Method and apparatus for significance testing and confidence interval construction based on user-specified distribution

• US 6,847,976 B1
• Filed: 06/15/2000
• Issued: 01/25/2005
• Est. Priority Date: 06/15/2000
• Status: Expired due to Fees

• Current Assignee: Terrence B. Peace
• Original Assignee: Terrence B. Peace
• Inventors: Peace, Terrence B.
• Primary Examiner(s): AMSBURY, WAYNE P
• Application Number:
  US09/594,144
• Time in Patent Office: 1,685 Days
• Field of Search: 707/102
• US Class Current: 1/1
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: Y10S 707/99943 Generating database or data structure, e.g. via user interface

Abstract

A computer and computer implemented method and program product for analyzing statistical data in which the data to be analyzed need not be transformed into a “Normal” distribution, thus avoiding introduction of error. Generally, the user first determines a test statistic (formula) and associated null hypothesis. Then the distribution from which the original data arose, consistent with the null hypothesis, is defined. The computer then produces numerous randomly-generated data sets of the identical size and dimensions of the original statistical data set, according to the distribution defined above. A numerical value of the test statistic is computed from the test statistic formula for each randomly generated data set and stored in a vectored array. The numerical value of the test statistic computed from the original statistical data is then compared with the array and the associated percentile determined. With this information, the significance of the numerical value of the test statistic derived from the original data can be determined and the null hypothesis may be rejected, as indicated. Embodiments of the invention may likewise be used in alternative statistical applications, including computation of confidence intervals and likelihood ratios.

Claims

1. An apparatus for analyzing statistical data, said apparatus comprising a computing device having an input device;

a data storage device in communication with said computing device; and

programming code means readable by said computing device which

a. receives a set of original statistical data in a data set DB;

b. receives a test statistic formula by which said data set DB will be analyzed;

c. receives a hypothesis in terms of said test statistic formula defining one of a property and a potential relationship among data contained in said data set DB;

d. calculates the numerical value NTS of said test statistic formula using said data set DB;

e. receives a probability distribution D relating to said statistical data set DB;

f. initiates an index i;

g. generates a random data set RDB(i) that is the same size and dimension as said data set DB and distributed according to said probability distribution D;

h. calculates the numerical value TS(i) of said test statistic formula using said randomly generated data set RDB(i);

i. stores, in said storage device, said numerical value TS(i) of said test statistic formula in a numerical test statistic array;

j. increments the index i and repeats steps g through i N times to create randomly generated data sets RDB(1) through RDB(N), calculates, for each random data set, a corresponding numerical value of its test statistic TS(1) through TS(N), and stores each numerical test statistic in said numerical test statistic array in said data storage device;

k. compares said numerical value NTS with said numerical test statistic array to determine a set of percentile values P corresponding to said numerical value NTS and an associated set of percentile indices p; and

l. output, by a computer output device, of a probability estimated from said set of percentile indices p to be used to accept or reject said hypothesis.

2. The apparatus of claim 1, further comprising programming code means readable by said computing device which specifies a confidence interval, having a low end and a high end, in place of said hypothesis at step c.;

determines numerical values corresponding to the low end and the high end of said confidence interval from said numerical test statistic array following step j.; and

outputs said confidence interval, defined by its low end and high end, and said numerical value NTS.

3. The apparatus of claim 1, further comprising programming code means readable by said computing device which generates said random data sets RDB(1) through RDB(N) in a single step, followed by programming code means for determining and storing in said numerical test statistic array in said computer data storage device each respective numerical value TS(1) through TS(N) using said randomly generated data sets.

4. The apparatus of claim 1, further comprising programming code means readable by said computing device which sorts said numerical test statistic array into ascending order from a lowest value OTS(1) to a highest value OTS(N) and determines between which two values said numerical value NTS falls, which identifies at least one percentile index p which is used to estimate said probability.

5. The apparatus of claim 1, further comprising programming code means readable by said computing device which sorts said numerical test statistic array into descending order from a highest value OTS(1) to lowest value OTS(N) and determines between which two values said numerical value NTS falls, which identifies at least one percentile index p which is used to estimate said probability.

6. The apparatus of claim 1, further comprising programming code means readable by said computing device which calculates the total number GDS of numerical values TS(1) through TS(N) greater than the numerical value NTS, determines the total number LDS of numerical values TS(1) through TS(N) less than the numerical value NTS, and derives said probability P from said GDS and said LDS.

7. The apparatus of claim 1, further comprising programming code means readable by said computing device which generates said random data sets RDB(1) through RDB(N) using random processes expressed in a Monte Carlo technique.

8. The apparatus of claim 1, further comprising programming code means readable by said computing device which receives and stores a plurality of probability distributions in said computer data storage device and determines said probability distribution D by comparing said original data set with said plurality of stored probability distributions.

9. The apparatus of claim 1, further comprising programming code means readable by said computing device which derives the probability distribution D relating to said statistical data set DB.

10. A method for analyzing statistical data, comprising the steps of:

a. collecting said statistical data in a data set DB;

b. specifying a test statistic formula by which said data set DB will be analyzed;

c. specifying a hypothesis in terms of said test statistic formula defining one of a property and potential relationship among data contained in said data set DB;

d. computing the numerical value NTS of said test statistic formula using said data set DB;

e. specifying a probability distribution D relating to said statistical data set DB;

f. initiating an index i;

g. generating random data to create a random data set RDB(i) that is the same size and dimension as said data set DB and distributed according to said probability distribution D;

h. computing the numerical value TS(i) of said test statistic using said randomly generated data set RDB(i);

i. storing said numerical value TS(i) of said test statistic in a numerical test statistic array;

j. incrementing index i and repeating steps g through i N times to create randomly generated date sets RDB(1) through RDB(N), to determine, for each random data set, a corresponding numerical value of its test statistic TS(1) through TS(N), and to store each numerical test statistic in said numerical test statistic array;

k. comparing said numerical value NTS of said test statistic with said numerical test statistic array to determine a set of percentile values P corresponding to said numerical value NTS and an associated set of percentile indices p; and

l. determining whether to accept or reject said hypothesis based on a probability estimated from said set of percentile indices p to be used to accept or reject said hypothesis.

11. The method of claim 10 further comprising the steps of:

specifying a confidence interval, having a low end and a high end, in place of said hypothesis in step c.;

determining numerical values of the low end and the high end of said confidence interval from said numerical test statistic array following step j.; and

determining whether said numerical value NTS is within the confidence interval defined by said numerical values corresponding to the low end and the high end of said confidence interval.

12. The method of claim 10, in which the steps of generating said random data sets RDB(1) through RDB(N) is performed in a single step, followed by the steps of computing and storing in said numerical test statistic array each respective numerical value TS(1) through TS(N) using said randomly generated data sets.

13. The method of claim 10, in which the step of comparing said numerical value NTS of said test statistic with said numerical test statistic array to determine a percentile index p is accomplished by sorting said numerical test statistic array into ascending order from lowest value OTS(1) to a highest value OTS(N) and determining between which two values said numerical value NTS falls, which identifies at least one percentile index p which is used to estimate said probability.

14. The method of claim 10, in which the step of comparing said numerical value NTS of said test statistic with said numerical test statistic array to determine a percentile index p is accomplished by sorting said numerical test statistic array into descending order from a highest value OTS(1) to a lowest value OTS(N) and determining between which two values said numerical value NTS falls, which identifies at least one percentile index p which is used to estimate said probability.

15. The method of claim 10 in which the step of comparing said numerical value NTS of said test statistic with said numerical test statistic array to determine a percentile index p is accomplished by determining the total number GDS of numerical values TS(1) through TS(N) less than the numerical value NTS, and derives said probability from said GDS and said LDS.

16. The method of claim 10, in which the steps of generating said random data sets RDB(1) through RDB(N) are accomplished using random processes expressed in the Monte Carlo technique.

17. The method of claim 10, in which the steps are implemented by a computing apparatus comprising a computing device having an input device, a data, storage device in communication with said computing device, and programming code means readable by said computing device.

18. A method for analyzing an original statistical data set, the original statistical data set having a size, a dimension and a distribution in accordance with a specified probability distribution, the method comprising:

generating a plurality of random data sets, each random data set having the size, the dimension and the distribution of the original statistical data set;

calculating a plurality of numerical values of test statistics corresponding to the plurality of random data sets, each numerical value being calculated according to a test statistic formula;

determining a relationship between the plurality of numerical values and a numerical value of a test statistic of the original data set, calculated in accordance with the test statistic formula;

determining a plurality of percentile values based on the plurality of numerical values with the numerical value of the test statistic of the random data sets; and

determining a plurality of percentile indices corresponding to the plurality of percentile values;

wherein the relationship between the plurality of numerical values to the numerical value of the test statistic of the original data set is determined based on the plurality of percentile values and the corresponding percentile indices.

19. The method for analyzing the original statistical data set according to claim 18, in which the relationship determined based on the plurality of percentile values indicates whether the original statistical data set is characterized by at least one factor that is not based on chance.