/* manual_statistics.c * * Copyright (C) 1992-2005 Paul Boersma * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * See the GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */ /* * pb 2005/04/27 GPL */ #include "ManPagesM.h" void manual_statistics_init (ManPages me); void manual_statistics_init (ManPages me) { MAN_BEGIN ("Statistics", "ppgb", 20060506) INTRO ("This is the tutorial about basic statistical techniques in Praat, which work " "with the @Table object or even directly from the @Goodies menu. It assumes that you are familiar with the @Intro.") NORMAL ("(Under construction..................)") NORMAL ("Goodies menu:") LIST_ITEM ("\\bu @@Difference of two proportions@") NORMAL ("For a selected Table:") LIST_ITEM ("\\bu @@Logistic regression@") NORMAL ("For more sophisticated techniques, see:") LIST_ITEM ("\\bu @@Principal component analysis@") LIST_ITEM ("\\bu @@Multidimensional scaling@") LIST_ITEM ("\\bu @@Discriminant analysis@") MAN_END MAN_BEGIN ("Difference of two proportions", "ppgb", 20060506) INTRO ("This page explains how you compute the significance of a difference between two proportions " "with a %\\ci^2 (chi-square) test.") ENTRY ("1. Example of normal use") NORMAL ("Suppose that you are interested in proving that for a certain experimental participant Task B is easier than Task A." "You let the participant perform Task A 110 times, and she turns out to perform this task correctly 71 times. " "You also let her perform Task B 120 times, and she performs this task correctly 93 times. " "The following table summarizes the results of your experiment:") CODE1 ("\t\tCorrect\tIncorrect") CODE1 ("\tTask A\t71\t39") CODE1 ("\tTask B\t93\t27") NORMAL ("The null hypothesis is that both tasks are equally difficult and " "and that the probability that the participant performs Task A correctly is equal to " "the probability that she performs Task B correctly.") NORMAL ("To compute the probability that the observed proportions are at least as different as 93/120 and 71/110 " "if the null hypothesis is true, go to ##Report difference of two proportions# in the @Goodies menu " "and fill in the four values 71, 39, 93, and 27. The resulting two-tailed %p is 0.04300, suggesting " "that the null hypothesis can be rejected and the two tasks are not equally difficult " "(if the possibility that Task A is easier than Task B can be ruled out a priori, " "then the resulting one-tailed %p is 0.02150).") ENTRY ("2. Example of incorrect use: areal features") NORMAL ("An anonymous linguist once proposed that there was a causal relation between blood groups and the incidence " "of dental fricatives. He noticed that dental fricatives occurred mainly in languages whose speakers " "predominantly had blood group O. To prove his point, he tabulated 100 languages:") CODE1 ("\t\t\tHas /\\tf/ or /\\dh/\t\tNo dental fricatives") CODE1 ("\tGroup O\t\t24\t\t11") CODE1 ("\tGroup A or B\t\t29\t\t36") NORMAL ("Since %p < 0.05, the linguist regarded his hypothesis as being supported by the facts. " "However, this %\\ci^2 test assumes that the 100 languages are independent, but they are not. " "Two adjacent languages tend to correlate in their probability of having dental fricatives, " "and their speakers tend to correlate in their blood groups. Both are %%areal features%, " "which undermine the independence assumed by the %\\ci^2 test. The actual null hypothesis " "that the test rejected was the combined hypothesis that dental fricatives correlate with blood group " "%and that the 100 languages are independent.") NORMAL ("Another anonymous linguist proposed that those Limburgian dialects that had lost their tone contrast " "compensated this by having larger vowel inventories. He drew up a table of the dialects of 100 villages:") CODE1 ("\t\t\tHas tone\t\tHas no tone") CODE1 ("\tHas over 25 vowels\t\t10\t\t7") CODE1 ("\tHas under 25 vowels\t\t80\t\t3") NORMAL ("This result is very significant (%p < 10^^-4^), but only shows that %either there is a relation between " "tone and the number of vowels %or that the dialects are not independent. And since adjacent dialects are " "arguably dependent both with respect to tone and the number of vowels, the statistical significance does " "not allow us to draw any conclusion about the relationship between tone and the number of vowels.") ENTRY ("3. Example of problematic use: pooling participants") NORMAL ("An anonymous student decided to do the Task A versus Task B experiment described above, " "but did not let one participant perform all the 230 tasks. Instead, she let 5 participants perform 46 tasks each " "(22 times task A, 24 times Task B). The pooled data were:") CODE1 ("\t\tCorrect\tIncorrect") CODE1 ("\tTask A\t71\t39") CODE1 ("\tTask B\t104\t16") NORMAL ("The resulting %p is 0.00016. So what is the conclusion, if the measurements can clearly be dependent? " "Well, if the null hypothesis is that all five participants are equally good at Task A as at Task B, " "then this hypothesis can be rejected. The conclusion must be that %%these five participants% have on average " "more trouble with Task A than with Task B. The student incorrectly concluded, however, that Task A was " "more difficult for the average population than Task B. In order to be able to draw such a conclusion, " "however, a different test would be required, namely one that takes into account that the five participants " "form a random sample from the total population. The simplest such test would be a sign test over " "the participants: count those participants who score better on Task A than on Task B and see whether this number " "is reliably less than 50 percent of all participants. For five participants, such a sign test " "would %never reach significance at a two-tailed 5 percent level (2*0.5^5 = 0.0625).") ENTRY ("4. Example of problematic use: pooling participants") NORMAL ("Our purpose was to disprove the null hypothesis that listeners' perception does not depend on the language " "they think they hear. However, certain vowel tokens acoustically in between the Dutch /\\as/ and the Dutch /\\ct/ " "were perceived 50 percent of the time as /\\as/ and 50 percent of the time as /\\ct/ when Dutch learners of Spanish thought " "they were hearing Dutch, but 60 percent of the time as /\\ct/ when they thought they were hearing Spanish. " "The responses of 40 listeners, all of whom underwent both language modes, is combined in the following table:") CODE1 ("\t\t/\\as/\t/\\ct/") CODE1 ("\tDutch mode\t200\t200") CODE1 ("\tSpanish mode\t160\t240") NORMAL ("The result was %p = 0.0056, which reliably showed that these 40 listeners on average shifted their category " "boundary toward /\\as/ when they thought that the language they were listening to was Spanish. " "The conclusion is that not all listeners were indifferent to the language mode, " "so that mode-dependent perception must exist. The explanation in this case was that the Spanish /a/ " "(which Dutch learners of Spanish identify with their /\\as/) is more auditorily front than Dutch /\\as/; " "in order to reject the null hypothesis that language modes exist but that their direction is random for each " "learner, i.e. the population average of the shift is zero, a separate test was required to show that the observed " "shift is representative of the population of Dutch learners of Spanish " "(this is easier to accomplish for 40 participants than for 5).") MAN_END MAN_BEGIN ("Logistic regression", "ppgb", 20050427) INTRO ("This page explains how you do logistic regression with Praat. " "You start by writing a table in a text file. " "The following example contains natural stimuli (female speaker) with measured F1 and duration values, " "and the responses of a certain listener who is presented each stimulus 10 times.") CODE1 (" F1 Dur /ae/ /E/") CODE1 (" 764 87 2 8") CODE1 (" 674 104 3 7") CODE1 (" 574 126 0 10") CODE1 (" 566 93 1 9") CODE1 (" 618 118 1 9") CODE1 ("1025 147 10 0") CODE1 (" 722 117 7 3") CODE1 (" 696 169 9 1") CODE1 ("1024 124 10 0") CODE1 (" 752 92 6 4") NORMAL ("In this table we see 10 different stimuli, each characterized by a certain combination " "of the independent variables %F1 (first formant in Hertz) and %Dur (duration in milliseconds). " "The first row of the table means that there was a stimulus with an F1 of 764 Hz and a duration of 87 ms, " "and that the listener responded to this stimulus 2 times with the response category /\\ae/, " "and the remaining 8 times with the category /\\ep/.") NORMAL ("A table as above can be typed into a text file. The columns can be separated with spaces and/or tab stops. " "The file can be read into Praat with ##Read Table from table file...#. " "The command \"To logistic regression\" will become available in the #Statistics menu.") ENTRY ("What does it do?") /*SCRIPT (4.5, 4, "Axes... 60 180 900 500\n" "Marks bottom every... 1 30 yes yes no\n" "Marks left every... 1 50 yes yes no\n" "Text bottom... yes Duration (ms)\n" "Text left... yes F1 (Hz)\n" "mdur_ae = 135\n" "mdur_ep = 95\n" "sdur = 25\n" "mf1_ae = 780\n" "mf1_ep = 620\n" "sf1 = 60\n" "Draw ellipse... mdur_ae-sdur mdur_ae+sdur mf1_ae-sf1 mf1_ae+sf1\n" "Text... mdur_ae Centre mf1_ae Half /\\ae/\n" "Draw ellipse... mdur_ep-sdur mdur_ep+sdur mf1_ep-sf1 mf1_ep+sf1\n" "Text... mdur_ep Centre mf1_ep Half /\\ep/\n" "Draw inner box\n" )*/ NORMAL ("The logistic regression method will find values %\\al, %%\\be__F1_% and %%\\be__dur_% " "that optimize") FORMULA ("%\\al + %%\\be__F1_% %F1__%k_ + %%\\be__dur_% %Dur__%k_ = ln (%p__%k_(/\\ep/)/%p__%k_(/\\ae/))") NORMAL ("where %k runs from 1 to 10, and %p__%k_(/\\ae/) + %p__%k_(/\\ep/) = 1.") NORMAL ("The optimization criterion is %%maximum likelihood%, i.e. those %\\al, %%\\be__F1_% and %%\\be__dur_% " "will be chosen that lead to values for %p__%k_(/\\ae/) and %p__%k_(/\\ep/) that make the observations in the table " "most likely.") NORMAL ("Praat will create an object of type #LogisticRegression in the list. " "When you then click the #Info button, Praat will write the values of %\\al (the %intercept), " "%%\\be__F1_% and %%\\be__dur_% into the Info window.") NORMAL ("The number of independent variables does not have to be 2; it can be 1 or more. " "The number of dependent categories is always 2, and they should always be put in the last two columns of the table. " "This will be made more flexible in a future version of Praat.") MAN_END } /* End of file manual_statistics.c */