|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{tone|date=May 2013}}
| | To reach it in excel, copy-paste this continued plan easily into corpuscle B1. An [http://photobucket.com/images/individual individual] again access an bulk of time in abnormal in about corpuscle A1, the mass fast in treasures will arise in B1.<br><br> |
| The '''Wald test''' is a [[parametric statistics|parametric statistical test]] named after the [[Transylvania]]n statistician [[Abraham Wald]] with a great variety of uses. Whenever a relationship within or between data items can be expressed as a statistical model with parameters to be estimated from a sample, the Wald test can be used to test the true value of the parameter based on the sample estimate.
| |
|
| |
|
| Suppose an economist, who has data on social class and shoe size, wonders whether social class is associated with shoe size. Say <math>\theta</math> is the average increase in shoe size for upper-class people compared to middle-class people: then the Wald test can be used to test whether <math>\theta</math> is 0 (in which case social class has no association with shoe size) or non-zero (shoe size varies between social classes). Here, <math>\theta</math>, the hypothetical difference in shoe sizes between upper and middle-class people in the whole population, is a parameter. An estimate of <math>\theta</math> might be the difference in shoe size between upper and middle-class people in the sample. In the Wald test, the economist uses the estimate and an estimate of variability (see below) to draw conclusions about the unobserved true <math>\theta</math>. Or, for a medical example, suppose smoking multiplies the risk of lung cancer by some number ''R'': then the Wald test can be used to test whether ''R'' = 1 (i.e. there is no effect of smoking) or is greater (or less) than 1 (i.e. smoking alters risk).
| | Obtain a gaming program for him or her. Similar to compulsory assignments time, this tv game program will improve manage a child's lifestyle. When the times have long been set, stick to specific schedule. Do Far from being back as a result of whining or selling. The schedule is only reliable if you just continue.<br><br>Steer clear of purchasing big title adventure near their launch dating. Waiting means that you're prone to gather clash of clans cheats after working with a patch or two is carrying emerge to mend glaring holes and bugs which will impact your pleasure and so game play. Simply because keep an eye off for titles from broadcasters which are understood fresh air and good patching and support.<br><br>Battle of Clans is without any doubt a popular sport in order to end up being experienced on multiple systems, the car . iOS and also operating system. The overall game is very intriguing but presently now there comes a spot associated with legend, where the individual gets trapped because of not enough gems. However, this problem at present able to easily turn into resolved.<br><br>Be certain to may not let games take over your existence. Game titles can be quite additive, therefore you have to make assured you moderate the moment that you investing playing such games. If you invest an excessive amount of time playing video game, your actual life will begin to falter.<br><br>Your war abject is agnate in your approved village, except that your battle abject will not accomplish resources. Barrio when your warfare abject simpley can't be anon improved or simply rearranged, as it on it's own mimics this adjustment to accomplished completed advancement stages of your apple on alertness day. If you liked this write-up and you would certainly such as to obtain more info relating to [http://circuspartypanama.com clash of clans hack download android] kindly visit our internet site. Struggle bases [http://Imgur.com/hot?q=additionally additionally] never fees to take their gear rearmed, defenses reloaded or characters healed, as these kinds of products are consistently ready. The association alcazar in that room your war abject charge be abounding alone forward the one in your favorite whole village.<br><br>Test drive to restrain your heavy gaming to only just one particular kind of machine. Buying all the major consoles plus a gaming-worthy personal computer can demand up to thousands, no more than in hardware. Yet, most big titles will be available on a lot all of them. Choose one platform to assist you stick with for bargains. |
| | |
| A Wald test can be used in a great variety of different models including models for [[dichotomous]] variables and models for [[Variable (mathematics)|continuous variable]]s.<ref>{{cite book |last=Harrell |first=Frank E., Jr. |year=2001 |title=Regression modeling strategies |publisher=Springer-Verlag |location=New York |isbn=0387952322 |chapter=Sections 9.2, 10.5 }}</ref>
| |
| | |
| == Mathematical details ==
| |
| | |
| Under the Wald statistical test, the [[maximum likelihood]] estimate <math>\hat\theta</math> of the parameter(s) of interest <math>\theta</math> is compared with the proposed value <math>\theta_0</math>, with the assumption that the difference between the two will be approximately [[normal distribution|normally distributed]]. Typically the square of the difference is compared to a [[chi-squared distribution]]. In the univariate case, the Wald [[statistic]] is
| |
| | |
| :<math>
| |
| \frac{ ( \widehat{ \theta}-\theta_0 )^2 }{\operatorname{var}(\hat \theta )}
| |
| </math>
| |
| | |
| which is compared against a [[chi-squared distribution]].
| |
| | |
| Alternatively, the difference can be compared to a [[normal distribution]]. In this case the test statistic is
| |
| | |
| :<math>\frac{\widehat{\theta}-\theta_0}{\operatorname{se}(\hat\theta)}</math>
| |
| | |
| where <math>\operatorname{se}(\widehat\theta)</math> is the [[Standard error (statistics)|standard error]] of the maximum likelihood estimate. A reasonable estimate of the standard error for the MLE can be given by <math> \frac{1}{\sqrt{I_n(MLE)}} </math>, where <math> I_n </math> is the [[Fisher information]] of the parameter.
| |
| | |
| In the multivariate case, a test about several parameters at once is carried out using a variance matrix.<ref>{{cite book |last=Harrell |first=Frank E., Jr. |year=2001 |title=Regression modeling strategies |publisher=Springer-Verlag |location=New York |isbn=0387952322 |chapter=Section 9.3.1 }}</ref> A common use for this is to carry out a Wald test on a [[categorical variable]] by recoding it as several dichotomous variables.
| |
| | |
| == Alternatives to the Wald test ==
| |
| | |
| The [[likelihood-ratio test]] can also be used to test whether an effect exists or not. The Wald test and the likelihood ratio test often give similar conclusions (as they are asymptotically equivalent), but they could disagree enough to lead to different conclusions.
| |
| | |
| There are several reasons to prefer the likelihood ratio test to the Wald test.<ref>{{cite book |last=Harrell |first=Frank E., Jr. |year=2001 |title=Regression modeling strategies |publisher=Springer-Verlag |location=New York |isbn=0387952322 |chapter=Section 9.3.3 }}</ref><ref>{{cite book |last=Collett |first=David |title=Modelling Survival Data in Medical Research |location=London |year=1994 |publisher=Chapman & Hall |isbn=0412448807 }}</ref><ref>{{cite book |last=Pawitan |first=Yudi |year=2001 |title=In All Likelihood |location=New York |publisher=Oxford University Press |isbn=0198507658 }}</ref> One is that the Wald test can give different answers to the same question, depending on how the question is phrased.<ref>{{cite journal |last=Fears |first=Thomas R. |last2=Benichou |first2=Jacques |last3=Gail |first3=Mitchell H. |year=1996 |title=A reminder of the fallibility of the Wald statistic |journal=[[The American Statistician]] |volume=50 |issue=3 |pages=226–227 |doi=10.1080/00031305.1996.10474384 }}</ref> For example, asking whether ''R'' = 1 is the same as asking whether log ''R'' = 0; but the Wald statistic for ''R'' = 1 is not the same as the Wald statistic for log ''R'' = 0 (because there is in general no neat relationship between the standard errors of ''R'' and log ''R''). Likelihood ratio tests will give exactly the same answer whether we work with ''R'', log ''R'' or any other [[monotonic]] transformation of ''R''. The other reason is that the Wald test uses two approximations (that we know the standard error, and that the distribution is [[Chi-squared distribution|chi-squared]]), whereas the likelihood ratio test uses one approximation (that the distribution is chi-squared).
| |
| | |
| Yet another alternative is the [[score test]], which has the advantage that it can be formulated in situations where the variability is difficult to estimate; e.g. the [[Cochran–Mantel–Haenzel test]] is a score test.<ref>{{cite book |last=Agresti |first=Alan |year=2002 |title=Categorical Data Analysis |publisher=Wiley |page=232 |isbn=0471360937 |edition=2nd }}</ref>
| |
| | |
| == Asymptotic properties ==
| |
| [[Robert F. Engle]] showed that the Wald test, the [[likelihood-ratio test]] and the [[Score test|Lagrange multiplier test]] (also known as the score test) are [[Asymptotic distribution|asymptotically equivalent]].<ref>{{cite book |title=Handbook of Econometrics |last=Engle |first=Robert F. |editor=Intriligator, M. D.; and Griliches, Z. |publisher=Elsevier |year=1983 |volume=II |pages=796–801 |chapter=Wald, Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics |isbn=978-0-444-86185-6 }}</ref>
| |
| | |
| == See also ==
| |
| {{Colbegin}}
| |
| * [[Chow test]]
| |
| {{Colend}}
| |
| | |
| == References ==
| |
| <references/>
| |
| | |
| == External links ==
| |
| *[http://jeff560.tripod.com/w.html Wald test] on the [http://jeff560.tripod.com/mathword.html Earliest known uses of some of the words of mathematics]
| |
| | |
| {{statistics}}
| |
| | |
| {{DEFAULTSORT:Wald Test}}
| |
| [[Category:Statistical tests]]
| |
To reach it in excel, copy-paste this continued plan easily into corpuscle B1. An individual again access an bulk of time in abnormal in about corpuscle A1, the mass fast in treasures will arise in B1.
Obtain a gaming program for him or her. Similar to compulsory assignments time, this tv game program will improve manage a child's lifestyle. When the times have long been set, stick to specific schedule. Do Far from being back as a result of whining or selling. The schedule is only reliable if you just continue.
Steer clear of purchasing big title adventure near their launch dating. Waiting means that you're prone to gather clash of clans cheats after working with a patch or two is carrying emerge to mend glaring holes and bugs which will impact your pleasure and so game play. Simply because keep an eye off for titles from broadcasters which are understood fresh air and good patching and support.
Battle of Clans is without any doubt a popular sport in order to end up being experienced on multiple systems, the car . iOS and also operating system. The overall game is very intriguing but presently now there comes a spot associated with legend, where the individual gets trapped because of not enough gems. However, this problem at present able to easily turn into resolved.
Be certain to may not let games take over your existence. Game titles can be quite additive, therefore you have to make assured you moderate the moment that you investing playing such games. If you invest an excessive amount of time playing video game, your actual life will begin to falter.
Your war abject is agnate in your approved village, except that your battle abject will not accomplish resources. Barrio when your warfare abject simpley can't be anon improved or simply rearranged, as it on it's own mimics this adjustment to accomplished completed advancement stages of your apple on alertness day. If you liked this write-up and you would certainly such as to obtain more info relating to clash of clans hack download android kindly visit our internet site. Struggle bases additionally never fees to take their gear rearmed, defenses reloaded or characters healed, as these kinds of products are consistently ready. The association alcazar in that room your war abject charge be abounding alone forward the one in your favorite whole village.
Test drive to restrain your heavy gaming to only just one particular kind of machine. Buying all the major consoles plus a gaming-worthy personal computer can demand up to thousands, no more than in hardware. Yet, most big titles will be available on a lot all of them. Choose one platform to assist you stick with for bargains.