Skip to content
Snippets Groups Projects
Commit 81cfeb43 authored by Luca Sander's avatar Luca Sander
Browse files

added effect size calculation with cohens d

parent d8c53d86
No related branches found
No related tags found
No related merge requests found
Hide whitespace changes
Inline Side-by-side
Showing
with 40 additions and 10 deletions
significance.ipynb
+ 40
− 10
View file @ 81cfeb43
%% Cell type:markdown id: tags:
 
## Data Plotting & Significance Test
 
Here we plot our results.
 
We also need to check if our results are statistically significant.
 
%% Cell type:code id: tags:
 
``` python
'''
We first load in all the data from Stats.ipynb to generate our plots in a seperate file.
'''
 
normalizedPreParticipant2 = [1760.8659687540287, 1790.4030833200948, 1791.3429200314777, 1806.9820719938807, 1813.2271261749622, 1817.8301670931542, 1824.8395408971103, 1831.6713046084842, 1836.92692880661, 1846.3935497199845, 1864.475743535093, 1901.1143800241207, 1919.423051794997, 1922.8104180484113, 1929.8897416154712, 1969.3998179531982, 1970.2101240525963, 2026.2518068559639, 2050.482911416422, 2096.34470779983, 2110.883183626843, 2112.0806964818203, 2117.919632878787, 2118.3796101061166, 2144.334271499391, 2150.386861418163, 2176.440125195469, 2213.8231610102507, 2224.6926118123897, 2231.741413185297, 2352.23753422273, 2394.0003655088526, 2409.481003755391, 2515.5359819779064, 2532.0298807876534, 2532.4791056453246, 2562.2535519091707, 2576.090171850277]
sortedThemesPreParticipant2 = ['Bishop', 'kingsideAttack', 'queensideAttack', 'enPassant',
'attraction', 'capturingDefender', 'pin', 'exposedKing', 'mateIn3',
'castling', 'xRayAttack', 'trappedPiece', 'intermezzo', 'mateIn5',
'hangingPiece', 'endgame', 'Knight', 'mateIn4', 'Rook', 'crushing',
'advantage', 'fork', 'defensiveMove', 'sacrifice', 'Queen',
'deflection', 'King', 'Pawn', 'interference', 'middlegame',
'promotion', 'discoveredAttack', 'clearance', 'skewer',
'advancedPawn', 'opening', 'mateIn2', 'doubleCheck']
normalizedPostParticipant2 = [1923.1466105009138, 1938.352882657784, 1989.0956842113226, 1991.519870621101, 1997.0486264113867, 2008.6279216347086, 2021.1269226419327, 2021.7601583121861, 2032.2896345157951, 2050.7027516814032, 2052.5178456458166, 2062.219225381035, 2070.4661567483163, 2182.774939568813, 2185.5906323193503, 2240.8273022092085, 2243.6828440513204, 2249.38123521424, 2264.6029122977056, 2265.795024605797, 2279.8269930740157, 2308.6716629477864, 2332.6832899830997, 2378.8631454253064, 2381.452539104512, 2391.589428037236, 2408.73953280257, 2566.7235192289895, 2595.016114384511, 2597.113613066645, 2640.198111184178, 2644.988851596221, 2647.507385671868, 2653.8878030181677, 2660.4991885810637, 2687.0614136541612, 2692.0794146929034, 2694.865747681343]
sortedThemesPostParticipant2 = ['clearance', 'mateIn5', 'pin', 'Queen', 'sacrifice', 'middlegame',
'hangingPiece', 'doubleCheck', 'queensideAttack', 'Pawn',
'endgame', 'interference', 'crushing', 'mateIn3',
'discoveredAttack', 'King', 'defensiveMove', 'promotion',
'capturingDefender', 'mateIn4', 'Knight', 'kingsideAttack',
'deflection', 'advancedPawn', 'advantage', 'attraction', 'Rook',
'xRayAttack', 'opening', 'castling', 'Bishop', 'exposedKing',
'skewer', 'trappedPiece', 'mateIn2', 'fork', 'enPassant',
'intermezzo']
normalizedPreParticipant1 = [1134.5983090393465, 1137.5533452518382, 1142.3798807288154, 1145.5372816760112, 1145.840478283102, 1153.0740214126572, 1166.7209063490789, 1187.709617888992, 1208.1265104508686, 1222.7149490744034, 1226.0301776155645, 1230.4230392619409, 1231.1793229401246, 1235.2113011838317, 1235.8725795541948, 1243.448544340419, 1244.25584489817, 1244.6755953712156, 1257.41159614939, 1262.1050620049564, 1268.3321504030757, 1277.3477153626816, 1282.5560443870702, 1339.2495360415735, 1380.117328583384, 1381.9529446483605, 1382.1689412077747, 1395.1144091616009, 1410.2295983302386, 1412.1988672277848, 1414.0613942065695, 1417.5458504724986, 1419.0273693913557, 1434.5544419044033, 1444.332052742745, 1453.51828586774, 1459.8328301443323, 1661.7103369310605]
sortedThemesPreParticipant1 = ['queensideAttack', 'Rook', 'promotion', 'capturingDefender', 'interference',
'advancedPawn', 'mateIn5', 'King', 'fork', 'trappedPiece', 'Queen', 'castling',
'opening', 'deflection', 'enPassant', 'sacrifice', 'Pawn', 'exposedKing',
'defensiveMove', 'doubleCheck', 'mateIn3', 'pin', 'skewer', 'attraction',
'Knight', 'Bishop', 'advantage', 'clearance', 'mateIn4', 'discoveredAttack',
'crushing', 'mateIn2', 'middlegame', 'kingsideAttack', 'hangingPiece',
'intermezzo', 'endgame', 'xRayAttack']
normalizedPostParticipant1 = [1220.512442812503, 1233.1459837768393, 1237.136429136798, 1238.5575180687647, 1238.6193526845748, 1263.3805571710757, 1273.7633288222157, 1280.7375056539504, 1283.3894335852785, 1293.9029434619208, 1299.9635695737202, 1309.0266198177026, 1312.629969173787, 1325.1094467923667, 1325.9246200578414, 1340.85013503331, 1352.069068639953, 1352.38540046192, 1354.860081933874, 1367.9489810309149, 1369.238136607794, 1437.8161040351824, 1442.542668852556, 1444.7360361257224, 1444.7945681645044, 1476.202627597243, 1480.5620266703875, 1503.438530744169, 1522.0735468962264, 1547.1354550267022, 1577.3725649343485, 1613.9083671758453, 1664.6053020218299, 1680.8186718142417, 1701.7435992866006, 1718.4589516136923, 1724.77077802921, 1735.5921059251086]
sortedThemesPostParticipant1 = ['attraction', 'pin', 'hangingPiece', 'interference', 'intermezzo',
'defensiveMove', 'endgame', 'mateIn3', 'exposedKing', 'Bishop', 'skewer',
'mateIn5', 'sacrifice', 'mateIn4', 'advancedPawn', 'castling', 'crushing',
'kingsideAttack', 'queensideAttack', 'promotion', 'capturingDefender',
'middlegame', 'King', 'Knight', 'mateIn2', 'doubleCheck', 'Queen',
'trappedPiece', 'fork', 'opening', 'enPassant', 'advantage', 'xRayAttack',
'Pawn', 'Rook', 'deflection', 'clearance', 'discoveredAttack']
normalizedPreParticipant4 = [1583.985073477031, 1591.6949260919594, 1602.5056965170004, 1616.3924677176994, 1616.7179847810469, 1621.6796432674807, 1623.1515937200447, 1624.6086938696826, 1637.8783962916675, 1641.6654121790486, 1656.3027965141994, 1669.6425047930934, 1679.6054707165122, 1732.4103228463216, 1733.4310634741523, 1772.1054561178414, 1773.8351217750496, 1784.1531388540234, 1789.474289430463, 1790.929634097801, 1817.706806385906, 1859.8245017848824, 1861.4801986584214, 1890.5388157339178, 1905.1643061049444, 1912.0242619041962, 1918.8019595034095, 1945.9398654035595, 1969.3922710576924, 2008.5791399701945, 2014.060576022228, 2054.50501709916, 2063.8562439215857, 2073.2803799044427, 2086.7479479886683, 2198.5780104255537, 2245.8383638783193, 2320.290472112747]
sortedThemesPreParticipant4 = ['mateIn3', 'discoveredAttack', 'attraction', 'kingsideAttack',
'endgame', 'skewer', 'opening', 'queensideAttack', 'advancedPawn',
'enPassant', 'advantage', 'intermezzo', 'xRayAttack',
'exposedKing', 'promotion', 'castling', 'clearance', 'middlegame',
'Knight', 'pin', 'mateIn5', 'deflection', 'doubleCheck', 'King',
'trappedPiece', 'Queen', 'Pawn', 'crushing', 'fork', 'Bishop',
'defensiveMove', 'mateIn2', 'Rook', 'interference',
'capturingDefender', 'mateIn4', 'sacrifice', 'hangingPiece']
normalizedPostParticipant4 = [1565.120930085286, 1604.9365972222352, 1610.1148857609323, 1612.5230083750057, 1616.4535189602673, 1617.647404433855, 1621.4587217409753, 1623.4973976838544, 1629.4883469315894, 1632.4610864804372, 1647.4592329055185, 1649.7948575345065, 1664.8420156774412, 1742.5880034576646, 1753.2755341141474, 1761.2969513670596, 1768.3418104975235, 1786.6835346014925, 1808.7205647240971, 1822.477402992303, 1850.809676930726, 1879.2648287582276, 1897.2633072536817, 1897.9653811375636, 1912.8623242674942, 1929.82837378227, 1931.612195117407, 1948.4868112819192, 1963.7756808614852, 1967.3972464717845, 1968.7117318538894, 1971.5122118977622, 1978.4337281396502, 1999.707053657073, 2003.1603385359147, 2047.8955269435974, 2049.4393471695344, 2297.014413369162]
sortedThemesPostParticipant4 = ['hangingPiece', 'attraction', 'castling', 'doubleCheck',
'exposedKing', 'opening', 'kingsideAttack', 'Rook', 'clearance',
'capturingDefender', 'mateIn3', 'crushing', 'defensiveMove',
'Pawn', 'mateIn5', 'advantage', 'mateIn2', 'pin', 'Queen', 'fork',
'xRayAttack', 'queensideAttack', 'deflection', 'King',
'advancedPawn', 'intermezzo', 'Bishop', 'Knight', 'sacrifice',
'trappedPiece', 'endgame', 'mateIn4', 'middlegame', 'skewer',
'promotion', 'discoveredAttack', 'interference', 'enPassant']
normalizedPreParticipant3 = [1511.203969982888, 1516.070176602095, 1521.54744880149, 1524.3710143362757, 1552.258156460718, 1563.0616930440103, 1571.6638616951186, 1582.0752957500579, 1582.6980042593568, 1592.8870628230036, 1610.6110363755126, 1626.999002836624, 1628.787094636793, 1660.7407478565365, 1661.188355311605, 1672.2682338966251, 1686.9514783051018, 1704.0045731641048, 1716.462930700672, 1725.7801149484105, 1744.7119797814776, 1749.199139265991, 1769.273274991142, 1793.6404872229487, 1794.296934610282, 1816.747089580156, 1821.7477048976107, 1835.6564456804488, 1848.0056120078916, 1864.1637439322694, 1865.8567693918314, 1868.6671484061892, 1890.3934047058829, 1928.0883051394267, 1975.0237062398403, 2213.4257173847805, 2214.6072891835743, 2215.509072086455]
sortedThemesPreParticipant3 = ['King', 'exposedKing', 'promotion', 'queensideAttack',
'deflection', 'hangingPiece', 'advantage', 'pin', 'fork',
'enPassant', 'defensiveMove', 'mateIn2', 'skewer', 'xRayAttack',
'mateIn3', 'kingsideAttack', 'mateIn5', 'interference', 'crushing',
'middlegame', 'Rook', 'discoveredAttack', 'attraction', 'Bishop',
'doubleCheck', 'intermezzo', 'advancedPawn', 'Knight', 'Queen',
'endgame', 'opening', 'sacrifice', 'trappedPiece', 'Pawn',
'capturingDefender', 'clearance', 'mateIn4', 'castling']
normalizedPostParticipant3 = [1590.831981537509, 1593.0716300711904, 1603.8168711946255, 1604.9032901042158, 1606.333660782174, 1607.6386852767585, 1618.9646390513642, 1628.1435235815518, 1631.8165166205897, 1643.7211571514483, 1661.9330159395977, 1667.2879368646363, 1689.5032001384054, 1692.4635186494936, 1733.8316358449872, 1737.5014200348712, 1751.1314113261153, 1768.8823294209487, 1770.6557960853931, 1789.4300274643501, 1849.7493957521665, 1857.8981974810583, 1874.818788838619, 1899.0653750355211, 1929.8719491998952, 1945.4324104568311, 1945.8443550219843, 1968.2355961803398, 1997.454577094734, 2026.6913905231268, 2090.9590655799934, 2105.5165422973814, 2138.962682766603, 2174.2801802486233, 2181.2772997958104, 2260.007292268188, 2263.696484694196, 2278.5869675924596]
sortedThemesPostParticipant3 = ['King', 'skewer', 'sacrifice', 'Bishop', 'exposedKing', 'Rook',
'clearance', 'defensiveMove', 'interference', 'enPassant',
'mateIn3', 'attraction', 'fork', 'Pawn', 'mateIn2', 'advancedPawn',
'Queen', 'mateIn5', 'advantage', 'hangingPiece', 'crushing',
'discoveredAttack', 'Knight', 'queensideAttack', 'deflection',
'xRayAttack', 'intermezzo', 'capturingDefender', 'opening',
'doubleCheck', 'trappedPiece', 'castling', 'kingsideAttack',
'middlegame', 'endgame', 'promotion', 'mateIn4', 'pin']
 
dictPreParticipant2 = {}
dictPostParticipant2 = {}
dictPreParticipant1 = {}
dictPostParticipant1 = {}
dictPreParticipant4 = {}
dictPostParticipant4 = {}
dictPreParticipant3 = {}
dictPostParticipant3 = {}
 
for i in range(len(sortedThemesPostParticipant2)):
dictPreParticipant2[sortedThemesPreParticipant2[i]] = normalizedPreParticipant2[i]
dictPostParticipant2[sortedThemesPostParticipant2[i]] = normalizedPostParticipant2[i]
dictPreParticipant1[sortedThemesPreParticipant1[i]] = normalizedPreParticipant1[i]
dictPostParticipant1[sortedThemesPostParticipant1[i]] = normalizedPostParticipant1[i]
dictPreParticipant4[sortedThemesPreParticipant4[i]] = normalizedPreParticipant4[i]
dictPostParticipant4[sortedThemesPostParticipant4[i]] = normalizedPostParticipant4[i]
dictPreParticipant3[sortedThemesPreParticipant3[i]] = normalizedPreParticipant3[i]
dictPostParticipant3[sortedThemesPostParticipant3[i]] = normalizedPostParticipant3[i]
 
differencesParticipant2 = {}
 
for key in dictPreParticipant2:
differencesParticipant2[key] = dictPostParticipant2[key] - dictPreParticipant2[key]
 
differencesParticipant1 = {}
 
for key in dictPreParticipant1:
differencesParticipant1[key] = dictPostParticipant1[key] - dictPreParticipant1[key]
 
differencesParticipant4 = {}
 
for key in dictPreParticipant4:
differencesParticipant4[key] = dictPostParticipant4[key] - dictPreParticipant4[key]
 
differencesParticipant3 = {}
 
for key in dictPreParticipant3:
differencesParticipant3[key] = dictPostParticipant3[key] - dictPreParticipant3[key]
 
names = ['Participant1', 'Participant2', 'Participant3', 'Participant4']
allPreDicts = []
allPreDicts.append(dictPreParticipant1)
allPreDicts.append(dictPreParticipant2)
allPreDicts.append(dictPreParticipant3)
allPreDicts.append(dictPreParticipant4)
allDiffDicts = []
allDiffDicts.append(differencesParticipant1)
allDiffDicts.append(differencesParticipant2)
allDiffDicts.append(differencesParticipant3)
allDiffDicts.append(differencesParticipant4)
allSortedThemes = []
allSortedThemes.append(sortedThemesPreParticipant1)
allSortedThemes.append(sortedThemesPreParticipant2)
allSortedThemes.append(sortedThemesPreParticipant3)
allSortedThemes.append(sortedThemesPreParticipant4)
 
allPreAbilities = []
allPreAbilities.append(normalizedPreParticipant1)
allPreAbilities.append(normalizedPreParticipant2)
allPreAbilities.append(normalizedPreParticipant3)
allPreAbilities.append(normalizedPreParticipant4)
 
allPostAbilities = []
allPostAbilities.append(normalizedPostParticipant1)
allPostAbilities.append(normalizedPostParticipant2)
allPostAbilities.append(normalizedPostParticipant3)
allPostAbilities.append(normalizedPostParticipant4)
```
 
%% Cell type:code id: tags:
 
``` python
'''
Plotting our graph, if the bar is green it is an improvement in rating for the subskill. If the bar is red it is a decrease in rating for the subskill.
When the bar is red, the initial rating is the top of the bar, the final rating is the bottom of the bar. If the bar is green, this is reversed.
'''
 
import matplotlib.pyplot as plt
 
 
for j in range(len(names)):
plt.figure(figsize=(12, 6))
for i, (theme, pre_rating) in enumerate(allPreDicts[j].items()):
diff_rating = allDiffDicts[j][theme]
color = 'green' if diff_rating >= 0 else 'red'
plt.bar(i, diff_rating, bottom=pre_rating, color=color, edgecolor='black')
 
# Setting the labels and title
plt.xlabel('Themes')
plt.ylabel('Rating')
plt.title('PreRating and Difference by Themes for: ' + names[j])
plt.xticks(range(len(allPreDicts[j])), labels=allPreDicts[j].keys(), rotation=90)
 
# Showing the plot
plt.show()
```
 
%% Output
 
 
 
 
 
%% Cell type:code id: tags:
 
``` python
'''
Plotting the same graphs as above, but now we have the same themes listed in the same order for all participants.
'''
 
 
import matplotlib.pyplot as plt
 
# Sort the themes in the same order for all participants
sorted_themes = sorted(allPreDicts[0].keys())
 
for j in range(len(names)):
plt.figure(figsize=(12, 6))
for i, theme in enumerate(sorted_themes):
pre_rating = allPreDicts[j][theme]
diff_rating = allDiffDicts[j][theme]
color = 'green' if diff_rating >= 0 else 'red'
plt.bar(i, diff_rating, bottom=pre_rating, color=color, edgecolor='black')
 
# Setting the labels and title
plt.xlabel('Themes')
plt.ylabel('Rating')
plt.title('PreRating and Difference by Themes for: ' + names[j])
plt.xticks(range(len(sorted_themes)), labels=sorted_themes, rotation=90)
 
# Showing the plot
plt.show()
```
 
%% Output
 
 
 
 
 
%% Cell type:markdown id: tags:
 
## Wilcoxon Test
 
We now perform a wilcoxon signed rank test to see if our results are significant. We do 3 tests:
 
1. Pre vs Post Ratings
2. WeakestWeak to StrongestStrong
3. WeakestWeak to WeakestStrong
 
All of these are explained in the paper.
 
We also calculate the effect size for all 3 for every participant
%% Cell type:code id: tags:
 
``` python
from scipy.stats import wilcoxon
import numpy as np
#function to calculate the effect size given 2 lists
def effect_size(list1, list2):
n1 = len(list1)
n2 = len(list2)
std1 = np.std(list1)
std2 = np.std(list2)
mean1 = np.mean(list1)
mean2 = np.mean(list2)
compromise_std = np.sqrt(((n1-1)*(std1**2) + (n2-1)*(std2**2)) / (n1+n2-2))
cohens_d = (mean1 - mean2) / compromise_std
return cohens_d
 
#Making lists for weak initial skills and strong initial skills. A weak initial skill are the first half of all skills ordered by their inital rating. All the other skills are strong skills.
for k in range(len(names)):
length = (len(sortedThemesPreParticipant2))
weakerSkillImprovements = []
strongerSkillImprovements = []
for i in range(round(length/2)):
weakerSkillImprovements.append(allDiffDicts[k][allSortedThemes[k][i]])
for j in range(round(length/2), length):
strongerSkillImprovements.append(allDiffDicts[k][allSortedThemes[k][j]])
 
#print(weakerSkillImprovements)
#print(strongerSkillImprovements)
 
weakerToWeakerImprov = []
weakerToStrongerImprov = []
 
reversedStrongerImprov = list(reversed(strongerSkillImprovements)) #this is used for the weakestWeak to strongestStrong comparison
for i in range(len(weakerSkillImprovements)):
weakerToWeakerImprov.append(weakerSkillImprovements[i] - strongerSkillImprovements[i])
weakerToStrongerImprov.append(weakerSkillImprovements[i] - reversedStrongerImprov[i])
 
#This was used to use a different rank, but can be neglected
positive_count_weakest_to_weakest = sum(1 for value in weakerToWeakerImprov if value > 0)
positive_count_weakest_to_strongest = sum(1 for value in weakerToStrongerImprov if value > 0)
 
sorted_diffs_WW = sorted(weakerToWeakerImprov, key=abs)
ranks_WW = [i + 1 if diff >= 0 else -(i + 1) for i, diff in enumerate(sorted_diffs_WW)]
signed_ranks_WW = [ranks_WW[sorted_diffs_WW.index(diff)] for diff in weakerToWeakerImprov]
print("Statistic WW:",sum(signed_ranks_WW))
 
sorted_diffs_WS = sorted(weakerToStrongerImprov, key=abs)
ranks_WS = [i + 1 if diff >= 0 else -(i + 1) for i, diff in enumerate(sorted_diffs_WS)]
signed_ranks_WS = [ranks_WS[sorted_diffs_WS.index(diff)] for diff in weakerToStrongerImprov]
print("Statistic WS:",sum(signed_ranks_WS))
 
# Perform Wilcoxon signed-rank test for weaker to weaker
stat_weak, p_weak = wilcoxon(x=weakerSkillImprovements, y=strongerSkillImprovements)
 
# Perform Wilcoxon signed-rank test for stronger to stronger
stat_strong, p_strong = wilcoxon(x=weakerSkillImprovements, y=reversedStrongerImprov)
print("-"*30, " WilcoxonTest ", names[k], "-" * 30)
print("Number of Positives in Weakest To Weakest:", positive_count_weakest_to_weakest)
print("Number of Positives in Weakest To Strongest:", positive_count_weakest_to_strongest)
 
#This is the comparison between pre and post data
statisticWilcoxon, pWilcoxon = wilcoxon(x=allPreAbilities[k], y=allPostAbilities[k])
 
#Printing the results for every Participant
print("Wilcoxon signed-rank test on Pre and Post Data:")
print("Statistic:", statisticWilcoxon)
print("p-value:", pWilcoxon)
print("effect size:", effect_size(allPreAbilities[k], allPostAbilities[k]))
# Print results
print("\nWilcoxon signed-rank test for weakestWeak to weakestStrong:")
print(weakerToWeakerImprov)
print("Statistic:", stat_weak)
print("p-value:", p_weak)
print("effect size:", effect_size(weakerSkillImprovements, strongerSkillImprovements))
 
print("\nWilcoxon signed-rank test for weakestWeak to strongestStrong:")
print(weakerToStrongerImprov)
print("Statistic:", stat_strong)
print("p-value:", p_strong, "\n")
print("p-value:", p_strong)
print("effect size:", effect_size(weakerSkillImprovements, reversedStrongerImprov), "\n")
```
 
%% Output
 
Statistic WW: 174
Statistic WS: 150
------------------------------ WilcoxonTest Participant1 ------------------------------
Number of Positives in Weakest To Weakest: 17
Number of Positives in Weakest To Strongest: 15
Wilcoxon signed-rank test on Pre and Post Data:
Statistic: 0.0
p-value: 7.275957614183426e-12
effect size: -0.8824506563369671
Wilcoxon signed-rank test for weakestWeak to weakestStrong:
[6.164207302240811, 551.7848987838877, 269.77083188794177, 206.29332974513295, 211.45413301473332, 108.2318911028458, 230.35571465506337, 23.09362499549343, -15.709332422251464, 365.84373320763734, -68.86138964250085, 172.41942133798557, 288.70741439457174, 464.4589157860339, 423.6690268226371, 276.3770484393151, 651.4617600992369, 224.78333953617948, 3.073995930916226]
Statistic: 8.0
p-value: 9.5367431640625e-05
effect size: 1.513423036321743
Wilcoxon signed-rank test for weakestWeak to strongestStrong:
[217.3668078037581, 750.2597553568789, 440.46803348526464, 430.89647853773, 174.88608122814617, 154.06186400135743, 115.0569957766179, 316.8253765301806, -9.446202251966042, 365.84373320763734, -75.12451981278627, -121.31233019670162, 404.0061332730172, 418.62894288752227, 460.2370786092242, 51.773899646718064, 480.76455850191405, 26.308482963188226, -208.12860457060106]
Statistic: 20.0
p-value: 0.00141143798828125
effect size: 1.513423036321743
Statistic WW: 170
Statistic WS: 172
------------------------------ WilcoxonTest Participant2 ------------------------------
Number of Positives in Weakest To Weakest: 16
Number of Positives in Weakest To Strongest: 16
Wilcoxon signed-rank test on Pre and Post Data:
Statistic: 0.0
p-value: 7.275957614183426e-12
effect size: -0.8457327848122473
Wilcoxon signed-rank test for weakestWeak to weakestStrong:
[905.2106934816627, 247.6992241500227, -334.0340026880235, 759.3341315264893, 699.6932855570035, 599.5871460828414, -18.040285250724537, 748.9303699739976, 508.96842009105035, 913.1934497780153, 925.3612672444849, 855.6297220025372, 983.852429075848, 501.8768578638501, -40.73422266750026, 236.28476305496542, 247.07986028223286, 141.29758107794032, 912.5866349242385]
Statistic: 10.0
p-value: 0.000164031982421875
effect size: 1.9181960580122943
Wilcoxon signed-rank test for weakestWeak to strongestStrong:
[1433.6621559682399, 420.0229429557987, 178.40970574513085, 1038.2640780613697, 446.3908981683119, 933.1071384590289, 372.66587650371457, 916.1738459962271, 568.9615023127913, 913.1934497780153, 865.368185022744, 688.3862459803076, 593.1462673214089, 168.35686548766262, 212.56816472119135, -42.64518347991498, -265.3638481509215, -31.026137727835703, 384.13517243766137]
Statistic: 9.0
p-value: 0.000125885009765625
effect size: 1.9181960580122943
Statistic WW: 122
Statistic WS: 116
------------------------------ WilcoxonTest Participant3 ------------------------------
Number of Positives in Weakest To Weakest: 14
Number of Positives in Weakest To Strongest: 14
Wilcoxon signed-rank test on Pre and Post Data:
Statistic: 0.0
p-value: 7.275957614183426e-12
effect size: -0.49172663351591134
Wilcoxon signed-rank test for weakestWeak to weakestStrong:
[-368.872053745592, 227.33677868479822, 629.7607852516308, 476.6796988257511, 566.35098985791, -6.026121492504899, 69.89466894844622, 780.7579567051412, 67.64285272087841, 147.70829501022104, -299.5810686575019, -24.765174694539382, 229.13481264596112, 84.12600172618409, 236.3694471179258, 473.4825589294783, 676.3919294492632, -121.27725205413685, 243.2789948405682]
Statistic: 34.0
p-value: 0.012359619140625
effect size: 0.9425120566029705
Wilcoxon signed-rank test for weakestWeak to strongestStrong:
[189.6205413436944, 41.17428866945738, 1332.9209218001142, 381.4824707587459, 613.2385792291102, 25.802673546229244, 463.84221160183824, 564.9138641394991, -210.30835998449243, 147.70829501022104, -21.629855952131038, 191.0789178711027, -164.8127300074309, 52.29720668744994, 189.4818577467256, 568.6797869964835, -26.768207099220263, 64.88523796120398, -315.2136002487182]
Statistic: 37.0
p-value: 0.0180816650390625
effect size: 0.9425120566029705
Statistic WW: 188
Statistic WS: 176
------------------------------ WilcoxonTest Participant4 ------------------------------
Number of Positives in Weakest To Weakest: 18
Number of Positives in Weakest To Strongest: 17
Wilcoxon signed-rank test on Pre and Post Data:
Statistic: 275.0
p-value: 0.17019062975305133
effect size: 0.09346534041465038
Wilcoxon signed-rank test for weakestWeak to weakestStrong:
[67.7202589247961, 520.6318731233966, -35.00790476356451, 254.02344430669154, 344.56718166919677, 315.7944700227522, 97.79950789390932, 430.8700909342899, 571.1289358448796, 802.2638692555026, 181.9610997056477, 609.4044293339634, 457.36741281585023, 324.402042351677, 293.5703077966707, 292.29629115132207, 82.7190236843312, 476.34327230246095, 914.1820638789172]
Statistic: 1.0
p-value: 7.62939453125e-06
effect size: 1.8037126162282808
Wilcoxon signed-rank test for weakestWeak to strongestStrong:
[818.6437014559485, 738.2632838684722, 229.49669923302622, 459.353115531507, 375.8347798077509, 818.3862566273235, 280.6590173154466, 603.8746952333317, 351.95087282861414, 802.2638692555026, 401.1391627219132, 436.3998250349216, 274.50790339431296, -178.18974425289434, 262.30270965811656, 86.96661992650661, -181.78558031225953, 258.7118615573854, 163.2586213477648]
Statistic: 7.0
p-value: 7.2479248046875e-05
effect size: 1.8037126162282813
......
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment