Track 23.
#> Warning: One or more tracks do not follow a normal distribution (p-value <= 0.05). Assumptions for ANOVA are not met. Consider using 'Kruskal-Wallis' or 'GLM'.
#> $normality_results
#> Track 01 Track 02 Track 03 Track 04 Track 07 Track 08
#> statistic.W 0.9651863 0.9159365 0.8835034 0.8785774 0.717041538 0.9574186
#> p_value 0.8507202 0.3596607 0.3254893 0.3029142 0.005672604 0.7996415
#> Track 09 Track 13 Track 15 Track 16 Track 18
#> statistic.W 0.78162330 0.8903881 0.8576212 0.9064091 0.9483026
#> p_value 0.05691451 0.3590583 0.2198329 0.3294686 0.7250578
#>
#> $homogeneity_test
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 10 1.8236 0.07643 .
#> 58
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> $GLM
#> $GLM$GLM
#>
#> Call:
#> glm(formula = dir ~ track, family = gaussian(), data = M_analysis)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 136.609 1.957 69.810 < 2e-16 ***
#> trackTrack 02 -8.081 2.767 -2.920 0.004978 **
#> trackTrack 03 -4.224 3.274 -1.290 0.202220
#> trackTrack 04 -8.907 3.274 -2.720 0.008595 **
#> trackTrack 07 -15.938 2.959 -5.387 1.36e-06 ***
#> trackTrack 08 -14.296 3.094 -4.621 2.18e-05 ***
#> trackTrack 09 -157.839 3.274 -48.203 < 2e-16 ***
#> trackTrack 13 -263.599 3.274 -80.501 < 2e-16 ***
#> trackTrack 15 -19.445 3.274 -5.938 1.72e-07 ***
#> trackTrack 16 -10.224 2.853 -3.584 0.000694 ***
#> trackTrack 18 -25.944 3.274 -7.923 8.24e-11 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for gaussian family taken to be 34.4641)
#>
#> Null deviance: 374423.4 on 68 degrees of freedom
#> Residual deviance: 1998.9 on 58 degrees of freedom
#> AIC: 452.09
#>
#> Number of Fisher Scoring iterations: 2
#>
#>
#> $GLM$pairwise_results
#> $emmeans
#> track emmean SE df lower.CL upper.CL
#> Track 01 136.6 1.96 58 132.7 141
#> Track 02 128.5 1.96 58 124.6 132
#> Track 03 132.4 2.63 58 127.1 138
#> Track 04 127.7 2.63 58 122.4 133
#> Track 07 120.7 2.22 58 116.2 125
#> Track 08 122.3 2.40 58 117.5 127
#> Track 09 -21.2 2.63 58 -26.5 -16
#> Track 13 -127.0 2.63 58 -132.2 -122
#> Track 15 117.2 2.63 58 111.9 122
#> Track 16 126.4 2.08 58 122.2 131
#> Track 18 110.7 2.63 58 105.4 116
#>
#> Confidence level used: 0.95
#>
#> $contrasts
#> contrast estimate SE df t.ratio p.value
#> Track 01 - Track 02 8.081 2.77 58 2.920 0.1422
#> Track 01 - Track 03 4.224 3.27 58 1.290 0.9670
#> Track 01 - Track 04 8.907 3.27 58 2.720 0.2165
#> Track 01 - Track 07 15.938 2.96 58 5.387 0.0001
#> Track 01 - Track 08 14.296 3.09 58 4.621 0.0010
#> Track 01 - Track 09 157.839 3.27 58 48.203 <.0001
#> Track 01 - Track 13 263.599 3.27 58 80.501 <.0001
#> Track 01 - Track 15 19.445 3.27 58 5.938 <.0001
#> Track 01 - Track 16 10.224 2.85 58 3.584 0.0264
#> Track 01 - Track 18 25.944 3.27 58 7.923 <.0001
#> Track 02 - Track 03 -3.857 3.27 58 -1.178 0.9825
#> Track 02 - Track 04 0.826 3.27 58 0.252 1.0000
#> Track 02 - Track 07 7.857 2.96 58 2.656 0.2456
#> Track 02 - Track 08 6.215 3.09 58 2.009 0.6437
#> Track 02 - Track 09 149.758 3.27 58 45.735 <.0001
#> Track 02 - Track 13 255.518 3.27 58 78.033 <.0001
#> Track 02 - Track 15 11.364 3.27 58 3.470 0.0362
#> Track 02 - Track 16 2.143 2.85 58 0.751 0.9995
#> Track 02 - Track 18 17.864 3.27 58 5.455 0.0001
#> Track 03 - Track 04 4.684 3.71 58 1.261 0.9716
#> Track 03 - Track 07 11.714 3.44 58 3.408 0.0429
#> Track 03 - Track 08 10.073 3.55 58 2.834 0.1715
#> Track 03 - Track 09 153.616 3.71 58 41.374 <.0001
#> Track 03 - Track 13 259.375 3.71 58 69.858 <.0001
#> Track 03 - Track 15 15.221 3.71 58 4.100 0.0057
#> Track 03 - Track 16 6.001 3.35 58 1.793 0.7792
#> Track 03 - Track 18 21.721 3.71 58 5.850 <.0001
#> Track 04 - Track 07 7.030 3.44 58 2.045 0.6192
#> Track 04 - Track 08 5.389 3.55 58 1.516 0.9084
#> Track 04 - Track 09 148.932 3.71 58 40.112 <.0001
#> Track 04 - Track 13 254.691 3.71 58 68.596 <.0001
#> Track 04 - Track 15 10.538 3.71 58 2.838 0.1699
#> Track 04 - Track 16 1.317 3.35 58 0.394 1.0000
#> Track 04 - Track 18 17.037 3.71 58 4.589 0.0011
#> Track 07 - Track 08 -1.641 3.27 58 -0.503 1.0000
#> Track 07 - Track 09 141.902 3.44 58 41.281 <.0001
#> Track 07 - Track 13 247.661 3.44 58 72.047 <.0001
#> Track 07 - Track 15 3.507 3.44 58 1.020 0.9941
#> Track 07 - Track 16 -5.713 3.04 58 -1.880 0.7269
#> Track 07 - Track 18 10.007 3.44 58 2.911 0.1450
#> Track 08 - Track 09 143.543 3.55 58 40.380 <.0001
#> Track 08 - Track 13 249.302 3.55 58 70.131 <.0001
#> Track 08 - Track 15 5.149 3.55 58 1.448 0.9303
#> Track 08 - Track 16 -4.072 3.17 58 -1.284 0.9679
#> Track 08 - Track 18 11.648 3.55 58 3.277 0.0605
#> Track 09 - Track 13 105.759 3.71 58 28.484 <.0001
#> Track 09 - Track 15 -138.394 3.71 58 -37.274 <.0001
#> Track 09 - Track 16 -147.615 3.35 58 -44.107 <.0001
#> Track 09 - Track 18 -131.895 3.71 58 -35.523 <.0001
#> Track 13 - Track 15 -244.154 3.71 58 -65.758 <.0001
#> Track 13 - Track 16 -253.374 3.35 58 -75.707 <.0001
#> Track 13 - Track 18 -237.654 3.71 58 -64.008 <.0001
#> Track 15 - Track 16 -9.221 3.35 58 -2.755 0.2019
#> Track 15 - Track 18 6.500 3.71 58 1.751 0.8029
#> Track 16 - Track 18 15.720 3.35 58 4.697 0.0008
#>
#> P value adjustment: tukey method for comparing a family of 11 estimates
#>
#>
#>
# Example 4: Test for Differences in Direction Means with Pairwise Comparisons in PaluxyRiver
# dataset
test_direction(PaluxyRiver, analysis = "ANOVA")
#> Warning: One or more tracks do not follow a normal distribution (p-value <= 0.05). Assumptions for ANOVA are not met. Consider using 'Kruskal-Wallis' or 'GLM'.
#> $normality_results
#> Track 1 Track 2
#> statistic.W 0.900319498 0.91666968
#> p_value 0.009971017 0.04932503
#>
#> $homogeneity_test
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 1 0.2935 0.5903
#> 51
#>
#> $ANOVA
#> $ANOVA$ANOVA
#> Df Sum Sq Mean Sq F value Pr(>F)
#> track 1 49 49.01 0.646 0.425
#> Residuals 51 3867 75.82
#>
#> $ANOVA$Tukey
#> Tukey multiple comparisons of means
#> 95% family-wise confidence level
#>
#> Fit: aov(formula = dir ~ track, data = M_analysis)
#>
#> $track
#> diff lwr upr p adj
#> Track 2-Track 1 -1.931824 -6.755731 2.892084 0.4251435
#>
#>
#>
# Example 5: Test for Differences in Direction Means with Pairwise Comparisons in PaluxyRiver
# dataset
test_direction(PaluxyRiver, analysis = "Kruskal-Wallis")
#> Warning: One or more tracks do not follow a normal distribution (p-value <= 0.05). Assumptions for ANOVA are not met. Consider using 'Kruskal-Wallis' or 'GLM'.
#> Kruskal-Wallis rank sum test
#>
#> data: x and group
#> Kruskal-Wallis chi-squared = 0.5368, df = 1, p-value = 0.46
#>
#>
#> Comparison of x by group
#> (No adjustment)
#> Col Mean-|
#> Row Mean | Track 1
#> ---------+-----------
#> Track 2 | 0.732639
#> | 0.2319
#>
#> alpha = 0.05
#> Reject Ho if p <= alpha/2
#> $normality_results
#> Track 1 Track 2
#> statistic.W 0.900319498 0.91666968
#> p_value 0.009971017 0.04932503
#>
#> $homogeneity_test
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 1 0.2935 0.5903
#> 51
#>
#> $Kruskal_Wallis
#> $Kruskal_Wallis$Kruskal_Wallis
#>
#> Kruskal-Wallis rank sum test
#>
#> data: dir by track
#> Kruskal-Wallis chi-squared = 0.53676, df = 1, p-value = 0.4638
#>
#>
#> $Kruskal_Wallis$Dunn
#> $Kruskal_Wallis$Dunn$chi2
#> [1] 0.536761
#>
#> $Kruskal_Wallis$Dunn$Z
#> [1] 0.7326398
#>
#> $Kruskal_Wallis$Dunn$P
#> [1] 0.2318891
#>
#> $Kruskal_Wallis$Dunn$P.adjusted
#> [1] 0.2318891
#>
#> $Kruskal_Wallis$Dunn$comparisons
#> [1] "Track 1 - Track 2"
#>
#>
#>
# Example 6: Test for Differences in Direction Means with Pairwise Comparisons in PaluxyRiver
# dataset
test_direction(PaluxyRiver, analysis = "GLM")
#> Warning: One or more tracks do not follow a normal distribution (p-value <= 0.05). Assumptions for ANOVA are not met. Consider using 'Kruskal-Wallis' or 'GLM'.
#> $normality_results
#> Track 1 Track 2
#> statistic.W 0.900319498 0.91666968
#> p_value 0.009971017 0.04932503
#>
#> $homogeneity_test
#> Levene's Test for Homogeneity of Variance (center = median)
#> Df F value Pr(>F)
#> group 1 0.2935 0.5903
#> 51
#>
#> $GLM
#> $GLM$GLM
#>
#> Call:
#> glm(formula = dir ~ track, family = gaussian(), data = M_analysis)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 85.550 1.617 52.909 <2e-16 ***
#> trackTrack 2 -1.932 2.403 -0.804 0.425
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for gaussian family taken to be 75.82002)
#>
#> Null deviance: 3915.8 on 52 degrees of freedom
#> Residual deviance: 3866.8 on 51 degrees of freedom
#> AIC: 383.77
#>
#> Number of Fisher Scoring iterations: 2
#>
#>
#> $GLM$pairwise_results
#> $emmeans
#> track emmean SE df lower.CL upper.CL
#> Track 1 85.6 1.62 51 82.3 88.8
#> Track 2 83.6 1.78 51 80.1 87.2
#>
#> Confidence level used: 0.95
#>
#> $contrasts
#> contrast estimate SE df t.ratio p.value
#> Track 1 - Track 2 1.93 2.4 51 0.804 0.4251
#>
#>
#>
#>