{{$index+1}}
{{row.periodOrder}}
{{row.date | date:'M/dd/yyyy'}}
{{row.return | number:3}}
{{median | number: 3}}
{{row.return > median ? 'Up' : 'Down'}}
{{row.flipIsHeads ? 'Up' : 'Down'}}
{{row.flip2IsHeads ? 'Up' : 'Down'}}
{{row.return > median ? 'U' : 'D'}}{{row.flipIsHeads ? 'U' : 'D'}}{{row.flip2IsHeads ? 'U' : 'D'}}
{{$index+1}}
{{row.periodOrder}}
{{row.flipIsHeads ? 'Heads': 'Tails'}}
{{row.flip2IsHeads ? 'Heads': 'Tails'}}
{{row.flip3IsHeads ? 'Heads': 'Tails'}}
{{row.flipIsHeads ? 'H' : 'T'}}{{row.flip2IsHeads ? 'H' : 'T'}}{{row.flip3IsHeads ? 'H' : 'T'}}
Row
Trial#
PRD#
Date
Return%
Median%
Market
Coin 1
Coin 2
Coin 3
Trio
«
‹
SORT
BY
RETURN
&
GO TO
MEDIAN
‹
«
^
IFA Index
Portfolios
^
IFA Index
Portfolios
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' UUU'}}
{{(data.length / 8) | number:0}} {{' HHH'}}
Observed: {{100 * upUpAboveMedian / data.length |number:2 }}%
Observed: {{100 * threeCoinsHeadsHeadsHeads / data.length |number:2 }}%
{{upUpAboveMedian | number}}
{{threeCoinsHeadsHeadsHeads | number}}
{{periodLabel + ' UUU'}}
{{' HHH'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' DDD'}}
{{(data.length / 8) | number:0}} {{' TTT'}}
Observed: {{100 * downDownBelowMedian / data.length |number:2 }}%
Observed: {{100 * threeCoinsTailsTailsTails / data.length |number:2 }}%
{{downDownBelowMedian | number}}
{{threeCoinsTailsTailsTails | number}}
{{periodLabel + ' DDD'}}
{{' TTT'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' UUD'}}
{{(data.length / 8) | number:0}} {{' HHT'}}
Observed: {{100 * upUpBelowMedian / data.length |number:2 }}%
Observed: {{100 * threeCoinsHeadsHeadsTails / data.length |number:2 }}%
{{upUpBelowMedian | number}}
{{threeCoinsHeadsHeadsTails | number}}
{{periodLabel + ' UUD'}}
{{' HHT'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' DDU'}}
{{(data.length / 8) | number:0}} {{' TTH'}}
Observed: {{100 * downDownAboveMedian / data.length |number:2}}%
Observed: {{100 * threeCoinsTailsTailsHeads / data.length |number:2}}%
{{downDownAboveMedian | number}}
{{threeCoinsTailsTailsHeads | number}}
{{periodLabel + ' DDU'}}
{{' TTH'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' UDU'}}
{{(data.length / 8) | number:0}} {{' HTH'}}
Observed: {{100 * upDownAboveMedian / data.length |number:2 }}%
Observed: {{100 * threeCoinsHeadsTailsHeads / data.length |number:2 }}%
{{upDownAboveMedian | number}}
{{threeCoinsHeadsTailsHeads | number}}
{{periodLabel + ' UDU'}}
{{' HTH'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' DUD'}}
{{(data.length / 8) | number:0}} {{' THT'}}
Observed: {{100 * downUpBelowMedian / data.length |number:2 }}%
Observed: {{100 * threeCoinsTailsHeadsTails / data.length |number:2 }}%
{{downUpBelowMedian | number}}
{{threeCoinsTailsHeadsTails | number}}
{{periodLabel + ' DUD'}}
{{' THT'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' DUU'}}
{{(data.length / 8) | number:0}} {{' THH'}}
Observed: {{100 * downUpAboveMedian / data.length |number:2 }}%
Observed: {{100 * threeCoinsTailsHeadsHeads / data.length |number:2 }}%
{{downUpAboveMedian | number}}
{{threeCoinsTailsHeadsHeads | number}}
{{periodLabel + ' DUU'}}
{{' THH'}}
Expected: 12.50%
{{(data.length / 8) | number:0}} {{periodLabel + ' UDD'}}
{{(data.length / 8) | number:0}} {{' HTT'}}
Observed: {{100 * upDownBelowMedian / data.length |number:2}}%
Observed: {{100 * threeCoinsHeadsTailsTails / data.length |number:2}}%
{{upDownBelowMedian | number}}
{{threeCoinsHeadsTailsTails | number}}
{{periodLabel + ' UDD'}}
{{' HTT'}}
Average Results of {{trialsCount | number}}▼ Trials of {{data.length | number}} Flips
Coin/Coin/Coin
Coin/Coin/Market
% of each outcome
Run Trial Again
The Runs Test (Wald-Wolfowitz Test)
A Statistical Test for Randomness
In a runs test, a run is defined as a sequence of consecutive, identical observations (or symbols) that are
preceded and followed by a different observation or by no observation at all (at the beginning or end of
the sequence). The data must first be converted into a binary sequence (dichotomous variable), typically
using the median as a cut-off point for numerical data (labeling values above the median as one symbol,
e.g., '+' and those below as another, e.g., '-').
Consider the following sequence of coin flips (Heads or Tails):
H H H T T T T H T T H H
This sequence contains 5 runs:
H H H, T T T T, H, T T, and H H
The runs test counts the total number of these runs and compares this observed count to the number
of runs expected if the sequence were truly random. Too many runs indicate rapid oscillation, while
too few runs suggest clustering or a trend (serial correlation).
The p-value from a runs test measures the probability that the observed sequence of data occurred randomly.
A small p-value (typically less than a significance level of 0.05) indicates that the data are not random,
suggesting a pattern or trend.
In summary, the p-value indicates the strength of the evidence against the null hypothesis that the data is
random. The smaller the p-value, the stronger the evidence for a non-random pattern.
1st Coin: P-Value
2nd Coin: P-Value
3rd Coin: P-Value
Market: P-Value
Definitions
▼
▲
Definitions
Runs:
A run is a sequence of consecutive observations that all fall on the same side of a chosen reference
point, usually the median
Expected Runs:
This is the number of runs you would expect to see if the data were purely random, given:
the number of observations above the median, the number below the median, and the fact
that random sequences switch direction unpredictably
z:
Measures how far the observed number of runs deviates from the expected number, in units of standard
deviation.
A z near 0 → consistent with randomness
A large |z| → unlikely under randomness
P-Value:
The p-value tells you the probability of observing a run count as extreme or more extreme than what you
got if the process were truly random.
If p > 0.05 → fail to reject randomness, if p ≤ 0.05 → reject randomness (evidence of structure)
Interpretation
P-value > 0.05: A sequence can be considered consistent with a random process.
This is the standard conclusion of a non-parametric Runs Test:
The data does not exhibit detectable non-random structure such as trends, clustering, or predictability.
{{pValueMode=='coin' ? '1st Coin': pValueMode == 'coincoin' ? '2nd Coin': pValueMode == 'coincoincoin' ? '3rd Coin': 'Market'}} Runs Test Results
Runs:
{{runs |number:0}}
Expected Runs:
{{expectedRuns | number:0}}
z:
{{z |number:2}}
P-Value:
{{pValue | number:2}}
{{pValue > 0.05 ? randomMessage : notRandomMessage}}
{{pValue > 0.05 ? randomMessage2 : notRandomMessage2}}
x
Flip Again
Coin•Coin•Coin
When flipping three standard coins, there are eight possible
outcomes: Heads on all coins (HHH), Tails on all coins (TTT),
Heads Heads Tails, Heads Tails Tails, Heads Tails Heads,
Tails Tails Heads, Tails Heads Tails, Tails Heads Heads.
Each of these outcomes is equally likely. Since there are eight
possible outcomes, the probability of each outcome is 12.5%.
Coin•Coin•Market
If the direction of the market, relative to the median return,
resembles a coin flip and you have two MarketCoins with UP
on one side and DOWN on the other, you now have a situation
that is like flipping two coins. The MarketCoins are shown on
the left and an Index Portfolio coin on the right. The table
below shows the expected 12.5% probability of each outcome
and observed outcomes for each flip of the coins.The observed
daily flipping of the MarketCoin (U or D) compared to the
actual daily returns of the index portfolio coin (U or D)
illustrates that the index portfolio is a reasonable substitute
for a third coin based on similarity of the observed outcomes
of each test to the expected outcomes of 3 coins.
Trials
Bar charts comparing the expected to the average (mean)
of the observations of the four outcomes of the coin/coin
and the coin/market over multiple trials. Daily, monthly
and annual periods are available. You can run the trails
multiple times.
Data
Two data tables are available. Click the Data icon from the
Coin/Coin/Coin mode or from Coin/Coin/Market mode.
Most columns are sortable, and the side controls allow for
scrolling and locating the mean return for the Coin/Market
mode. The most recent returns data are shown on the top
row. Up and down relative to the median and the random
flip of the coin are also displayed. The four possible pairs
of Up and Downs are shown in the last column. Click the
blue Flip Again button to flip the coin for each row.
U = Up - Above the Median Return
D = Down – Below the Median Return
H = Heads side of coin
T = Tails side of coin
RUNS
TEST
More Coins▼
Statistician Series
{{coin.name}}
Tune Out the Noise©
<
{{coin.name}}
IFA Coins
{{coin.name}}
{{coin.name}}
▼
Daily
Monthly
Annual
1
100
1,000
1
100
1,000
10,000
1
3
5
10
30
100
1,000
10,000
100,000
{{periodLabel=='Days' ? 'Daily' : periodLabel=='Months' ? 'Monthly' : 'Annual'}}▼
Daily
Monthly
Annual
The median is one of the three types of averages, along
with the mean and the mode. The median return for IFA
Indexes and Index Portfolios for any time horizon (daily,
monthly, or annual) is the middle value when returns are
sorted from high to low or low to high, splitting the
historical data into 50% above and 50% below the median.
▲
Market Ups and Downs Relative to Median
Market Ups and Downs Relative to 0.00%
Market Ups and Downs Relative to the Mean
Set the Market to All Up Periods
Set the Market to All Down Periods
Market Ups and Downs Relative to Median
Market Ups and Downs Relative to 0.00%
Market Ups and Downs Relative to the Mean
Set the Market to All Up Periods
Set the Market to All Down Periods
{{month}}
{{day}}
{{year}}
APPLY
Invalid dates selected will be changed to nearest trading date
START
DATE
{{startDate | date: 'MMMM'}}
{{startDate | date: 'd'}},
{{startDate | date: 'yyyy'}}
{{month}}
{{day}}
{{year}}
APPLY
Invalid dates selected will be changed to nearest trading date
END
DATE
{{endDate | date: 'MMMM'}}
{{endDate | date: 'd'}},
{{endDate | date: 'yyyy'}}