fix

README.md

@@ -23,28 +23,48 @@ based upon a (very) small sample (selection).
 Goal is to calculate the interval for which there is a certain confidence e.g. 95%, 
 that the population mean lies between the estimated mean from the sample +- some intervalDelta.
 
-The 0.1.x version of the library uses a lookup table for sample size is 2..20, and for the 
-discrete confidence levels 80%, 90%, 95%, 98% and 99%.
-This look up table is defined in the file **StudentTable.h** and generated from a spreadsheet.
-Note: values in the LUT are single sided.
+The 0.1.x version of the library is limited to a maximum of 20 samples to keep RAM usage 
+relative low. 
+It uses a lookup table (LUT) for a sample size up to 20, and for five discrete confidence 
+levels 80%, 90%, 95%, 98% and 99% ==> size table = 20 x 5 = 100 floats. 
+The table encodes the 100 floats as uint16_t to save 50% of the RAM needed.
 
 The library allows to calculate the interval after every addition until the internal buffer
-of 20 samples is full. (At least 2 samples needed)
+of 20 samples is full. Note that at least 2 samples are needed to calculate the interval.
+
+
+### StudentTable.h
+
+The table is defined in the file **StudentTable.h** and generated from a spreadsheet.
+
+If one need to extend the sample size, the file contains commented values for sample size 21-100.
+One has to adjust **STUDENT_MAX_SIZE** in **StudentTable.h** too (max 255).
+Note this will cost extra RAM.
+
+If one wants to reduce the sample size / RAM, one can comment part of the table not needed.
+One has to adjust **STUDENT_MAX_SIZE** too.
 
 
 ### History
 
-The T-distribution is developed by W.A. Gosset in 1908 while working for Guinness Beer.
-His goal was to guard a constant quality of the beer. For this he needed a method to determine
-the quality of the raw materials like grains, malt and hops to 
+The T-distribution is developed by William Gosset, head experimental brewer, in 1908 while 
+working for Guinness Beer. His goal was to guard a constant quality of the beer brewed.
+He needed a method to determine the quality of the raw materials like grains, malt and hops,
+based on small samples from the fields. 
+For this he invented the t-distribution and published it under the name Student. 
+Therefore this distribution is also known as the Student distribution.
+
 
 ### Accuracy / precision
 
+The version 0.1.x uses float for internal storage. This means precision is at most 6-7 digits.
+
 The version 0.1.x lookup table has 20 x 5 values with 3 decimals, coded as an uint16_t (for RAM)
-This allows about 3-4 digits precision in the found interval.
+This allows about 3-4 digits precision for the found interval.
 
-The 0.1.x version does not interpolate the confidence level yet, and only support 5 distinct levels.
+The 0.1.x version does not interpolate the confidence level (yet), and only support 5 distinct levels.
 This interpolation (between 80-99) is planned to be implemented in the future.
+If a non supported confidence level is used, the library will use 95%.
 
 If you need only one confidence interval you could strip the lookup table to one column.
 
@@ -78,11 +98,10 @@ If you need only one confidence interval you could strip the lookup table to one
 #include Student.h
 ```
 
-
 ### Constructor + meta
 
-- **Student()** constructor. 0.1.x has a fixed max sample size = 20.
-- **uint8_t getSize()** returns 20.
+- **Student()** constructor. 0.1.x has a fixed max sample size STUDENT_MAX_SIZE = 20.
+- **uint8_t getSize()** returns STUDENT_MAX_SIZE == 20.
 - **uint8_t getCount()** returns the number of samples added.
 Returns value between 0 .. getSize().
 - **void reset()** resets internal counter to zero.
@@ -96,9 +115,10 @@ Returns false if the internal buffer would "overflow".
 
 ### Math
 
-- **float mean()** returns estimated mean based upon samples added.
-- **float variance()** idem
-- **float deviation()** idem
+- **float mean()** returns mean (average) of the samples added. 
+This is the estimated mean of the population from which the samples are taken.
+- **float variance()** returns variance of the samples added.
+- **float deviation()** returns standard deviation of the samples added.
 - **float estimatedDeviation()** returns estimated deviation of the 
 estimated mean (based upon the samples).
 
@@ -107,7 +127,6 @@ estimated mean (based upon the samples).
 Confidence should be 80, 90, 95, 98 or 99. 
 The confidence level is not interpolated and incorrect values are replaced by 95%.
 
-
 - **float intervalDelta(int confidence)** returns the delta to be added
 oor subtracted to the mean to determine the confidence interval.
 - **float meanLower(int confidence)** returns mean - intervalDelta.
@@ -128,13 +147,18 @@ oor subtracted to the mean to determine the confidence interval.
 - optimize lookup table, PROGMEM for footprint?
 - dynamic allocation for sizes > 20
   - or derived classes, student30, student40, student50, student100?
+  - linear interpolation for values > 10 (performance?)
 - add interpolation to **intervalDelta()** so confidence level (0.2.x)
   could be any integer value from 80-99 (maybe even float?)
 
 #### Could
 
 - add examples
 - add unit tests
+- replace look up table with a formula? (performance drop!!)
+- access function for internal array to access samples?
+- template class instead of STUDENT_MAX_SIZE? (becomes different types).
+- circular buffer for the samples? Running T-test?
 
 #### Won't (unless requested)
 

Student.h

@@ -18,7 +18,7 @@ class Student
 public:
   Student()
   {
-    _size = 10;
+    _size = STUDENT_MAX_SIZE;
     _count = 0;
   }
 
@@ -133,7 +133,7 @@ class Student
   uint8_t _size;
   uint8_t _count;
   float   _mean = 0;
-  float   _value[20];
+  float   _value[STUDENT_MAX_SIZE];
 
 };
 

StudentTable.h

@@ -6,18 +6,24 @@
 // PURPOSE: Arduino library for Student or T-distribution math.
 //    DATE: 2024-07-22
 
-//  lookup table, do not change.
+//  lookup table, do not change (unless you know what you do).
 //
 //  spreadsheet = ROUND(1000 * T.INV.2T(C$4;$B7))
 //
 //  x = degrees of freedom
-//  y = confidence level 0.1, 0.05, 0.025, 0.01, 0.005 (right only)
+//  y = confidence level 0.1, 0.05, 0.025, 0.01, 0.005 (single ended)
 //  values are multiplied by 1000, to save RAM.
-//  
+//
+
+
+//  command line overrule possible
+#ifndef STUDENT_MAX_SIZE
+#define STUDENT_MAX_SIZE          (20)
+#endif
 
 
 //  uses 200 bytes of RAM
-uint16_t StudentLUT[20][5]
+uint16_t StudentLUT[STUDENT_MAX_SIZE][5]
 {
   // 80%   90%    95%    98%    99%
   //---------------------------------
@@ -60,12 +66,94 @@ uint16_t StudentLUT[20][5]
   { 1311, 1699, 2045, 2462, 2756},
   { 1310, 1697, 2042, 2457, 2750},   //  n = 30
 
+  { 1309, 1696, 2040, 2453, 2744},
+  { 1309, 1694, 2037, 2449, 2738},
+  { 1308, 1692, 2035, 2445, 2733},
+  { 1307, 1691, 2032, 2441, 2728},
+  { 1306, 1690, 2030, 2438, 2724},
+
+  { 1306, 1688, 2028, 2434, 2719},
+  { 1305, 1687, 2026, 2431, 2715},
+  { 1304, 1686, 2024, 2429, 2712},
+  { 1304, 1685, 2023, 2426, 2708},
+  { 1303, 1684, 2021, 2423, 2704},  //  n = 40
+
+  { 1303, 1683, 2020, 2421, 2701},
+  { 1302, 1682, 2018, 2418, 2698},
+  { 1302, 1681, 2017, 2416, 2695},
+  { 1301, 1680, 2015, 2414, 2692},
+  { 1301, 1679, 2014, 2412, 2690},
+
+  { 1300, 1679, 2013, 2410, 2687},
+  { 1300, 1678, 2012, 2408, 2685},
+  { 1299, 1677, 2011, 2407, 2682},
+  { 1299, 1677, 2010, 2405, 2680},
+  { 1299, 1676, 2009, 2403, 2678},  //  n = 50
+
+  { 1298, 1675, 2008, 2402, 2676},
+  { 1298, 1675, 2007, 2400, 2674},
+  { 1298, 1674, 2006, 2399, 2672},
+  { 1297, 1674, 2005, 2397, 2670},
+  { 1297, 1673, 2004, 2396, 2668},
+
+  { 1297, 1673, 2003, 2395, 2667},
+  { 1297, 1672, 2002, 2394, 2665},
+  { 1296, 1672, 2002, 2392, 2663},
+  { 1296, 1671, 2001, 2391, 2662},
+  { 1296, 1671, 2000, 2390, 2660},  //  n = 60
+
+  { 1296, 1670, 2000, 2389, 2659},
+  { 1295, 1670, 1999, 2388, 2657},
+  { 1295, 1669, 1998, 2387, 2656},
+  { 1295, 1669, 1998, 2386, 2655},
+  { 1295, 1669, 1997, 2385, 2654},
+
+  { 1295, 1668, 1997, 2384, 2652},
+  { 1294, 1668, 1996, 2383, 2651},
+  { 1294, 1668, 1995, 2382, 2650},
+  { 1294, 1667, 1995, 2382, 2649},
+  { 1294, 1667, 1994, 2381, 2648},  //  n = 70
+
+  { 1294, 1667, 1994, 2380, 2647},
+  { 1293, 1666, 1993, 2379, 2646},
+  { 1293, 1666, 1993, 2379, 2645},
+  { 1293, 1666, 1993, 2378, 2644},
+  { 1293, 1665, 1992, 2377, 2643},
+
+  { 1293, 1665, 1992, 2376, 2642},
+  { 1293, 1665, 1991, 2376, 2641},
+  { 1292, 1665, 1991, 2375, 2640},
+  { 1292, 1664, 1990, 2374, 2640},
+  { 1292, 1664, 1990, 2374, 2639},  // n = 80
+
+  { 1292, 1664, 1990, 2373, 2638},
+  { 1292, 1664, 1989, 2373, 2637},
+  { 1292, 1663, 1989, 2372, 2636},
+  { 1292, 1663, 1989, 2372, 2636},
+  { 1292, 1663, 1988, 2371, 2635},
+
+  { 1291, 1663, 1988, 2370, 2634},
+  { 1291, 1663, 1988, 2370, 2634},
+  { 1291, 1662, 1987, 2369, 2633},
+  { 1291, 1662, 1987, 2369, 2632},
+  { 1291, 1662, 1987, 2368, 2632},  //  n = 90
+
+  { 1291, 1662, 1986, 2368, 2631},
+  { 1291, 1662, 1986, 2368, 2630},
+  { 1291, 1661, 1986, 2367, 2630},
+  { 1291, 1661, 1986, 2367, 2629},
+  { 1291, 1661, 1985, 2366, 2629},
+
+  { 1290, 1661, 1985, 2366, 2628},
+  { 1290, 1661, 1985, 2365, 2627},
+  { 1290, 1661, 1984, 2365, 2627},
+  { 1290, 1660, 1984, 2365, 2626},
+  { 1290, 1660, 1984, 2364, 2626}  //  n = 100
 
-40	1303	1684	2021	2423	2704
-60	1296	1671	2000	2390	2660
 120	1289	1658	1980	2358	2617
 10000	1282	1645	1960	2327	2576  //  effectively infinity.
 */
 
+
 //  -- END OF FILE --