t-statistics

Prob. is the two-sided probability of the absolute value of the reported t with the reported d.f., so that a statistically significant finding for a single two-sided t-test is Prob.<.05, and a highly significant finding is Prob.<.01. Please interpret this conservatively, i.e., "barely significant is probably not significant". If you wish to make a Bonferroni multiple-comparison correction, compare this Prob. with your chosen significance level, e.g., p<.05, divided by the number of DIF tests in this Table. This is approximate because of dependencies between the statistics underlying the computation.

 

Many statistical tests are reported as Student's t statistics. This table shows the significance-level values for different degrees of freedom (d.f.). Often the reported t-statistics have effectively infinite degrees of freedom and so approximate a unit normal distribution. t-statistics with infinite degrees of freedom are also called z-statistics, paralleling the use of "z" in z-scores.

 

Table of the two-sided t distribution

d.f.

p=.05

p=.01

1

12.71

63.66

2

4.30

9.93

3

3.18

5.84

4

2.78

4.60

5

2.57

4.03

6

2.45

3.71

7

2.37

3.50

8

2.31

3.36

9

2.26

3.25

10

2.23

3.17

d.f.

p=.05

p=.01

11

2.20

3.11

12

2.18

3.06

13

2.16

3.01

14

2.15

2.98

15

2.13

2.95

16

2.12

2.92

17

2.11

2.90

18

2.10

2.88

19

2.09

2.86

20

2.09

2.85

d.f.

p=.05

p=.01

21

2.08

2.83

22

2.07

2.82

23

2.07

2.81

24

2.06

2.80

25

2.06

2.79

30

2.04

2.75

100

1.98

2.63

1000

1.96

2.58

Infinite

1.96

2.58

(z-statistic)

 

A calculator for the probability of any t value and d.f. is at http://www.danielsoper.com/statcalc3/calc.aspx?id=8

 


 

Welch's refinement of Student's t-test for possibly unequal variances:

 

For sample 1,

M1 = mean of the sample

SS1 = sum of squares of observations from the individual sample means

N1 = sample size (or number of observations)

SS1 / (N1 - 1) = sample variance around the mean (or the measure)

SS1 / ((N1 - 1)(N1)) = standard error variance = EV1 = SE1²

SE1 = Sqrt(EV1) = standard error of the mean (or the measure)

 

Similarly for sample 2, then

t = (M1 - M2) / sqrt (EV1 + EV2) = (M1 - M2) / sqrt (SE1² + SE2²)

 

with Welch-Satterthwaite d.f. = (EV1 + EV2)² / (EV1²/ (N1-1) + EV2² /(N2-1))

which is the same as d.f = (SE1² + SE2²)² / (SE14 / (N1-1) + SE24 / (N2-1))

 

A calculator for this is at http://www.graphpad.com/quickcalcs/ttest1.cfm?Format=SEM

 

Satterthwaite, F. E. (1946), "An Approximate Distribution of Estimates of Variance Components.", Biometrics Bulletin 2: 110-114  

Welch, B. L. (1947), "The generalization of "Student's" problem when several different population variances are involved.", Biometrika 34: 28-35

 

Example: Gender subtotals for Example0.txt Table 28:

M1 = 1.62, M2 = .76, SE1 = .38, SE2 = .16, N1 = 18, N2 = 57

Welch: t = 2.08, d.f. = 23, p = .049


Help for Winsteps Rasch Measurement Software: www.winsteps.com. Author: John Michael Linacre

Masterchef Australia 2018 ongoing: track contestants' abilities

Facets Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download

State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied
 
Rasch, Winsteps, Facets online Tutorials

Forum Rasch Measurement Forum to discuss any Rasch-related topic

To receive News Emails about Winsteps and Facets by subscribing to the Winsteps.com email list,
enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Winsteps.com
The Winsteps.com email list is only used to email information about Winsteps, Facets and associated Rasch Measurement activities. Your email address is not shared with third-parties. Every email sent from the list includes the option to unsubscribe.

Questions, Suggestions? Want to update Winsteps or Facets? Please email Mike Linacre, author of Winsteps mike@winsteps.com

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
Winsteps Tutorials Facets Tutorials Rasch Discussion Groups

 


 

 
Coming Winsteps & Facets Events
May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 27 - 29, 2018, Wed.-Fri. Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 25 - July 27, 2018, Wed.-Fri. Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

 

Our current URL is www.winsteps.com

Winsteps® is a registered trademark