Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

From |
Nahla Betelmal <nahlaib@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: sign test output |

Date |
Fri, 18 Jan 2013 12:34:42 +0000 |

Dear Paul, Thank you for your kind feedback. Briefly I am looking if firms manage earnings upwardly via discretionary accruals prior certain event. The literature suggests that the discretionary accruals (DA) should be positive (i.e.. greater than zero). In order to calculate DA for my sample (346 firms), I must first perform a cross sectional regression on the whole population available from the database (thousands firms). Then generate the estimated (normal level of accrual) substitute the coefficient values generated into my sample' variables. Finally subtract the normal from the actual (reported level) to get DA (abnormal level) of accruals. Again According to the literature DA should be positive. So, I performed t-test on DA to see if there is sufficient evidence that mean DA >0, but as you can see the test shows that there is no sufficient evidence. ttest wDA_T_1== 0 One-sample t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- wDA_T_1 | 346 -.0137077 .0645203 1.200146 -.1406103 .1131949 ------------------------------------------------------------------------------ mean = mean(wDA_T_1) t = -0.2125 Ho: mean = 0 degrees of freedom = 345 Ha: mean < 0 Ha: mean != 0 Ha: mean > 0 Pr(T < t) = 0.4159 Pr(|T| > |t|) = 0.8319 Pr(T > t) = 0.5841 On the other hand when I performed the non-parametric sign test on DA, the test shows that there is sufficient evidence that median DA >0 signtest wDA_T_1= 0 sign | observed expected -------------+------------------------ positive | 221 173 negative | 125 173 zero | 0 0 -------------+------------------------ all | 346 346 One-sided tests: Ho: median of wDA_T_1 = 0 vs. Ha: median of wDA_T_1 > 0 Pr(#positive >= 221) = Binomial(n = 346, x >= 221, p = 0.5) = 0.0000 Ho: median of wDA_T_1 = 0 vs. Ha: median of wDA_T_1 < 0 Pr(#negative >= 125) = Binomial(n = 346, x >= 125, p = 0.5) = 1.0000 Two-sided test: Ho: median of wDA_T_1 = 0 vs. Ha: median of wDA_T_1 != 0 Pr(#positive >= 221 or #negative >= 221) = min(1, 2*Binomial(n = 346, x >= 221, p = 0.5)) = 0.0000 I got the same conclusion even after I winsorized DA, Also, the normality test show rejection of normality both before and after I winsorized the data Skewness/Kurtosis tests for Normality ------- joint ------ Variable | Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 -------------+--------------------------------------------------------------- wDA_T_1 | 346 0.000 0.000 . 0.0000 Shapiro-Wilk W test for normal data Variable | Obs W V z Prob>z -------------+-------------------------------------------------- wDA_T_1 | 346 0.41873 140.579 11.689 0.00000 This is what initially made me go for the sign test instead of t-test as I first thought that if the data is not normally distributed, then use non-parametric test, but from previous discussions in statalist , no agreement on that! So, now I am confused how to interpret the results. Using the sign test: there is sufficient evidence that earnings are managed upwardly. Using the t-test: earnings are not managed at all!! and this is what I meant by irrationality in previous email. Also, As I am not using regression in my 346 firm sample, robust or bootstrapped regression would not solve the normality issue. Thank you all again, I do appreciate all the feedback and time you gave me, Nahla On 18 January 2013 10:48, Seed, Paul <paul.seed@kcl.ac.uk> wrote: > Dear Statalist, > > While the discussion of Nahla Betelmal's query has been interesting and > informative, one point seems to have been missed: the question is ill-defined. > > It appears that Nahla Betelmal has a variable that she wants/expects > for good theoretical reasons to have an average of 0; and wants to test > if this is true. We are not told any more. > > If (s)he came to me for statistical advice, I would instantly want to know > - what the theoretical reasons were > - which average (the mean or the median) was expected to be 0 > - how large a tolerance was acceptable > - what the implications would be if the average was not 0. > Until I had a clear understanding, I would not want start analysing data. > > The second question is crucial. For a seriously non-normal distribution, > the mean and the median can be quite different, and it is possible > to construct examples where the mean is significantly > 0, while > the median is significantly < 0. > > Normality checks would be mainly graphical, for the reasons discussed; > but I might look at measures of skewness, kurtosis and in particular compare > whether the mean and median were sufficiently close for it not to matter which > I used. (Estimates of the mean are usually more robust, so with low skew and > mean close to median, I might prefer to use the mean even if the median were > the main object of interest.) > > Assuming interest was in the mean, I would advise one or more of > one-sample t-test (quick simple, and usually sufficient) > linear regression with robust standard errors (a basic correction for non-Normality) > bootstrapped linear regression with BCa confidence intervals, (a fuller correction, > that can give asymmetrical CI where appropriate, e.g. in cases of extreme non-Normality). > > All methods are well described in the Stata manual, and usually give very similar answers > (except for extreme cases of non-Normality). > > If interest was in the median, and I didn't trust the Normal approximation, > I would use the -centile- command with the -cci- option to get a confidence interval > for the median. > > In each case I would direct attention to the confidence interval, and to the question of whether > the answer was sufficiently close to 0 (As defined by the third question.) > > All this assumes that the ultimate interest is in the answer to this question. > If it was just a preliminary to another analysis, or the answer was wanted for > some deduction that could be made from it, I would also look for other > ways of addressing the real question, whatever it might be. > > On Jan 17, 2013, at 5:13, Nahla Betelmal <nahlaib@gmail.com> wrote: > >> Again, thank you both for your comments. >> >> However, if normality test is proved to be useful only for huge sample >> as Maarten mentioned. How can we determine which test (i.e. parametric >> or non-parametric ) to be used for smaller sample size in hundreds?! >> >> I personally think it is irrational to run both t-test and sign test >> on the same sample and hope they both produce the same conclusion! and >> what if they don't! >> >> I will follow Nick's advise to look deeper in the data, but I still >> believe that there must be another way to give obvious solution to >> this situation. >> >> Thank you both again, I highly appreciate your kind help and time, >> >> Nahla >> >> > > > Paul T Seed, Senior Lecturer in Medical Statistics, > Division of Women's Health, King's College London > Women's Health Academic Centre, King's Health Partners > (+44) (0) 20 7188 3642. > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: sign test output***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: sign test output***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: sign test output***From:*Maarten Buis <maartenlbuis@gmail.com>

**References**:**Re: st: sign test output***From:*"Seed, Paul" <paul.seed@kcl.ac.uk>

- Prev by Date:
**Re: st: sign test output** - Next by Date:
**Re: st: sign test output** - Previous by thread:
**Re: st: sign test output** - Next by thread:
**Re: st: sign test output** - Index(es):