Knowledge

Standard score

Source 📝

4589: 1735: 47: 1014:
predictor variables in the model 
 The magnitudes of the standardized regression coefficients are affected not only by the presence of correlations among the predictor variables but also by the spacings of the observations on each of these variables. Sometimes these spacings may be quite arbitrary. Hence, it is ordinarily not wise to interpret the magnitudes of standardized regression coefficients as reflecting the comparative importance of the predictor variables."
756: 816: 4575: 1448: 4613: 1010:"The standardized regression slope is the slope in the regression equation if X and Y are standardized 
 Standardization of X and Y is done by subtracting the respective means from each set of observations and dividing by the respective standard deviations 
 In multiple regression, where several X variables are used, the standardized regression coefficients quantify the relative contribution of each X variable." 4601: 1730:{\displaystyle {\begin{array}{l}\operatorname {Var} \left(\sum x_{i}\right)=\sum \operatorname {Var} (x_{i})=n\operatorname {Var} (x_{i})=n\sigma ^{2}\\\operatorname {Var} ({\overline {X}})=\operatorname {Var} \left({\frac {\sum x_{i}}{n}}\right)={\frac {1}{n^{2}}}\operatorname {Var} \left(\sum x_{i}\right)={\frac {n\sigma ^{2}}{n^{2}}}={\frac {\sigma ^{2}}{n}}\end{array}}} 987:"For some multivariate techniques such as multidimensional scaling and cluster analysis, the concept of distance between the units in the data is often of considerable interest and importance
 When the variables in a multivariate data set are on different scales, it makes more sense to calculate the distances after some form of standardization." 1013:
However, Kutner et al. (p 278) give the following caveat: "
 one must be cautious about interpreting any regression coefficients, whether standardized or not. The reason is that when the predictor variables are correlated among themselves, 
 the regression coefficients are affected by the other
387:
Though it should always be stated, the distinction between use of the population and sample statistics often is not made. In either case, the numerator and denominator of the equations have the same units of measure so that the units cancel out through division and
265:
using this formula requires use of the population mean and the population standard deviation, not the sample mean or sample deviation. However, knowing the true mean and standard deviation of a population is often an unrealistic expectation, except in cases such as
775:
high school tests. The table shows the mean and standard deviation for total scores on the SAT and ACT. Suppose that student A scored 1800 on the SAT, and student B scored 24 on the ACT. Which student performed better relative to other test-takers?
612: 1435: 893: 273:
When the population mean and the population standard deviation are unknown, the standard score may be estimated by using the sample mean and sample standard deviation as estimates of the population values.
1133: 963: 1335: 1199: 1770:
In bone density measurements, the T-score is the standard score of the measurement compared to the population of healthy 30-year-old adults, and has the usual mean of 0 and standard deviation of 1.
672: 737: 332: 216: 514: 1255: 767:
When scores are measured on different scales, they may be converted to z-scores to aid comparison. Dietz et al. give the following example, comparing student scores on the (old)
1076: 367: 533: 461: 89:
value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.
419:
for a population whose parameters are known, rather than estimated. As it is very unusual to know the entire population, the t-test is much more widely used.
979:(which is approximately correct), then the z-scores may be used to calculate the percentage of test-takers who received lower scores than students A and B. 823:
score for Student B was 0.6, meaning Student B was 0.6 standard deviation above the mean. Thus, Student B performed in the 72.57 percentile on the SAT.
1346: 151:
Computing a z-score requires knowledge of the mean and standard deviation of the complete population to which a data point belongs; if one only has a
995:
In principal components analysis, "Variables measured on different scales or on a common scale with widely differing ranges are often standardized."
763:
score for Student A was 1, meaning Student A was 1 standard deviation above the mean. Thus, Student A performed in the 84.13 percentile on the SAT.
3710: 4215: 4365: 3989: 2630: 830: 967:
Because student A has a higher z-score than student B, student A performed better compared to other test-takers than did student B.
3763: 1084: 155:
of observations from the population, then the analogous computation using the sample mean and sample standard deviation yields the
900: 4202: 1267: 1140: 747:
In process control applications, the Z value provides an assessment of the degree to which a process is operating off-target.
2256: 2199: 2172: 2145: 1915: 1835: 2625: 2325: 1767:
in Japanese, where the concept is much more widely known and used in the context of high school and university admissions.
3229: 2377: 623: 2119: 2095: 2056: 1987: 1963: 1939: 683: 4012: 3904: 2282: 2014: 1890: 267: 4617: 4190: 4064: 1761:
is a standard score Z shifted and scaled to have a mean of 50 and a standard deviation of 10. It is also known as
4248: 3909: 3654: 3025: 2615: 2215: 998: 124:; the two terms may be used interchangeably, as they are in this article. Other equivalent terms in use include 4299: 3511: 3318: 3207: 3165: 3239: 287: 180: 4542: 3501: 2404: 1852: 469: 17: 975:
Continuing the example of ACT and SAT scores, if it can be further assumed that both ACT and SAT scores are
4093: 4042: 4027: 4017: 3886: 3758: 3725: 3551: 3506: 3336: 1004: 1211: 4639: 4605: 4437: 4238: 4162: 3463: 3217: 2886: 2350: 2164:
Essentials of Testing and Assessment: A Practical Guide for Counselors, Social Workers, and Psychologists
1049: 4322: 4294: 4289: 4037: 3796: 3702: 3682: 3590: 3301: 3119: 2602: 2474: 1789: 1023: 110: 4054: 3822: 3543: 3468: 3397: 3326: 3246: 3234: 3104: 3092: 3085: 2793: 2514: 4537: 4304: 4167: 3852: 3817: 3781: 3566: 3008: 2917: 2876: 2788: 2479: 2318: 40: 607:{\displaystyle P\left({\frac {L-\mu }{\sigma }}<Z<{\frac {U-\mu }{\sigma }}\right)=\gamma .} 4446: 4059: 3999: 3936: 3574: 3558: 3296: 3158: 3148: 2998: 2912: 1799: 1029: 343: 4484: 4414: 4207: 4144: 3899: 3786: 2783: 2680: 2587: 2466: 2365: 393: 97: 2189: 2162: 4509: 4451: 4394: 4220: 4113: 4022: 3748: 3632: 3491: 3483: 3373: 3365: 3180: 3076: 3054: 3013: 2978: 2945: 2891: 2866: 2821: 2760: 2720: 2522: 2345: 2135: 999:
Relative importance of variables in multiple regression: standardized regression coefficients
446: 4432: 4007: 3956: 3932: 3894: 3812: 3791: 3743: 3622: 3600: 3569: 3478: 3355: 3306: 3224: 3197: 3153: 3109: 2871: 2647: 2527: 2031: 1804: 1784: 100:
standard deviation. This process of converting a raw score into a standard score is called
8: 4579: 4504: 4427: 4108: 3872: 3865: 3827: 3735: 3715: 3687: 3420: 3286: 3281: 3271: 3263: 3081: 3042: 2932: 2922: 2831: 2610: 2566: 2484: 2409: 2311: 976: 428: 416: 152: 145: 51: 4593: 4404: 4258: 4154: 4103: 3979: 3876: 3860: 3837: 3614: 3348: 3331: 3291: 3202: 3097: 3059: 3030: 2990: 2950: 2896: 2813: 2499: 2494: 1763: 1079: 380: 239: 78: 55: 4588: 4499: 4469: 4461: 4281: 4272: 4197: 4128: 3984: 3969: 3944: 3832: 3773: 3639: 3627: 3253: 3170: 3114: 3037: 2881: 2803: 2582: 2456: 2278: 2252: 2195: 2168: 2141: 2115: 2091: 2052: 2010: 1983: 1959: 1935: 1911: 1886: 1831: 415:
The z-score is often used in the z-test in standardized testing – the analog of the
4524: 4479: 4243: 4230: 4123: 4098: 4032: 3964: 3842: 3450: 3343: 3276: 3189: 3136: 2955: 2826: 2620: 2504: 2419: 2386: 1860: 4441: 4185: 4047: 3974: 3649: 3523: 3496: 3473: 3442: 3069: 3064: 3018: 2748: 2399: 2246: 1430:{\displaystyle Z={\frac {{\bar {X}}-\operatorname {E} }{\sigma (X)/{\sqrt {n}}}}} 1033: 750: 170:
If the population mean and population standard deviation are known, a raw score
93: 33: 3931: 1864: 4390: 4385: 2848: 2778: 2424: 2002: 1878: 1779: 1044: 1827:
2015 European School of High-Energy Physics: Bansko, Bulgaria 02 - 15 Sep 2015
1007:
is sometimes used as an aid to interpretation. (page 95) state the following.
4633: 4547: 4514: 4377: 4338: 4149: 4118: 3582: 3536: 3141: 2843: 2670: 2434: 2429: 4489: 4422: 4399: 4314: 3644: 2940: 2838: 2773: 2715: 2700: 2637: 2592: 1825: 46: 32:"Standardize" redirects here. For industrial and technical standards, see 4532: 4494: 4177: 4078: 3940: 3753: 3720: 3212: 3129: 3124: 2768: 2725: 2705: 2685: 2675: 2444: 1794: 1748: 1453: 1205: 755: 156: 1441:
Where the standardised sample mean's variance was calculated as follows:
815: 3378: 2858: 2558: 2489: 2439: 2414: 2334: 772: 258:
is negative when the raw score is below the mean, positive when above.
70: 59: 3531: 3383: 3003: 2798: 2710: 2695: 2690: 2655: 2133: 96:
from an individual raw score and then dividing the difference by the
82: 27:
How many standard deviations apart from the mean an observed datum is
1954:
Glantz, Stanton A.; Slinker, Bryan K.; Neilands, Torsten B. (2016),
431:. A prediction interval , consisting of a lower endpoint designated 3047: 2665: 2542: 2537: 2532: 2220:
NIH Osteoporosis and Related Bone Diseases National Resource Center
2160: 4552: 4253: 982: 888:{\displaystyle z={x-\mu \over \sigma }={1800-1500 \over 300}=1} 4474: 3455: 3429: 3409: 2660: 2451: 2298: 2275:
An Introduction to Mathematical Statistics and Its Applications
2086:
Afifi, Abdelmonem; May, Susanne K.; Clark, Virginia A. (2012),
2030:
Diez, David; Barr, Christopher; Çetinkaya-Rundel, Mine (2012),
410: 108:(however, "normalizing" can refer to many types of ratios; see 751:
Comparison of scores measured on different scales: ACT and SAT
85:(i.e., an observed value or data point) is above or below the 2303: 2134:
John Salvia; James Ysseldyke; Sara Witmer (29 January 2009).
2110:
Kutner, Michael; Nachtsheim, Christopher; Neter, John (204),
1128:{\displaystyle \sigma (X)={\sqrt {\operatorname {Var} (X)}}:} 970: 958:{\displaystyle z={x-\mu \over \sigma }={24-21 \over 5}=0.6} 254:
and the population mean in units of the standard deviation.
2394: 1017: 370: 229: 86: 1330:{\displaystyle {\bar {X}}={1 \over n}\sum _{i=1}^{n}X_{i}} 1830:. CERN Yellow Reports: School Proceedings. Geneva: CERN. 1194:{\displaystyle Z={X-\operatorname {E} \over \sigma (X)}} 768: 2191:
Clinical Assessment of Child and Adolescent Intelligence
2161:
Edward S. Neukrug; R. Charles Fawcett (1 January 2014).
2029: 2049:
An Introduction to Applied Multivariate Analysis with R
1956:
Primer of Applied Regression & Analysis of Variance
1953: 1451: 1349: 1270: 1214: 1143: 1087: 1052: 903: 833: 686: 626: 536: 472: 449: 427:
The standard score can be used in the calculation of
346: 290: 183: 4216:
Autoregressive conditional heteroskedasticity (ARCH)
2109: 2103: 1824:Mulders, Martijn; Zanderighi, Giulia, eds. (2017). 3678: 2251:(illustrated ed.). Rowman & Littlefield. 2245:Carroll, Susan Rovezzi; Carroll, David J. (2002). 2064: 2040: 1982:(First ed.), Chapman & Hall / CRC Press, 1980:Foundational and Applied Statistics for Biologists 1899: 1747:"T-score" redirects here. Not to be confused with 1729: 1429: 1329: 1249: 1204:If the random variable under consideration is the 1193: 1127: 1070: 957: 887: 731: 667:{\displaystyle P\left(-z<Z<z\right)=\gamma } 666: 606: 508: 455: 361: 326: 210: 2187: 2079: 1929: 1823: 732:{\displaystyle L=\mu -z\sigma ,\ U=\mu +z\sigma } 4631: 1947: 990: 439:, is an interval such that a future observation 3764:Multivariate adaptive regression splines (MARS) 1905: 443:will lie in the interval with high probability 250:represents the distance between that raw score 50:Comparison of the various grading methods in a 2244: 2216:"Bone Mass Measurement: What the Numbers Mean" 2137:Assessment: In Special and Inclusive Education 2070: 2046: 2009:(Fourth ed.). Wiley. p. 880, eq. 6. 1906:Spiegel, Murray R.; Stephens, Larry J (2008), 1885:(Fourth ed.). Wiley. p. 880, eq. 5. 1853:"Practical Statistics for High Energy Physics" 39:"Z-score" redirects here. For other uses, see 2319: 2085: 1923: 983:Cluster analysis and multidimensional scaling 2273:Larsen, Richard J.; Marx, Morris L. (2000). 1930:Mendenhall, William; Sincich, Terry (2007), 2071:Johnson, Richard; Wichern, Wichern (2007), 2047:Everitt, Brian; Hothorn, Torsten J (2011), 2001: 1934:(Fifth ed.), Pearson / Prentice Hall, 1932:Statistics for Engineering and the Sciences 1877: 270:, where the entire population is measured. 2364: 2326: 2312: 2272: 2090:(Fifth ed.), Chapman & Hall/CRC, 971:Percentage of observations below a z-score 2977: 2248:Statistics Made Simple for School Leaders 2073:Applied Multivariate Statistical Analysis 117:Standard scores are most commonly called 1018:Standardizing in mathematical statistics 814: 754: 617:By determining the quantile z such that 327:{\displaystyle z={x-{\bar {x}} \over S}} 211:{\displaystyle z={x-\mu \over \sigma }} 45: 2023: 1857:CERN Yellow Reports: School Proceedings 509:{\displaystyle P(L<X<U)=\gamma ,} 422: 14: 4632: 4290:Kaplan–Meier estimator (product limit) 1971: 1003:Standardization of variables prior to 174:is converted into a standard score by 4363: 3930: 3677: 2976: 2746: 2363: 2307: 1850: 4600: 4300:Accelerated failure time (AFT) model 2188:Randy W. Kamphaus (16 August 2005). 1250:{\displaystyle \ X_{1},\dots ,X_{n}} 92:It is calculated by subtracting the 4612: 3895:Analysis of variance (ANOVA, anova) 2747: 2167:. Cengage Learning. pp. 133–. 1977: 1078:and dividing the difference by its 24: 3990:Cochran–Mantel–Haenszel statistics 2616:Pearson product-moment correlation 2238: 2140:. Cengage Learning. pp. 43–. 1374: 1159: 1071:{\displaystyle \operatorname {E} } 1053: 742: 25: 4651: 2292: 1340:then the standardized version is 435:and an upper endpoint designated 4611: 4599: 4587: 4574: 4573: 4364: 2114:(Fourth ed.), McGraw Hill, 2112:Applied Linear Regression Models 2036:(Second ed.), openintro.org 2007:Advanced Engineering Mathematics 1910:(Fourth ed.), McGraw Hill, 1883:Advanced Engineering Mathematics 4249:Least-squares spectral analysis 2277:(Third ed.). p. 282. 2208: 2181: 2154: 2127: 2088:Practical Multivariate Analysis 1958:(Third ed.), McGraw Hill, 399: 3230:Mean-unbiased minimum-variance 2333: 2222:. National Institute of Health 1995: 1871: 1844: 1817: 1580: 1567: 1538: 1525: 1510: 1497: 1409: 1403: 1395: 1389: 1380: 1365: 1277: 1185: 1179: 1171: 1165: 1117: 1111: 1097: 1091: 1065: 1059: 494: 476: 353: 312: 165: 13: 1: 4543:Geographic information system 3759:Simultaneous equations models 1810: 991:Principal components analysis 897:The z-score for student B is 827:The z-score for student A is 3726:Coefficient of determination 3337:Uniformly most powerful test 1908:Schaum's Outlines Statistics 1575: 1005:multiple regression analysis 63: 7: 4295:Proportional hazards models 4239:Spectral density estimation 4221:Vector autoregression (VAR) 3655:Maximum posterior estimator 2887:Randomized controlled trial 2194:. Springer. pp. 123–. 1865:10.23730/CYRSP-2017-004.165 1851:Gross, Eilam (2017-11-06). 1773: 1757:In educational assessment, 10: 4656: 4055:Multivariate distributions 2475:Average absolute deviation 1790:Normalization (statistics) 1746: 1742: 1024:Normalization (statistics) 1021: 408: 362:{\displaystyle {\bar {x}}} 58:, cumulative percentages, 38: 31: 4569: 4523: 4460: 4413: 4376: 4372: 4359: 4331: 4313: 4280: 4271: 4229: 4176: 4137: 4086: 4077: 4043:Structural equation model 3998: 3955: 3951: 3926: 3885: 3851: 3805: 3772: 3734: 3701: 3697: 3673: 3613: 3522: 3441: 3405: 3396: 3379:Score/Lagrange multiplier 3364: 3317: 3262: 3188: 3179: 2989: 2985: 2972: 2931: 2905: 2857: 2812: 2794:Sample size determination 2759: 2755: 2742: 2646: 2601: 2575: 2557: 2513: 2465: 2385: 2376: 2372: 2359: 2341: 2075:, Pearson / Prentice Hall 404: 4538:Environmental statistics 4060:Elliptical distributions 3853:Generalized linear model 3782:Simple linear regression 3552:Hodges–Lehmann estimator 3009:Probability distribution 2918:Stochastic approximation 2480:Coefficient of variation 81:by which the value of a 41:Z-score (disambiguation) 4198:Cross-correlation (XCF) 3806:Non-standard predictors 3240:Lehmann–ScheffĂ© theorem 2913:Adaptive clinical trial 1800:Standard normal deviate 1030:mathematical statistics 519:For the standard score 456:{\displaystyle \gamma } 62:equivalents, z-scores, 4594:Mathematics portal 4415:Engineering statistics 4323:Nelson–Aalen estimator 3900:Analysis of covariance 3787:Ordinary least squares 3711:Pearson product-moment 3115:Statistical functional 3026:Empirical distribution 2859:Controlled experiments 2588:Frequency distribution 2366:Descriptive statistics 1731: 1431: 1331: 1316: 1251: 1195: 1129: 1072: 959: 889: 824: 764: 733: 668: 608: 510: 457: 394:dimensionless quantity 363: 328: 246:The absolute value of 212: 66: 4510:Population statistics 4452:System identification 4186:Autocorrelation (ACF) 4114:Exponential smoothing 4028:Discriminant analysis 4023:Canonical correlation 3887:Partition of variance 3749:Regression validation 3593:(Jonckheere–Terpstra) 3492:Likelihood-ratio test 3181:Frequentist inference 3093:Location–scale family 3014:Sampling distribution 2979:Statistical inference 2946:Cross-sectional study 2933:Observational studies 2892:Randomized experiment 2721:Stem-and-leaf display 2523:Central limit theorem 1732: 1432: 1332: 1296: 1252: 1196: 1130: 1073: 1022:Further information: 960: 890: 818: 758: 734: 669: 609: 511: 458: 364: 329: 213: 138:standardized variable 49: 4433:Probabilistic design 4018:Principal components 3861:Exponential families 3813:Nonlinear regression 3792:General linear model 3754:Mixed effects models 3744:Errors and residuals 3721:Confounding variable 3623:Bayesian probability 3601:Van der Waerden test 3591:Ordered alternative 3356:Multiple comparisons 3235:Rao–Blackwellization 3198:Estimating equations 3154:Statistical distance 2872:Factorial experiment 2405:Arithmetic-Geometric 2033:OpenIntro Statistics 1978:Aho, Ken A. (2014), 1805:Studentized residual 1785:Mahalanobis distance 1449: 1347: 1268: 1212: 1141: 1085: 1050: 977:normally distributed 901: 831: 684: 624: 534: 470: 447: 429:prediction intervals 423:Prediction intervals 344: 288: 277:In these cases, the 268:standardized testing 181: 4505:Official statistics 4428:Methods engineering 4109:Seasonal adjustment 3877:Poisson regressions 3797:Bayesian regression 3736:Regression analysis 3716:Partial correlation 3688:Regression analysis 3287:Prediction interval 3282:Likelihood interval 3272:Confidence interval 3264:Interval estimation 3225:Unbiased estimators 3043:Model specification 2923:Up-and-down designs 2611:Partial correlation 2567:Index of dispersion 2485:Interquartile range 1859:. 4/2017: 165–186. 1208:of a random sample 1043:by subtracting its 803:Standard deviation 281:-score is given by 146:high energy physics 79:standard deviations 56:standard deviations 52:normal distribution 4640:Statistical ratios 4525:Spatial statistics 4405:Medical statistics 4305:First hitting time 4259:Whittle likelihood 3910:Degrees of freedom 3905:Multivariate ANOVA 3838:Heteroscedasticity 3650:Bayesian estimator 3615:Bayesian inference 3464:Kolmogorov–Smirnov 3349:Randomization test 3319:Testing hypotheses 3292:Tolerance interval 3203:Maximum likelihood 3098:Exponential family 3031:Density estimation 2991:Statistical theory 2951:Natural experiment 2897:Scientific control 2814:Survey methodology 2500:Standard deviation 2299:z-score calculator 1727: 1725: 1427: 1327: 1247: 1191: 1125: 1080:standard deviation 1068: 955: 885: 825: 765: 729: 664: 604: 506: 453: 381:standard deviation 359: 324: 242:of the population. 240:standard deviation 232:of the population, 208: 67: 4627: 4626: 4565: 4564: 4561: 4560: 4500:National accounts 4470:Actuarial science 4462:Social statistics 4355: 4354: 4351: 4350: 4347: 4346: 4282:Survival function 4267: 4266: 4129:Granger causality 3970:Contingency table 3945:Survival analysis 3922: 3921: 3918: 3917: 3774:Linear regression 3669: 3668: 3665: 3664: 3640:Credible interval 3609: 3608: 3392: 3391: 3208:Method of moments 3077:Parametric family 3038:Statistical model 2968: 2967: 2964: 2963: 2882:Random assignment 2804:Statistical power 2738: 2737: 2734: 2733: 2583:Contingency table 2553: 2552: 2420:Generalized/power 2258:978-0-8108-4322-6 2201:978-0-387-26299-4 2174:978-1-305-16183-2 2147:978-0-547-13437-6 1917:978-0-07-148584-5 1837:978-92-9083-472-4 1721: 1701: 1640: 1616: 1578: 1425: 1422: 1392: 1368: 1294: 1280: 1217: 1189: 1120: 947: 926: 877: 856: 813: 812: 710: 588: 561: 356: 322: 315: 206: 77:is the number of 16:(Redirected from 4647: 4615: 4614: 4603: 4602: 4592: 4591: 4577: 4576: 4480:Crime statistics 4374: 4373: 4361: 4360: 4278: 4277: 4244:Fourier analysis 4231:Frequency domain 4211: 4158: 4124:Structural break 4084: 4083: 4033:Cluster analysis 3980:Log-linear model 3953: 3952: 3928: 3927: 3869: 3843:Homoscedasticity 3699: 3698: 3675: 3674: 3594: 3586: 3578: 3577:(Kruskal–Wallis) 3562: 3547: 3502:Cross validation 3487: 3469:Anderson–Darling 3416: 3403: 3402: 3374:Likelihood-ratio 3366:Parametric tests 3344:Permutation test 3327:1- & 2-tails 3218:Minimum distance 3190:Point estimation 3186: 3185: 3137:Optimal decision 3088: 2987: 2986: 2974: 2973: 2956:Quasi-experiment 2906:Adaptive designs 2757: 2756: 2744: 2743: 2621:Rank correlation 2383: 2382: 2374: 2373: 2361: 2360: 2328: 2321: 2314: 2305: 2304: 2288: 2269: 2267: 2265: 2232: 2231: 2229: 2227: 2212: 2206: 2205: 2185: 2179: 2178: 2158: 2152: 2151: 2131: 2125: 2124: 2107: 2101: 2100: 2083: 2077: 2076: 2068: 2062: 2061: 2044: 2038: 2037: 2027: 2021: 2020: 1999: 1993: 1992: 1975: 1969: 1968: 1951: 1945: 1944: 1927: 1921: 1920: 1903: 1897: 1896: 1875: 1869: 1868: 1848: 1842: 1841: 1821: 1736: 1734: 1733: 1728: 1726: 1722: 1717: 1716: 1707: 1702: 1700: 1699: 1690: 1689: 1688: 1675: 1670: 1666: 1665: 1664: 1641: 1639: 1638: 1626: 1621: 1617: 1612: 1611: 1610: 1597: 1579: 1571: 1556: 1555: 1537: 1536: 1509: 1508: 1484: 1480: 1479: 1478: 1436: 1434: 1433: 1428: 1426: 1424: 1423: 1418: 1416: 1398: 1394: 1393: 1385: 1370: 1369: 1361: 1357: 1336: 1334: 1333: 1328: 1326: 1325: 1315: 1310: 1295: 1287: 1282: 1281: 1273: 1256: 1254: 1253: 1248: 1246: 1245: 1227: 1226: 1215: 1200: 1198: 1197: 1192: 1190: 1188: 1174: 1151: 1134: 1132: 1131: 1126: 1121: 1104: 1077: 1075: 1074: 1069: 964: 962: 961: 956: 948: 943: 932: 927: 922: 911: 894: 892: 891: 886: 878: 873: 862: 857: 852: 841: 779: 778: 738: 736: 735: 730: 708: 673: 671: 670: 665: 657: 653: 613: 611: 610: 605: 594: 590: 589: 584: 573: 562: 557: 546: 515: 513: 512: 507: 462: 460: 459: 454: 417:Student's t-test 368: 366: 365: 360: 358: 357: 349: 333: 331: 330: 325: 323: 318: 317: 316: 308: 298: 217: 215: 214: 209: 207: 202: 191: 21: 4655: 4654: 4650: 4649: 4648: 4646: 4645: 4644: 4630: 4629: 4628: 4623: 4586: 4557: 4519: 4456: 4442:quality control 4409: 4391:Clinical trials 4368: 4343: 4327: 4315:Hazard function 4309: 4263: 4225: 4209: 4172: 4168:Breusch–Godfrey 4156: 4133: 4073: 4048:Factor analysis 3994: 3975:Graphical model 3947: 3914: 3881: 3867: 3847: 3801: 3768: 3730: 3693: 3692: 3661: 3605: 3592: 3584: 3576: 3560: 3545: 3524:Rank statistics 3518: 3497:Model selection 3485: 3443:Goodness of fit 3437: 3414: 3388: 3360: 3313: 3258: 3247:Median unbiased 3175: 3086: 3019:Order statistic 2981: 2960: 2927: 2901: 2853: 2808: 2751: 2749:Data collection 2730: 2642: 2597: 2571: 2549: 2509: 2461: 2378:Continuous data 2368: 2355: 2337: 2332: 2295: 2285: 2263: 2261: 2259: 2241: 2239:Further reading 2236: 2235: 2225: 2223: 2214: 2213: 2209: 2202: 2186: 2182: 2175: 2159: 2155: 2148: 2132: 2128: 2122: 2108: 2104: 2098: 2084: 2080: 2069: 2065: 2059: 2045: 2041: 2028: 2024: 2017: 2000: 1996: 1990: 1976: 1972: 1966: 1952: 1948: 1942: 1928: 1924: 1918: 1904: 1900: 1893: 1876: 1872: 1849: 1845: 1838: 1822: 1818: 1813: 1776: 1755: 1745: 1724: 1723: 1712: 1708: 1706: 1695: 1691: 1684: 1680: 1676: 1674: 1660: 1656: 1652: 1648: 1634: 1630: 1625: 1606: 1602: 1598: 1596: 1592: 1570: 1558: 1557: 1551: 1547: 1532: 1528: 1504: 1500: 1474: 1470: 1466: 1462: 1452: 1450: 1447: 1446: 1417: 1412: 1399: 1384: 1383: 1360: 1359: 1358: 1356: 1348: 1345: 1344: 1321: 1317: 1311: 1300: 1286: 1272: 1271: 1269: 1266: 1265: 1241: 1237: 1222: 1218: 1213: 1210: 1209: 1175: 1152: 1150: 1142: 1139: 1138: 1103: 1086: 1083: 1082: 1051: 1048: 1047: 1034:random variable 1026: 1020: 1001: 993: 985: 973: 933: 931: 912: 910: 902: 899: 898: 863: 861: 842: 840: 832: 829: 828: 753: 745: 743:Process control 685: 682: 681: 634: 630: 625: 622: 621: 574: 572: 547: 545: 544: 540: 535: 532: 531: 471: 468: 467: 448: 445: 444: 425: 413: 407: 402: 348: 347: 345: 342: 341: 307: 306: 299: 297: 289: 286: 285: 192: 190: 182: 179: 178: 168: 94:population mean 44: 37: 34:Standardization 28: 23: 22: 15: 12: 11: 5: 4653: 4643: 4642: 4625: 4624: 4622: 4621: 4609: 4597: 4583: 4570: 4567: 4566: 4563: 4562: 4559: 4558: 4556: 4555: 4550: 4545: 4540: 4535: 4529: 4527: 4521: 4520: 4518: 4517: 4512: 4507: 4502: 4497: 4492: 4487: 4482: 4477: 4472: 4466: 4464: 4458: 4457: 4455: 4454: 4449: 4444: 4435: 4430: 4425: 4419: 4417: 4411: 4410: 4408: 4407: 4402: 4397: 4388: 4386:Bioinformatics 4382: 4380: 4370: 4369: 4357: 4356: 4353: 4352: 4349: 4348: 4345: 4344: 4342: 4341: 4335: 4333: 4329: 4328: 4326: 4325: 4319: 4317: 4311: 4310: 4308: 4307: 4302: 4297: 4292: 4286: 4284: 4275: 4269: 4268: 4265: 4264: 4262: 4261: 4256: 4251: 4246: 4241: 4235: 4233: 4227: 4226: 4224: 4223: 4218: 4213: 4205: 4200: 4195: 4194: 4193: 4191:partial (PACF) 4182: 4180: 4174: 4173: 4171: 4170: 4165: 4160: 4152: 4147: 4141: 4139: 4138:Specific tests 4135: 4134: 4132: 4131: 4126: 4121: 4116: 4111: 4106: 4101: 4096: 4090: 4088: 4081: 4075: 4074: 4072: 4071: 4070: 4069: 4068: 4067: 4052: 4051: 4050: 4040: 4038:Classification 4035: 4030: 4025: 4020: 4015: 4010: 4004: 4002: 3996: 3995: 3993: 3992: 3987: 3985:McNemar's test 3982: 3977: 3972: 3967: 3961: 3959: 3949: 3948: 3924: 3923: 3920: 3919: 3916: 3915: 3913: 3912: 3907: 3902: 3897: 3891: 3889: 3883: 3882: 3880: 3879: 3863: 3857: 3855: 3849: 3848: 3846: 3845: 3840: 3835: 3830: 3825: 3823:Semiparametric 3820: 3815: 3809: 3807: 3803: 3802: 3800: 3799: 3794: 3789: 3784: 3778: 3776: 3770: 3769: 3767: 3766: 3761: 3756: 3751: 3746: 3740: 3738: 3732: 3731: 3729: 3728: 3723: 3718: 3713: 3707: 3705: 3695: 3694: 3691: 3690: 3685: 3679: 3671: 3670: 3667: 3666: 3663: 3662: 3660: 3659: 3658: 3657: 3647: 3642: 3637: 3636: 3635: 3630: 3619: 3617: 3611: 3610: 3607: 3606: 3604: 3603: 3598: 3597: 3596: 3588: 3580: 3564: 3561:(Mann–Whitney) 3556: 3555: 3554: 3541: 3540: 3539: 3528: 3526: 3520: 3519: 3517: 3516: 3515: 3514: 3509: 3504: 3494: 3489: 3486:(Shapiro–Wilk) 3481: 3476: 3471: 3466: 3461: 3453: 3447: 3445: 3439: 3438: 3436: 3435: 3427: 3418: 3406: 3400: 3398:Specific tests 3394: 3393: 3390: 3389: 3387: 3386: 3381: 3376: 3370: 3368: 3362: 3361: 3359: 3358: 3353: 3352: 3351: 3341: 3340: 3339: 3329: 3323: 3321: 3315: 3314: 3312: 3311: 3310: 3309: 3304: 3294: 3289: 3284: 3279: 3274: 3268: 3266: 3260: 3259: 3257: 3256: 3251: 3250: 3249: 3244: 3243: 3242: 3237: 3222: 3221: 3220: 3215: 3210: 3205: 3194: 3192: 3183: 3177: 3176: 3174: 3173: 3168: 3163: 3162: 3161: 3151: 3146: 3145: 3144: 3134: 3133: 3132: 3127: 3122: 3112: 3107: 3102: 3101: 3100: 3095: 3090: 3074: 3073: 3072: 3067: 3062: 3052: 3051: 3050: 3045: 3035: 3034: 3033: 3023: 3022: 3021: 3011: 3006: 3001: 2995: 2993: 2983: 2982: 2970: 2969: 2966: 2965: 2962: 2961: 2959: 2958: 2953: 2948: 2943: 2937: 2935: 2929: 2928: 2926: 2925: 2920: 2915: 2909: 2907: 2903: 2902: 2900: 2899: 2894: 2889: 2884: 2879: 2874: 2869: 2863: 2861: 2855: 2854: 2852: 2851: 2849:Standard error 2846: 2841: 2836: 2835: 2834: 2829: 2818: 2816: 2810: 2809: 2807: 2806: 2801: 2796: 2791: 2786: 2781: 2779:Optimal design 2776: 2771: 2765: 2763: 2753: 2752: 2740: 2739: 2736: 2735: 2732: 2731: 2729: 2728: 2723: 2718: 2713: 2708: 2703: 2698: 2693: 2688: 2683: 2678: 2673: 2668: 2663: 2658: 2652: 2650: 2644: 2643: 2641: 2640: 2635: 2634: 2633: 2628: 2618: 2613: 2607: 2605: 2599: 2598: 2596: 2595: 2590: 2585: 2579: 2577: 2576:Summary tables 2573: 2572: 2570: 2569: 2563: 2561: 2555: 2554: 2551: 2550: 2548: 2547: 2546: 2545: 2540: 2535: 2525: 2519: 2517: 2511: 2510: 2508: 2507: 2502: 2497: 2492: 2487: 2482: 2477: 2471: 2469: 2463: 2462: 2460: 2459: 2454: 2449: 2448: 2447: 2442: 2437: 2432: 2427: 2422: 2417: 2412: 2410:Contraharmonic 2407: 2402: 2391: 2389: 2380: 2370: 2369: 2357: 2356: 2354: 2353: 2348: 2342: 2339: 2338: 2331: 2330: 2323: 2316: 2308: 2302: 2301: 2294: 2293:External links 2291: 2290: 2289: 2283: 2270: 2257: 2240: 2237: 2234: 2233: 2207: 2200: 2180: 2173: 2153: 2146: 2126: 2121:978-0073014661 2120: 2102: 2097:978-1439816806 2096: 2078: 2063: 2058:978-1441996497 2057: 2039: 2022: 2015: 1994: 1989:978-1439873380 1988: 1970: 1965:978-0071824118 1964: 1946: 1941:978-0131877061 1940: 1922: 1916: 1898: 1891: 1870: 1843: 1836: 1815: 1814: 1812: 1809: 1808: 1807: 1802: 1797: 1792: 1787: 1782: 1780:Error function 1775: 1772: 1744: 1741: 1740: 1739: 1737: 1720: 1715: 1711: 1705: 1698: 1694: 1687: 1683: 1679: 1673: 1669: 1663: 1659: 1655: 1651: 1647: 1644: 1637: 1633: 1629: 1624: 1620: 1615: 1609: 1605: 1601: 1595: 1591: 1588: 1585: 1582: 1577: 1574: 1569: 1566: 1563: 1560: 1559: 1554: 1550: 1546: 1543: 1540: 1535: 1531: 1527: 1524: 1521: 1518: 1515: 1512: 1507: 1503: 1499: 1496: 1493: 1490: 1487: 1483: 1477: 1473: 1469: 1465: 1461: 1458: 1455: 1454: 1444: 1442: 1439: 1437: 1421: 1415: 1411: 1408: 1405: 1402: 1397: 1391: 1388: 1382: 1379: 1376: 1373: 1367: 1364: 1355: 1352: 1338: 1337: 1324: 1320: 1314: 1309: 1306: 1303: 1299: 1293: 1290: 1285: 1279: 1276: 1244: 1240: 1236: 1233: 1230: 1225: 1221: 1202: 1201: 1187: 1184: 1181: 1178: 1173: 1170: 1167: 1164: 1161: 1158: 1155: 1149: 1146: 1124: 1119: 1116: 1113: 1110: 1107: 1102: 1099: 1096: 1093: 1090: 1067: 1064: 1061: 1058: 1055: 1045:expected value 1019: 1016: 1000: 997: 992: 989: 984: 981: 972: 969: 954: 951: 946: 942: 939: 936: 930: 925: 921: 918: 915: 909: 906: 884: 881: 876: 872: 869: 866: 860: 855: 851: 848: 845: 839: 836: 811: 810: 807: 804: 800: 799: 796: 793: 789: 788: 785: 782: 752: 749: 744: 741: 740: 739: 728: 725: 722: 719: 716: 713: 707: 704: 701: 698: 695: 692: 689: 675: 674: 663: 660: 656: 652: 649: 646: 643: 640: 637: 633: 629: 615: 614: 603: 600: 597: 593: 587: 583: 580: 577: 571: 568: 565: 560: 556: 553: 550: 543: 539: 517: 516: 505: 502: 499: 496: 493: 490: 487: 484: 481: 478: 475: 452: 424: 421: 409:Main article: 406: 403: 401: 398: 385: 384: 383:of the sample. 374: 373:of the sample, 355: 352: 335: 334: 321: 314: 311: 305: 302: 296: 293: 244: 243: 233: 219: 218: 205: 201: 198: 195: 189: 186: 167: 164: 75:standard score 26: 9: 6: 4: 3: 2: 4652: 4641: 4638: 4637: 4635: 4620: 4619: 4610: 4608: 4607: 4598: 4596: 4595: 4590: 4584: 4582: 4581: 4572: 4571: 4568: 4554: 4551: 4549: 4548:Geostatistics 4546: 4544: 4541: 4539: 4536: 4534: 4531: 4530: 4528: 4526: 4522: 4516: 4515:Psychometrics 4513: 4511: 4508: 4506: 4503: 4501: 4498: 4496: 4493: 4491: 4488: 4486: 4483: 4481: 4478: 4476: 4473: 4471: 4468: 4467: 4465: 4463: 4459: 4453: 4450: 4448: 4445: 4443: 4439: 4436: 4434: 4431: 4429: 4426: 4424: 4421: 4420: 4418: 4416: 4412: 4406: 4403: 4401: 4398: 4396: 4392: 4389: 4387: 4384: 4383: 4381: 4379: 4378:Biostatistics 4375: 4371: 4367: 4362: 4358: 4340: 4339:Log-rank test 4337: 4336: 4334: 4330: 4324: 4321: 4320: 4318: 4316: 4312: 4306: 4303: 4301: 4298: 4296: 4293: 4291: 4288: 4287: 4285: 4283: 4279: 4276: 4274: 4270: 4260: 4257: 4255: 4252: 4250: 4247: 4245: 4242: 4240: 4237: 4236: 4234: 4232: 4228: 4222: 4219: 4217: 4214: 4212: 4210:(Box–Jenkins) 4206: 4204: 4201: 4199: 4196: 4192: 4189: 4188: 4187: 4184: 4183: 4181: 4179: 4175: 4169: 4166: 4164: 4163:Durbin–Watson 4161: 4159: 4153: 4151: 4148: 4146: 4145:Dickey–Fuller 4143: 4142: 4140: 4136: 4130: 4127: 4125: 4122: 4120: 4119:Cointegration 4117: 4115: 4112: 4110: 4107: 4105: 4102: 4100: 4097: 4095: 4094:Decomposition 4092: 4091: 4089: 4085: 4082: 4080: 4076: 4066: 4063: 4062: 4061: 4058: 4057: 4056: 4053: 4049: 4046: 4045: 4044: 4041: 4039: 4036: 4034: 4031: 4029: 4026: 4024: 4021: 4019: 4016: 4014: 4011: 4009: 4006: 4005: 4003: 4001: 3997: 3991: 3988: 3986: 3983: 3981: 3978: 3976: 3973: 3971: 3968: 3966: 3965:Cohen's kappa 3963: 3962: 3960: 3958: 3954: 3950: 3946: 3942: 3938: 3934: 3929: 3925: 3911: 3908: 3906: 3903: 3901: 3898: 3896: 3893: 3892: 3890: 3888: 3884: 3878: 3874: 3870: 3864: 3862: 3859: 3858: 3856: 3854: 3850: 3844: 3841: 3839: 3836: 3834: 3831: 3829: 3826: 3824: 3821: 3819: 3818:Nonparametric 3816: 3814: 3811: 3810: 3808: 3804: 3798: 3795: 3793: 3790: 3788: 3785: 3783: 3780: 3779: 3777: 3775: 3771: 3765: 3762: 3760: 3757: 3755: 3752: 3750: 3747: 3745: 3742: 3741: 3739: 3737: 3733: 3727: 3724: 3722: 3719: 3717: 3714: 3712: 3709: 3708: 3706: 3704: 3700: 3696: 3689: 3686: 3684: 3681: 3680: 3676: 3672: 3656: 3653: 3652: 3651: 3648: 3646: 3643: 3641: 3638: 3634: 3631: 3629: 3626: 3625: 3624: 3621: 3620: 3618: 3616: 3612: 3602: 3599: 3595: 3589: 3587: 3581: 3579: 3573: 3572: 3571: 3568: 3567:Nonparametric 3565: 3563: 3557: 3553: 3550: 3549: 3548: 3542: 3538: 3537:Sample median 3535: 3534: 3533: 3530: 3529: 3527: 3525: 3521: 3513: 3510: 3508: 3505: 3503: 3500: 3499: 3498: 3495: 3493: 3490: 3488: 3482: 3480: 3477: 3475: 3472: 3470: 3467: 3465: 3462: 3460: 3458: 3454: 3452: 3449: 3448: 3446: 3444: 3440: 3434: 3432: 3428: 3426: 3424: 3419: 3417: 3412: 3408: 3407: 3404: 3401: 3399: 3395: 3385: 3382: 3380: 3377: 3375: 3372: 3371: 3369: 3367: 3363: 3357: 3354: 3350: 3347: 3346: 3345: 3342: 3338: 3335: 3334: 3333: 3330: 3328: 3325: 3324: 3322: 3320: 3316: 3308: 3305: 3303: 3300: 3299: 3298: 3295: 3293: 3290: 3288: 3285: 3283: 3280: 3278: 3275: 3273: 3270: 3269: 3267: 3265: 3261: 3255: 3252: 3248: 3245: 3241: 3238: 3236: 3233: 3232: 3231: 3228: 3227: 3226: 3223: 3219: 3216: 3214: 3211: 3209: 3206: 3204: 3201: 3200: 3199: 3196: 3195: 3193: 3191: 3187: 3184: 3182: 3178: 3172: 3169: 3167: 3164: 3160: 3157: 3156: 3155: 3152: 3150: 3147: 3143: 3142:loss function 3140: 3139: 3138: 3135: 3131: 3128: 3126: 3123: 3121: 3118: 3117: 3116: 3113: 3111: 3108: 3106: 3103: 3099: 3096: 3094: 3091: 3089: 3083: 3080: 3079: 3078: 3075: 3071: 3068: 3066: 3063: 3061: 3058: 3057: 3056: 3053: 3049: 3046: 3044: 3041: 3040: 3039: 3036: 3032: 3029: 3028: 3027: 3024: 3020: 3017: 3016: 3015: 3012: 3010: 3007: 3005: 3002: 3000: 2997: 2996: 2994: 2992: 2988: 2984: 2980: 2975: 2971: 2957: 2954: 2952: 2949: 2947: 2944: 2942: 2939: 2938: 2936: 2934: 2930: 2924: 2921: 2919: 2916: 2914: 2911: 2910: 2908: 2904: 2898: 2895: 2893: 2890: 2888: 2885: 2883: 2880: 2878: 2875: 2873: 2870: 2868: 2865: 2864: 2862: 2860: 2856: 2850: 2847: 2845: 2844:Questionnaire 2842: 2840: 2837: 2833: 2830: 2828: 2825: 2824: 2823: 2820: 2819: 2817: 2815: 2811: 2805: 2802: 2800: 2797: 2795: 2792: 2790: 2787: 2785: 2782: 2780: 2777: 2775: 2772: 2770: 2767: 2766: 2764: 2762: 2758: 2754: 2750: 2745: 2741: 2727: 2724: 2722: 2719: 2717: 2714: 2712: 2709: 2707: 2704: 2702: 2699: 2697: 2694: 2692: 2689: 2687: 2684: 2682: 2679: 2677: 2674: 2672: 2671:Control chart 2669: 2667: 2664: 2662: 2659: 2657: 2654: 2653: 2651: 2649: 2645: 2639: 2636: 2632: 2629: 2627: 2624: 2623: 2622: 2619: 2617: 2614: 2612: 2609: 2608: 2606: 2604: 2600: 2594: 2591: 2589: 2586: 2584: 2581: 2580: 2578: 2574: 2568: 2565: 2564: 2562: 2560: 2556: 2544: 2541: 2539: 2536: 2534: 2531: 2530: 2529: 2526: 2524: 2521: 2520: 2518: 2516: 2512: 2506: 2503: 2501: 2498: 2496: 2493: 2491: 2488: 2486: 2483: 2481: 2478: 2476: 2473: 2472: 2470: 2468: 2464: 2458: 2455: 2453: 2450: 2446: 2443: 2441: 2438: 2436: 2433: 2431: 2428: 2426: 2423: 2421: 2418: 2416: 2413: 2411: 2408: 2406: 2403: 2401: 2398: 2397: 2396: 2393: 2392: 2390: 2388: 2384: 2381: 2379: 2375: 2371: 2367: 2362: 2358: 2352: 2349: 2347: 2344: 2343: 2340: 2336: 2329: 2324: 2322: 2317: 2315: 2310: 2309: 2306: 2300: 2297: 2296: 2286: 2284:0-13-922303-7 2280: 2276: 2271: 2260: 2254: 2250: 2249: 2243: 2242: 2221: 2217: 2211: 2203: 2197: 2193: 2192: 2184: 2176: 2170: 2166: 2165: 2157: 2149: 2143: 2139: 2138: 2130: 2123: 2117: 2113: 2106: 2099: 2093: 2089: 2082: 2074: 2067: 2060: 2054: 2050: 2043: 2035: 2034: 2026: 2018: 2016:0-471-02140-7 2012: 2008: 2004: 1998: 1991: 1985: 1981: 1974: 1967: 1961: 1957: 1950: 1943: 1937: 1933: 1926: 1919: 1913: 1909: 1902: 1894: 1892:0-471-02140-7 1888: 1884: 1880: 1874: 1866: 1862: 1858: 1854: 1847: 1839: 1833: 1829: 1828: 1820: 1816: 1806: 1803: 1801: 1798: 1796: 1793: 1791: 1788: 1786: 1783: 1781: 1778: 1777: 1771: 1768: 1766: 1765: 1760: 1753: 1751: 1738: 1718: 1713: 1709: 1703: 1696: 1692: 1685: 1681: 1677: 1671: 1667: 1661: 1657: 1653: 1649: 1645: 1642: 1635: 1631: 1627: 1622: 1618: 1613: 1607: 1603: 1599: 1593: 1589: 1586: 1583: 1572: 1564: 1561: 1552: 1548: 1544: 1541: 1533: 1529: 1522: 1519: 1516: 1513: 1505: 1501: 1494: 1491: 1488: 1485: 1481: 1475: 1471: 1467: 1463: 1459: 1456: 1445: 1443: 1440: 1438: 1419: 1413: 1406: 1400: 1386: 1377: 1371: 1362: 1353: 1350: 1343: 1342: 1341: 1322: 1318: 1312: 1307: 1304: 1301: 1297: 1291: 1288: 1283: 1274: 1264: 1263: 1262: 1260: 1242: 1238: 1234: 1231: 1228: 1223: 1219: 1207: 1182: 1176: 1168: 1162: 1156: 1153: 1147: 1144: 1137: 1136: 1135: 1122: 1114: 1108: 1105: 1100: 1094: 1088: 1081: 1062: 1056: 1046: 1042: 1038: 1035: 1031: 1025: 1015: 1011: 1008: 1006: 996: 988: 980: 978: 968: 965: 952: 949: 944: 940: 937: 934: 928: 923: 919: 916: 913: 907: 904: 895: 882: 879: 874: 870: 867: 864: 858: 853: 849: 846: 843: 837: 834: 822: 817: 808: 805: 802: 801: 797: 794: 791: 790: 786: 783: 781: 780: 777: 774: 770: 762: 757: 748: 726: 723: 720: 717: 714: 711: 705: 702: 699: 696: 693: 690: 687: 680: 679: 678: 661: 658: 654: 650: 647: 644: 641: 638: 635: 631: 627: 620: 619: 618: 601: 598: 595: 591: 585: 581: 578: 575: 569: 566: 563: 558: 554: 551: 548: 541: 537: 530: 529: 528: 526: 522: 503: 500: 497: 491: 488: 485: 482: 479: 473: 466: 465: 464: 450: 442: 438: 434: 430: 420: 418: 412: 397: 395: 392:is left as a 391: 382: 378: 375: 372: 350: 340: 339: 338: 319: 309: 303: 300: 294: 291: 284: 283: 282: 280: 275: 271: 269: 264: 259: 257: 253: 249: 241: 237: 234: 231: 227: 224: 223: 222: 203: 199: 196: 193: 187: 184: 177: 176: 175: 173: 163: 161: 159: 154: 149: 147: 143: 139: 135: 131: 127: 123: 121: 115: 113: 112: 111:Normalization 107: 103: 102:standardizing 99: 95: 90: 88: 84: 80: 76: 72: 65: 61: 57: 54:, including: 53: 48: 42: 35: 30: 19: 18:Standardizing 4616: 4604: 4585: 4578: 4490:Econometrics 4440: / 4423:Chemometrics 4400:Epidemiology 4393: / 4366:Applications 4208:ARIMA model 4155:Q-statistic 4104:Stationarity 4000:Multivariate 3943: / 3939: / 3937:Multivariate 3935: / 3875: / 3871: / 3645:Bayes factor 3544:Signed rank 3456: 3430: 3422: 3410: 3105:Completeness 2941:Cohort study 2839:Opinion poll 2774:Missing data 2761:Study design 2716:Scatter plot 2638:Scatter plot 2631:Spearman's ρ 2593:Grouped data 2274: 2262:. Retrieved 2247: 2224:. Retrieved 2219: 2210: 2190: 2183: 2163: 2156: 2136: 2129: 2111: 2105: 2087: 2081: 2072: 2066: 2051:, Springer, 2048: 2042: 2032: 2025: 2006: 1997: 1979: 1973: 1955: 1949: 1931: 1925: 1907: 1901: 1882: 1873: 1856: 1846: 1826: 1819: 1769: 1762: 1758: 1756: 1749: 1339: 1258: 1203: 1041:standardized 1040: 1036: 1027: 1012: 1009: 1002: 994: 986: 974: 966: 896: 826: 820: 766: 760: 746: 677:it follows: 676: 616: 524: 520: 518: 440: 436: 432: 426: 414: 400:Applications 389: 386: 376: 336: 278: 276: 272: 262: 261:Calculating 260: 255: 251: 247: 245: 235: 225: 220: 171: 169: 157: 150: 141: 137: 134:normal score 133: 129: 125: 119: 118: 116: 114:for more). 109: 105: 101: 91: 74: 68: 29: 4618:WikiProject 4533:Cartography 4495:Jurimetrics 4447:Reliability 4178:Time domain 4157:(Ljung–Box) 4079:Time-series 3957:Categorical 3941:Time-series 3933:Categorical 3868:(Bernoulli) 3703:Correlation 3683:Correlation 3479:Jarque–Bera 3451:Chi-squared 3213:M-estimator 3166:Asymptotics 3110:Sufficiency 2877:Interaction 2789:Replication 2769:Effect size 2726:Violin plot 2706:Radar chart 2686:Forest plot 2676:Correlogram 2626:Kendall's τ 2003:E. Kreyszig 1879:E. Kreyszig 1795:Omega ratio 1206:sample mean 166:Calculation 130:z-statistic 106:normalizing 4485:Demography 4203:ARMA model 4008:Regression 3585:(Friedman) 3546:(Wilcoxon) 3484:Normality 3474:Lilliefors 3421:Student's 3297:Resampling 3171:Robustness 3159:divergence 3149:Efficiency 3087:(monotone) 3082:Likelihood 2999:Population 2832:Stratified 2784:Population 2603:Dependence 2559:Count data 2490:Percentile 2467:Dispersion 2400:Arithmetic 2335:Statistics 1811:References 1752:-statistic 527:it gives: 160:-statistic 98:population 71:statistics 60:percentile 3866:Logistic 3633:posterior 3559:Rank sum 3307:Jackknife 3302:Bootstrap 3120:Bootstrap 3055:Parameter 3004:Statistic 2799:Statistic 2711:Run chart 2696:Pie chart 2691:Histogram 2681:Fan chart 2656:Bar chart 2538:L-moments 2425:Geometric 1710:σ 1682:σ 1654:∑ 1646:⁡ 1600:∑ 1590:⁡ 1576:¯ 1565:⁡ 1549:σ 1523:⁡ 1495:⁡ 1489:∑ 1468:∑ 1460:⁡ 1401:σ 1390:¯ 1378:⁡ 1372:− 1366:¯ 1298:∑ 1278:¯ 1232:… 1177:σ 1163:⁡ 1157:− 1109:⁡ 1089:σ 1057:⁡ 938:− 924:σ 920:μ 917:− 868:− 854:σ 850:μ 847:− 727:σ 718:μ 703:σ 697:− 694:μ 662:γ 636:− 599:γ 586:σ 582:μ 579:− 559:σ 555:μ 552:− 501:γ 451:γ 354:¯ 313:¯ 304:− 204:σ 200:μ 197:− 83:raw score 4634:Category 4580:Category 4273:Survival 4150:Johansen 3873:Binomial 3828:Isotonic 3415:(normal) 3060:location 2867:Blocking 2822:Sampling 2701:Q–Q plot 2666:Box plot 2648:Graphics 2543:Skewness 2533:Kurtosis 2505:Variance 2435:Heronian 2430:Harmonic 2226:5 August 2005:(1979). 1881:(1979). 1774:See also 1764:hensachi 64:T-scores 4606:Commons 4553:Kriging 4438:Process 4395:studies 4254:Wavelet 4087:General 3254:Plug-in 3048:L space 2827:Cluster 2528:Moments 2346:Outline 1759:T-score 1743:T-score 463:, i.e. 379:is the 369:is the 337:where: 238:is the 228:is the 221:where: 126:z-value 122:-scores 4475:Census 4065:Normal 4013:Manova 3833:Robust 3583:2-way 3575:1-way 3413:-test 3084:  2661:Biplot 2452:Median 2445:Lehmer 2387:Center 2281:  2264:7 June 2255:  2198:  2171:  2144:  2118:  2094:  2055:  2013:  1986:  1962:  1938:  1914:  1889:  1834:  1216:  709:  411:Z-test 405:Z-test 153:sample 73:, the 4099:Trend 3628:prior 3570:anova 3459:-test 3433:-test 3425:-test 3332:Power 3277:Pivot 3070:shape 3065:scale 2515:Shape 2495:Range 2440:Heinz 2415:Cubic 2351:Index 795:1500 792:Mean 4332:Test 3532:Sign 3384:Wald 2457:Mode 2395:Mean 2279:ISBN 2266:2009 2253:ISBN 2228:2017 2196:ISBN 2169:ISBN 2142:ISBN 2116:ISBN 2092:ISBN 2053:ISBN 2011:ISBN 1984:ISBN 1960:ISBN 1936:ISBN 1912:ISBN 1887:ISBN 1832:ISBN 1032:, a 871:1500 865:1800 819:The 806:300 787:ACT 784:SAT 771:and 759:The 648:< 642:< 570:< 564:< 489:< 483:< 371:mean 230:mean 142:pull 140:and 87:mean 3512:BIC 3507:AIC 1861:doi 1643:Var 1587:Var 1562:Var 1520:Var 1492:Var 1457:Var 1257:of 1106:Var 1039:is 1028:In 953:0.6 875:300 798:21 773:ACT 769:SAT 523:of 148:. 144:in 104:or 69:In 4636:: 2218:. 1855:. 1261:: 941:21 935:24 809:5 396:. 162:. 136:, 132:, 128:, 3457:G 3431:F 3423:t 3411:Z 3130:V 3125:U 2327:e 2320:t 2313:v 2287:. 2268:. 2230:. 2204:. 2177:. 2150:. 2019:. 1895:. 1867:. 1863:: 1840:. 1754:. 1750:t 1719:n 1714:2 1704:= 1697:2 1693:n 1686:2 1678:n 1672:= 1668:) 1662:i 1658:x 1650:( 1636:2 1632:n 1628:1 1623:= 1619:) 1614:n 1608:i 1604:x 1594:( 1584:= 1581:) 1573:X 1568:( 1553:2 1545:n 1542:= 1539:) 1534:i 1530:x 1526:( 1517:n 1514:= 1511:) 1506:i 1502:x 1498:( 1486:= 1482:) 1476:i 1472:x 1464:( 1420:n 1414:/ 1410:) 1407:X 1404:( 1396:] 1387:X 1381:[ 1375:E 1363:X 1354:= 1351:Z 1323:i 1319:X 1313:n 1308:1 1305:= 1302:i 1292:n 1289:1 1284:= 1275:X 1259:X 1243:n 1239:X 1235:, 1229:, 1224:1 1220:X 1186:) 1183:X 1180:( 1172:] 1169:X 1166:[ 1160:E 1154:X 1148:= 1145:Z 1123:: 1118:) 1115:X 1112:( 1101:= 1098:) 1095:X 1092:( 1066:] 1063:X 1060:[ 1054:E 1037:X 950:= 945:5 929:= 914:x 908:= 905:z 883:1 880:= 859:= 844:x 838:= 835:z 821:z 761:z 724:z 721:+ 715:= 712:U 706:, 700:z 691:= 688:L 659:= 655:) 651:z 645:Z 639:z 632:( 628:P 602:. 596:= 592:) 576:U 567:Z 549:L 542:( 538:P 525:X 521:Z 504:, 498:= 495:) 492:U 486:X 480:L 477:( 474:P 441:X 437:U 433:L 390:z 377:S 351:x 320:S 310:x 301:x 295:= 292:z 279:z 263:z 256:z 252:x 248:z 236:σ 226:ÎŒ 194:x 188:= 185:z 172:x 158:t 120:z 43:. 36:. 20:)

Index

Standardizing
Standardization
Z-score (disambiguation)

normal distribution
standard deviations
percentile
T-scores
statistics
standard deviations
raw score
mean
population mean
population
Normalization
high energy physics
sample
t-statistic
mean
standard deviation
standardized testing
mean
standard deviation
dimensionless quantity
Z-test
Student's t-test
prediction intervals

SAT
ACT

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑