{{$index+1}}
{{row.periodOrder}}
{{row.date | date:'M/dd/yyyy'}}
{{row.return | number:3}}
{{median | number: 3}}
{{row.return > median ? 'Up' : 'Down'}}
{{row.flipIsHeads ? 'Heads' : 'Tails'}}
{{row.return > median ? 'U' : 'D'}}{{row.flipIsHeads ? 'H' : 'T'}}
{{$index+1}}
{{row.periodOrder}}
{{row.flipIsHeads ? 'Heads': 'Tails'}}
Row
Trial#
PRD#
Date
Return%
Median%
Market
Coin
Pair
«
‹
SORT
BY
RETURN
&
GO TO
MEDIAN
‹
«
^
IFA Index
Portfolios
^
IFA Index
Portfolios
Expected: 50.00%
{{(data.length / 2) | number:0}} {{periodLabel + ' U'}}
{{(data.length / 2) | number:0}} {{' H'}}
Observed: {{100 * aboveMedian / data.length |number:2 }}%
Observed: {{100 * heads / data.length |number:2 }}%
{{aboveMedian | number}}
{{heads | number}}
{{periodLabel + ' U'}}
{{' H'}}
Expected: 50.00%
{{(data.length / 2) | number:0}} {{periodLabel + ' D'}}
{{(data.length / 2) | number:0}} {{' T'}}
Observed: {{100 * belowMedian / data.length |number:2 }}%
Observed: {{100 * tails / data.length |number:2 }}%
{{belowMedian | number}}
{{tails | number}}
{{periodLabel + ' D'}}
{{' T'}}
Average Results of {{trialsCount | number}}▼ Trials of {{data.length | number}} Flips
Coin
Market
Coin/Market
% of each outcome
Run Trial Again
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.
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.
Definitions
‹
‹
The Runs Test (Wald-Wolfowitz Test)
A Statistical Test for Randomness
{{pValueMode=='coin' ? '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
Coin: P-Value
Market: P-Value
Flip Again
Coin
When flipping a standard coin, there are two possible
outcomes: Heads (H), and Tails (T). Since there are two
possible outcomes, the probability of each outcome is 50%.
Market
If the direction of the market, relative to the median return,
resembles a coin flip and you have a oin with heads on one side
and tails on the other, you now have a situation like flipping two
coins. The MarketCoin is shown that is on the left and an Index
Portfolio coin on the right. The table below shows the expected
50% probability of each outcome and observed outcomes for each
flip of the coins. The observed daily flipping of the coin (H or T)
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 second coin based on similarity of the observed
outcomes of each test to the expected outcomes of 2 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 mode or from Market mode. Most columns are
sortable, and the side controls allow for scrolling and
locating the median return for the 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'}}