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FCA 2.4 Resident Floating Point Scientific Calculator by Bob Eyer [73230,2620] May 10, 1992 ┌────────────────── SHAREWARE NOTICE and TERMS ────────────────────────┐ │ │ │ The content of this archive is shareware: if you think it's a │ │ worthy addition to your personal software, you might make a │ │ contribution to the author. In return for your contribution you │ │ will receive the most recent updates of the items mentioned in the │ │ list below. │ │ │ │ Simply purchase a money order from your bank in the amount of $20 │ │ US made out to Bob Eyer and send with your return address to: │ │ │ │ Bob Eyer │ │ 1100 Bloor Street West │ │ Suite 16 │ │ Toronto, Canada M6H 1M8 │ │ │ │ Please mention in your accompanying note whether you wish 5.25" or │ │ 3.5" diskette format, and state the name in which you wish │ │ registration-only utilities to be registered. │ │ │ │ Do not send checks. Checks cause problems across international │ │ borders which make them unsuitable for small purchases by mail │ │ order. Checks will be returned with your order unfilled. │ │ │ │ Enquiries may be placed by writing directly to the author via │ │ Easyplex at Compuserve [73230,2620]. │ │ │ │ Warranty and Disclaimer: │ │ ----------------------- │ │ The author, Bob Eyer, of this and all items below guarantees the │ │ physical integrity of the diskette covering the points above, and │ │ will replace free of charge, if it is received defective. │ │ However, in no case will the author be responsible for any damages │ │ due to loss of data or any other reason. In no event does the │ │ author's liability for any damages exceed the price paid for the │ │ buyer's order of this software, regardless of the form of the │ │ claim. The person using the software bears all risk as to the │ │ quality and performance of the software. │ │ │ │ │ │ DESCRIPTION OF PROGRAMS YOU WILL RECEIVE FOR YOUR CONTRIBUTION │ │ -------------------------------------------------------------- │ │ │ │ The items listed below, except the ones with asterisk in the left │ │ margin, are registered to you personally. As personally │ │ registered to you, these particular copies may not be distributed │ │ without the author's consent. Names of programs falling into this │ │ category are all versions of MG, versions of SPC after SPC 5.4, │ │ all versions of HOST, CA, and FCA. These programs may be freely │ │ circulated only in their 'shareware' form. Versions of these │ │ programs which are personally registered to the user must not be │ │ so circulated. When you place an order by making your shareware │ │ contribution under these terms, you are agreeing to abide by this │ │ principle. │ │ │ │ The asterisked items mentioned below are in fact collections of │ │ new versions of Eyer utilities, most of the older versions of │ │ which were posted separately. They have been combined into │ │ packages in order to simplify processing orders at this end. │ │ │ │ MG 3.0 │ │ ------ │ │ Moving average ASCII graphing program. Especially designed for │ │ obtaining graphic updates on stock-market activity in practical │ │ trading environments, in which it is essential that the user get a │ │ quick graph immediately, with points of the graph directly │ │ associated with the numerical and other text information which │ │ these points represent (a feat impractical in Lotus graphics). │ │ Designed to be used with SETV in the SUTL package. │ │ │ │ SPC 5.5 │ │ ------- │ │ Multidrive columnar drive report, with fairly complete description │ │ of your machine including communications, important chips, │ │ printer, BIOS, memory, processor and coprocessor speed, │ │ multitasking, networking, and so on, all in one single snapshot. │ │ New version doubles the amount of information on each │ │ communications port and displays the information in columnar mode │ │ above the drive report, adds an environment usage readout as well │ │ as a new P parameter to pause the PRINT multiplexer, when it is │ │ used to feed data to your printer. (DOS PRINT lacks a pause │ │ command). │ │ │ │ HOST 2.4 │ │ -------- │ │ Provides a simple BBS host for occasional use. Fully │ │ configurable, but capable of being run 'right out of the box', │ │ HOST provides ringback, file transfer, mail, chat, userlog, shell, │ │ and much more - in an executable only 30K in size. Version 2.4 │ │ adds options to limit medium speed noise filtering, and │ │ facilities for reading in the user's own list of file protocols. │ │ │ │ CA 2.4 │ │ ------ │ │ 7-function fixed point TSR calculator with formatted displays and │ │ scientific notation for direct paste to text. Also has │ │ accumulator. Four mode groups. About 13K of memory. │ │ │ │ FCA 2.4 │ │ ------- │ │ Memory resident calculator with formatted displays and direct │ │ paste to text, minimum screen overlay. 29 functions, including │ │ trig, factorials & combinations, mean & standard deviation, │ │ regression analysis, binomial, Poisson, normal, and Student │ │ distributions. Six mode groups. FCA is the most sophisticated │ │ calculator in the business for its size. 39K of memory. │ │ │ │* FUTL 2.0 │ │ -------- │ │ A collection of file processing utilities including - │ │ CHG 2.8 - File/directory attribute/date/time reader/changer │ │ ELIM 2.6 - Replacement for DOS DEL │ │ FVER 2.1 - BBS file list verifier - automatic, redirectable │ │ MV 2.8 - File mover, large improvement over MV 2.6. │ │ MVA 2.1 - BBS file mover, reads from list, uses download path │ │ OTL 3.0 - Operation to List, generalisation of MVA, for BBSes │ │ RNF 2.2 - Puts special flags on filenames │ │ SWP 2.0 - Single level sweep program, faster than SWEEP.COM │ │ TYME 2.3 - Program execution timer │ │ WD 2.6 - Applies wildcard to any program │ │ Each is the best and smallest in the business for what it does. │ │ │ │* SUTL 2.2 │ │ -------- │ │ A collection of small utilities covering batch file, diagnostic, │ │ communications analysis, file, video, and other areas, including │ │ AL, CFIX, DOSV, DTR, EL, EMS, KALL, LF, PAUZ, PF, PORT, RING, RTS, │ │ SETV, SS, and TSTF. Includes a number of very useful memory │ │ resident programs, such as AL(alarm) and PORT(analyser). Colour │ │ fix for SS, some new programs such as a very small keystroke │ │ counter. │ │ │ │* TUTL 2.1 │ │ -------- │ │ A collection of text-processing utilities, including ADD, CBRO, │ │ CITM, COMB, DIV, ESRT, LCNT, REV, and SPLT. Except for LCNT (a │ │ very fast wildcarded text linecounter), these programs cover │ │ important ground in text processing for which there exists no │ │ other alternative in the shareware market. Users who do much │ │ work with ASCII text should not be without these utilities. │ │ │ └──────────────────────────────────────────────────────────────────────┘ ┌────────────────────────────────────────────────────────────┐ │ WARNING: THIS SOFTWARE MAY NOT WORK PROPERLY WITH CERTAIN │ │ APPLICATIONS. SEE CAUTION BELOW. │ └────────────────────────────────────────────────────────────┘ Help screen ----------- Syntax: FCA [/U] Hotkey: Rightshift-/ Modes: places COLOR y RAD/DEG TWO/NAP/TEN STUF/D DMS/NODMS Review: ST Registers: E PI A B C F K L M N Q R S X Y Z Data entry areas: MEAN REGRESSION (Use Esc to paste result) Binary operations: + - * / ^ CO PE Unary operations: SQ SQRT EXP LOG SIN ASN COS ACS TAN ATN SINH COSH TANH ! X= Y= Probability fcns: BIN NORM POIS STUD See the note about Errors below. Changes since CAF 2.3 --------------------- - Operation symbols for combinations and permutations changed to CO and PE from C and P respectively, to prevent conflict with data registers. - Second extra register Y added for calculation purposes. May now set Y = C just as X = C. - Meaning of certain registers changed to accommodate syntax used in new probability routines. The slope of a regression line is now L, not M. M is used to store means and is shared amongst several routines. See detailed discussions below. - Binomial, Poisson, Normal, and Student t probability functions, See sections below about these new functions. - Further development of FCA's error recovery system. Changes since CAF 2.0 --------------------- - Much better input editor, allowing use of Esc key to exit; no more jerky cursor action. - Adds MEAN and REGRESSION special areas. ADD now integrated into MEAN chiefly to save space. New display prompts put results to the left the prompt. - C added to binary functions - number of combinations of n things taken r at a time. The math notation 'nCr' is somewhat modified as 'a C b'. - P added to binary functions - number of permutations, same type of syntax as for combinations. - ! added to unary functions - the factorial function. As for all other unary functions, the function name MUST precede its argument, and be separated by a blank. Thus the math notation '10!' reads in CAF as '! 10'. - MEAN area added - enables user to find the total, mean and standard deviation of a list of numbers. Reserved for registered users only. - REGRESSION area added - enables user to find the correlation coefficient of a series of paired data. Also computes the least square regression line and other data for this series. Registered users only. - New registers for direct readout or paste: K (the y-intercept of the regression line), M (the slope), N (the number of data in the supplied scatter of points), R (the correlation coefficient), S (the standard deviation for the MEAN). - New storage register X, for saving old results for re-entry into subsequent calculations. - Introduces DMS format ('degree-minute-second') for trig functions. Default is No DMS (NODMS). Where DMS is set, CAF treats the first two digits following the decimal point of angles as the number of minutes, and the next four digits as seconds correct to the nearest hundredth of a second. Only works when DEG (degree) mode is set, and only on the trig functions and their inverses. - The PLACES mode is simplified so that the mere entry of a single digit number causes CAF to change the number of places. Formerly, the user had to type 'x PLACES' to get it to recognise x as the number of places. Entry of the number of places now affects all displayed numbers, as well as all those which are pasted to the underlying application. In the MEAN and REGRESSION areas, however, results are formatted to a minimum of 3 places within those areas unless places is set higher than 3. If set to 0, results rounded to 3 places in the area windows will appear to maximum precision on exit from those windows. - The N/D modes are now changed to STUF/D. The reason is to avoid conflict with the N register readout for the number of pairs of data entered in the MEAN and REGRESSION areas. - Extends to all unary functions the same coverage of register input as applies to binary functions. INTRODUCTORY NOTE: FCA is a floating point companion alternative to CA (see program listing in Shareware Notice above), which is restricted to four function fixed point arithmetic. FCA supports 29 functions. Registered versions of CA use about 12K of memory; FCA uses about 40K. This is comparable to some of the simpler floating point calculators, such as FFC, but, unlike these (which are usually restricted to the standard four arithmetic functions), FCA currently offers 29 functions. FCA is not a general formula evaluator. If you need to do many different kinds of calculations on the same text in one shot, it may be more appropriate to use Lotus 1-2-3 or similar, print results as a file, edit, and then insert into your text. FCA, however, does provide a simple means of re-using input data for subsequent calculations (see section below about Automatic Store/Recall and also the discussion about register operations). Also, FCA provides a method of adding many numbers before injecting the sum to text (See Special Accumulator section below). FCA's floating point emulator will take advantage of the coprocessor, if one is installed. This advantage is noticeable primarily with regard to the probability functions. The slowest and least accurate function is the Student probability integral, which may require up to 8 seconds and beyond to find results arising from certain rare combinations of input variables on a 386 machine WITH installed 80387. This function works up to 60 times more slowly when run on a machine lacking a coprocessor. While the transcendentals generally have an accuracy of the order of 12 decimal places, the Student is generally accurate to only 5. See below about the STUD function. FCA's real number range, apart from sign, is roughly between 1e-294 and 1.7e+308. This is much larger than is possible in the companion program CA, and is also larger than the usual range for many scientific calculators. IMPORTANT: This program does not provide a menu or picture of a calculator - so as to avoid obscuring portions of the underlying editing application, and to avoid requiring the user to employ only 25 x 80 screens (some TSR calculators require this, to make use of Line 25 for calculator monitoring). FCA responds equally well in 50 x 80 or 44 x 132 video environments; generally, it is indifferent to the manner in which the video raster is defined. FCA is designed to respond just to the hotkey, which provides merely a 'calculation window', in which the user enters his calculations or mode changes. Hitting ENTER after supplying a calculation or mode change to the window, simply executes the job and returns to the application. Where a result is generated, it is pasted directly to the underlying application where the cursor was last located. In examples seen below, EACH calculation or mode change is preceded by invoking the hotkey. This, however, does not apply to special areas dealing with more complex problems, such as MEAN and REGRESSION. FCA is also designed to return the cursor to the initial position in the main calculation window, to permit making mode adjustments without line skipping. Once a task is completed, you may exit the window merely by hitting ENTER one additional time or by using the spacebar to delete the window. The old window always disappears in an editing environment after the result is injected to the text, but mode change information will, in general, remain. Modes/review ------------ FCA provides 6 groups of mode selections - number of decimal places to which to round results, colour of calculation window, whether to use Radian or Degree measure, what base to use for the EXP and LOG operations, whether to echo the result to display or paste to text, and whether to use DMS format in trig calculations. The current mode situation may be viewed simply by entering ST in the calculation window (ST is short for 'status'). Mode changes are entered directly in the calculation window and the new mode specs are resummarised in the calculation window, just as though ST had been issued. x Entry of 5 in the calculation window will cause FCA to operate so as to round all results to five decimal places. Entry of 0 means that no formatting will occur. The default value is 0. COLOR y: Entry of 'COLOR 30' will cause the calculation window to have a bright yellow foreground and a blue background. For colour details see below. The default colour scheme is black on white (112). Color 0 automatically converts to 112, so as to avoid black on black. RAD/DEG: Entry of RAD in the window causes FCA to assume all angles entered as arguments in trig functions are in radian measure. Entry of DEG puts FCA into Degree mode. The default is Degree mode. TWO/NAP/TEN: FCA supports three bases for use with the LOG or EXP functions. TWO means Base 2; NAP is short for the Napierian base (2.718 ...) and means Base e; and TEN means Base 10. The default is Base e. STUF/D: STUF means normal (stuff the result to the underlying application), and D means display (that is, display at TSR video level). STUF is the default. STUF mode injects results to the underlying application; display mode echoes results to the screen without pasting to the application at all. Register operations ------------------- FCA supports pasting 11 registers direct to text. For example, after invoking the hotkey, we simply enter e [= 2.7182818284590 (the use of the left bracket here merely signifies that the result appears at the underlying application, not at TSR level) In addition, the user may simply enter A, B, or C to examine the last value stored in FCA's "store/recall" facilities (see below), as well as the general storage register X, and the statistics registers. Binary operations ----------------- FCA supports seven two-variable ('binary') operations: + - * / ^ C P, or add, subtract, multiply, divide, raise to a power, combinations and permutations, respectively. For example, 1991-1917 [= 74 7e-6+3e-4 [= 0.000307 3.33e+1+4.56e-3 [= 33.30456 When entering exponentially formatted numbers one must specify a sign (+ or -) immediately after the 'e' symbol. Additional examples: 35/34 [= 1.0294117647058 35*34 [= 1190 35^34 [= 3.1500214e+52 10 CO 4 [= 210 (210 combinations of 10 things taken 4 at a time) Unary operations ---------------- FCA also supports 10 unary transcendental functions, grouped by inverses, as well as three hyperbolic functions, and the factorial function. Here, a blank must separate the name of the operation and the number which the operation takes as its argument. Examples, ! 6 [= 720 (factorial 6) SIN 45 [= 0.7071067811865 COS 1 [= 0.9998476951563 LOG 2 [= 0.6931471805599 EXP 1 [= 2.7182818284590 SQRT 2 [= 1.4142135623731 If you wish to use Base 10 logarithms, just enter TEN in the window, and then LOG 2 [= 0.3010299956639 Note: the EXP function is in fact an antilog function, since it is subject to the same range of base changes as is the LOG function. This may be inconvenient to some users who assume that the exponential function must always have base e, but implementing a separate antilog function seemed, in the circumstances, merely to be useless duplication of what is, essentially, a quite flexible function. The internal setup for the hyperbolic functions is the same as for the trig functions. If you select DEGree mode, FCA will convert your degree measure into the radian equivalent before calculating the function. If you select RADian mode, FCA will do no such conversion, but will inject your argument directly to the function. Automatic store/recall ---------------------- If you are doing several calculations which involve use of the same term, you may reduce typing further by using variables. Calculation window variables are A, B, and C. The first time you execute a calculation with numbers, the first number is always stored into A, the second number into B, and the result into C. These values can be re-used, simply by employing these variables in subsequent calculations [except, of course, for the fact that, as each new calculation is done, the value of C will be updated with the new result]. Example (after entering 3 in the window): Suppose we wish to perform the following calculations - 34.21102 x 435, and 34.21102 / 355.5 Here, each calculation uses the same initial term. We proceed as follows, each time by hitting Rightshift-slash, and entering the calculation shown: 34.21102 * 435 [= 1.488e+4 a/355.5 [= 9.623e-2 The second calculation above could be repeated merely by entering a/b The user may also proceed to obtain results for the other three operations, using the same numbers, as follows: a*b [= 12162.018 a+b [= 389.711 a-b [= -321.289 The output C-variable can also be used in calculations. For example, we may first calculate with no scientific notation 2/3 [= 0.667 ] Here, A = 2, B = 3, and C is the result in brackets. Now, if we multiply the result C by 3, we should get back the numerator A: C * 3 [= 2.000 This example illustrates the fact that FCA, like handheld calculators with the store/recall function, stores results in a separate register before rounding. It is this separate register that is used for input, when the user employs C in a calculation. [otherwise, the user might get back 2.001]. This type of 'result protection' on use of a previous result is not, however, found in most TSR calculators. All these remarks apply also to FCA's trig functions. For example (using 5 decimal places), SIN 89 [= 0.99985 We may now get back the value of the argument, simply by performing the inverse (ARCSINE or ASN) on the result: ASN C [= 89.00000 The same principle also works with squares and squareroots, as well as logs and exponentials. For example, LOG 2 [= 0.69315 but the argument '2' may be had by performing the inverse on the result: EXP C [= 2.00000 You may also store a previous input or result into either of the extra storage registers X or Y. Just use, for example, X= C or Y = B to store the value of C into X or B into Y. Note that FCA is indifferent on whether the entry formula is 'X=C' or 'X = C'. X may be recalled simply by entering X by itself, or by using it as an argument in any function. MEAN (Total, Mean and Standard deviation) ----------------------------------------- Entry of the keyword MEAN in the calculation window will transfer control to a special area of FCA which displays the following type of prompt: X> Numbers entered at this prompt are totalled and in passing FCA also computes the mean and standard deviation for all numbers entered, displaying these results in the stated order to the left of the prompt. If the next number in the series is the same as the previous one, you may simply enter X at the prompt; FCA interprets X in the MEAN window as the value last entered. The same principle applies where the user wishes merely add the previous total to itself: use the result register C. The data displayed to the left of the prompt are displayed as rounded to a minimum of 3 places. When finished entering data, simply hit the Esc key to paste the Total to the underlying application. The other data are available by entering the following variable names: C - Total M - Mean S - Standard deviation N - Number of data entered. F - Degrees of freedom (for MEAN calculations this will be N - 1). The main result, the total, may be accessed by using register C. The values listed above may be used, for example, in the Normal distribution to obtain automatic calculation of a z-score (see below). For the interest of statistics people, the definition of standard deviation used in FCA assumes the "n - 1" basis. That is, it is based on multiplying the the root mean square of the data by the square root of the ratio of N to N - 1. The purpose of the n-1 basis is to obtain a more realistic value for the standard deviation in small sample applications than is possible with a mere variance calculation. The value of this routine is primarily to obtain quick results on small amounts of data found directly on the screen in the underlying application. If you have a large job to do, involving many points, your best bet is to use a large program such as LOTUS 1-2-3, not a small program like FCA. MEAN is available only to registered users. REGRESSION (regression analysis) -------------------------------- Entry of the keyword REGRESSION in the calculation window will transfer control to the REGRESSION area of FCA. Here, the prompt will change between X> and Y> and FCA will issue a beep to the speaker each time a Y value is entered. Three running results are displayed to the left of the prompt: The correlation coefficient, the y-intercept of the regression line, and the slope of that line. The previous value of X may be entered at either prompt by using X, and the previous value of Y may be entered at either prompt by using Y. If you enter C (the result register) the current correlation coefficient will be entered at the prompt in question. Avoid, unless you really want to do that. But otherwise, operation of the REGRESSION area is similar to that in MEAN. On use of Esc to exit, FCA will paste the correlation coefficient to the underlying application. To paste the y-intercept, use K; and to paste the slope, use L. The regression line has the standard form, Y = K + LX As usual, N is the number of pairs of data entered in the REGRESSION window. The correlation coefficient may be obtained by entering R. F is also calculated by FCA, and in the REGRESSION window, will always be set to N - 2. REGRESSION is available only to registered users. BIN --- This function returns the cumulative binomial probability of the occurrence of X or fewer events in a sample of size N, where the probability of a single event is Q, as well as the point probability in register Y. The syntax is BIN X N Q corresponding to the summation of all values of the binomial frequency distribution for occurrences ranging between 0 and X. Taking an example from Spiegel's Statistics (Schaum Outline Series, p 127), find the probability that at most 2 bolts (i.e. either 0, 1, or 2) will be defective in a sample of 4 taken from a production process in which 20% of all bolts produced are defective. Here, we use BIN 2 4 0.2 [= 0.9728 the same answer given by Spiegel. The probability that exactly 2 bolts will be defective in this problem is obtained merely by entering the Y register Y [= 0.1536 POIS ---- This is the Poisson cumulative probability of the occurrence of X or fewer events in a sample of size N, where the probability of a single event is Q - using same syntax as BIN: POIS X N Q The 'integration' logic used by FCA here is the same as for the binomial distribution. That is, the result found is the summation of the individual Poisson probabilities from 0 to X. The point probability is found in register Y. The primary reason why this distribution is needed to supplement the Binomial, is that the latter has a restricted range, owing to the fact that it uses the factorial function to operate on the sample size. This function explodes beyond the number range intelligible to FCA for arguments larger than 170. The Poisson distribution also uses the factorial function, but only on the value of X. It is therefore capable of dealing with very large sample sizes. The disadvantage of the Poisson is that it is only an approximation to the Binomial. Using another example out of Spiegel's text, we may find the probability that more than 2 individuals out of a sample of 2000 will suffer a bad reaction from a certain injection, if the probability that any individual will suffer is 0.001. This problem is clearly beyond the capabilities of the binomial distribution. The problem is solved first by finding the probability that at least 2 will suffer. This is: POIS 2 2000 0.001 [= 0.6767 The probability that more than 2 will suffer is obviously 1 minus this result: 1 - C [= 0.3233 which is the same as Spiegel's result. The probability that exactly 2 persons will suffer in this problem is found in register Y: Y [= 0.2707 NORM ---- The syntax for the normal probability is NORM [X M S F] | [Z] The form here indicates two modes of data entry; one which involves inputting the sample mean X, the population mean M, the sample standard deviation S, and the degrees of freedom F associated with that sample - or simply the z-score. The value of F should be equal to N - 1; that is, it should be one minus the sample size. FCA will automatically calculate the appropriate z-score if the first data entry method is used. The result is found in register Z. The terminology used here is compatible with the terminology used in the MEAN section of FCA. Since FCA only uses the absolute value of the z-score to calculate the probability of the null hypothesis, it does not matter whether MEAN is used to compute population or sample means. Thus, after entering the sample in MEAN, the user may exit and test a particular value of X, say 5, against those results by entering NORM 5 M S F FCA will pick up the values of M, S, F and proceed to calculate the z-score for the X-value 5. The result returned in C (and pasted to text, if STUF mode is active) is the probability of the null hypothesis - that is, the 'one-tailed' cumulative Normal probability associated with values of X equal to or greater than 5. If only one parameter is entered, NORM assumes that this value is the raw z-score. For example, the one-tailed Normal probability for a z-score of 1.96 is: NORM 1.96 [= 2.500e-02 which checks exactly with any standard table of Normal probabilities. 1.96 will be recognised by statisticians as the usual z-score associated with defining a two-tailed 95% confidence interval about a mean [2.500e-02 = 1 - 0.95/2]. The Normal ordinate for the input value of 1.96 is available in Y: Y STUD ---- The Normal distribution is not very useful except on large samples, for which reason the Student distribution was developed earlier this Century by Gosset. The syntax is - STUD [X M S F] | [Z F] Same remarks for these variables and their purpose as given above for NORM. Note that, if the calculation of the t-score is avoided and direct entry is desired, the user must enter degrees of freedom F along with the score. For example, if the t-score is 12.706 based on a sample size only two data, so that there is only 1 degree of freedom, then the probability of the null hypothesis is STUD 12.706 1 [= 2.500e-02 which agrees exactly with statistical tables on the Student distribution. FCA does not yet support recovery of the Student ordinate values. The point about the importance of large samples for the Normal distribution may be seen by noting how many degrees of freedom are necessary to bring the Student probability into line with the Normal, using a constant score of 1.96. This can be seen in the following brief chart: Z = 1.96 ------------------- Degrees of freedom Student probability ------------------ ------------------- 1 0.150 10 3.922e-02 30 2.967e-02 100 2.639e-02 500 2.528e-02 5000 2.503e-02 Note how the Student probability converges to the Normal as very large amounts of data are used to calculate the sample mean. Note also the probability with a sample size of 31 (F = 30): the value there is close enough to the Normal value of 2.500e-02 to let the Normal present a reasonably accurate picture of a two-tailed 95% confidence interval on that sample size. This is the reason why most statisticians don't consider a Normal test to be good unless the sample is based on at least 30 pieces of data. In text editing applications, where the user is evaluating a small number of results, say, sample sizes of the order of 3 to 12 pieces of data, and wants a quick analysis, the Normal distribution will not be helpful at all: The Student distribution will be required. And it is quite handy to have such a distribution immediately accessible at the touch of a hotkey. I have referred here to the "t-score"; but the syntax of the STUD function uses the variable Z. This is due to the fact that FCA uses the same definition for the standard deviation throughout all its statistics routines, resulting in the fact that the z-score and the t-score use the same formulas. This being the case, it was not necessary to distinguish a "T" variable for separate use with the Student distribution. Wait time --------- The Student integral is a relatively complex and slowly converging infinite series, and so, certain combinations of values will cause FCA to display the message Wait ... for an appreciable length of time. This means that the integral is being calculated. As stated above in the introductory portion of this file, FCA will take full advantage of a numeric coprocessor, if one is installed. Experiment shows that Student probability calculations run between 30 and 60 times faster when when there is an installed coprocessor. Normally, this wait time problem is not significant. But for very large t-scores and small values of F, execution time for the Student probability may prove to be substantial, even for fast machines. For example, STUD 64 1 [= 4.973e-03 requires 8 seconds on a 20 Mhz 386/387 machine. On a 486 machine, the expectation is that this result would require somewhat less than 2 seconds, since all such machines have numeric coprocessor capability built-in. On a 6 MHz AT without coprocessor, however, this calculation will require more than 22 MINUTES. So, if you see 'Wait ...' just wait: your machine is NOT hung. And avoid Z values substantially larger than 10, unless you have a coprocessor, or are prepared to wait for the result. Execution time rises about as the square of Z and drops in rough linear proportion to the value of F. Nearly always, however, the user will not be considering such large t-scores and will have samples which are larger than just two pieces of data (1 degree of freedom). For example, a t-score of 2.78 based on a calculated mean of a sample of size 5 - STUD 2.78 4 [= 2.491e-02 executes virtually instantaneously on a 386/387, and requires about 3 seconds on a 6 MHz AT without coprocessor. Prompt Colour ------------- As stated above, to change the colour of the calculation window, simply enter COLOR x in the window, where x is a COLOR number. The default is 112, which describes black foreground on a white background. 0 is impossible (black on black), and so FCA converts that number to 112 automatically. Foreground and Background colours may be determined by using the following table: Back Fore Bright Fore ---- ---- ----------- Black 0 0 8 Blue 16 1 9 Green 32 2 10 Cyan 48 3 11 Red 64 4 12 Magenta 80 5 13 Brown 96 6 14 White 112 7 15 The correct COLOR number is found merely by adding the Foreground number to the Background number desired. For example, Bright Green on Blue background is 10 + 16 = 26. Avoid setting COLOR above 127. Values above that limit will produce blinking displays. In my estimation the COLORs best for the eye are 10, 11, 14, 15, 26, 27, 30, 31, 74, 75, 78, 79 and 112. But you may have other ideas. Example, COLOR 75 sets the window to Bright Cyan on a Red background. Errors ------ FCA supports error reports as follows - xyz: illegal - This message occurs where your entered instruction, 'xyz', is not recognised by FCA. For example, 'TAN89' is illegal; should be 'TAN 89'. Read examples in documentation above to be sure you understand how to enter expressions. Illegal X setting - This means that you have tried to save the value of unsupported register into X. The supported registers are listed on the help screen. Zero divide error - Attempt to divide by zero. This can be an explicit mistake, like '5 / 0', or it may be an attempt to calculate the value of a unary function which divides two other functions to obtain its result. For example, the TAN, or Tangent of an angle, is really the ratio of the Sine and the Cosine of that angle; but the Cosine of 90 degrees is zero, so trying to find the Tangent of 90 will generate this error. Negative base error - You tried raising a negative number to a power (cannot be done on real numbers). Negative argument error - You tried taking the LOG of a negative number (cannot be done on real numbers). Requires registration - This means you are trying to access a function accessible only to registered users. (Send in your contribution, and get full access!) FCA 2.4 also adds numerous other specific error message readouts, providing diagnostics on values of special variables, especially in reference to the probility and statistics functions. These are all self-explanatory. CAUTION ------- Certain types of editors will not work consistently with FCA - in particular, editors which simulate the Macintosh console environment, such as the Microsoft DOS 5.0 Editor. Like Microsoft Windows, these environments do certain tricks with video display - and, so I understand, certain tricks to redefine one or more interrupt functions - which lead to machine hangs when FCA and other similar TSR's are run concurrently with them. (The problem here is not unique to FCA, as collateral testing of other TSR calculators has shown). Further, like all memory resident programs, FCA is vulnerable to compatibility problems which may arise from its use with other TSR's. If you find you must reboot, try removing other memory resident programs from your AUTOEXEC.BAT file, or try changing the sequence in which they are loaded until you find the best combination. However, tests have shown that FCA is much less vulnerable to interrupt collisions and other compatibility problems than other resident floating point calculators. One category of TSR which is almost guaranteed to cause trouble for FCA (and for any program which stuffs keystrokes into the keyboard buffer) are programs like 128KEY.COM, which lengthen or change the effective size of the keyboard buffer. Don't use such programs with FCA. FCA is primarily intended to work with editors and wordprocessors, and has been tested on Wordperfect 5.0, Galaxy 2.42, Captain Blackbeard 1.13, SLED 1.1, QEDIT 2.08, pEDIT 2.10, and a number of other editors/wordprocessors, with no confirmed problem or abnormality. FCA is recommended for use as the last memory resident program loaded, so as to permit the use of the /U commandline option to unload it from memory, and only in standard text-editing or wordprocessing applications. Unless you have found that FCA works with your non-standard application, it is recommended that you take the precaution of unloading FCA before you invoke such an application. ---------------------- End of documentation