t scores :t scores headlessprofessor


What it is :What it is A t score is an inferential statistic.


What it is :What it is A t score is an inferential statistic. Used to infer the significance of the difference between two means


Restrictions :Restrictions A t score is parametric.


Restrictions :Restrictions A t score is parametric. The parent population must be normally distributed.


Types of t tests :Types of t tests One sample


Types of t tests :Types of t tests One sample Dependent samples


Types of t tests :Types of t tests One sample Dependent samples Independent samples


Types of t tests :Types of t tests One sample Dependent samples Independent samples Correlation coefficient


Degrees of Freedom :Degrees of Freedom One sample = N - 1 Dependent samples = N - 1 Independent samples = N - 2 Correlation coefficient = N - 2


One sample t formula :One sample t formula Sample mean – Population mean


One sample t formula :One sample t formula Sample mean – Population mean Divided by Std Dev


One sample t formula :One sample t formula Sample mean – Population mean Divided by Std Dev Times square root of (N – 1)


Example :Example Norms Mean = 80 S.D. = 10


Example :Example Norms: Mean = 80, S.D. = 10 Sample mean = 85 N = 9


Calculations :Calculations 85 – 80 = 5


Calculations :Calculations 85 – 80 = 5 5 / 10 = .50


Calculations :Calculations 85 – 80 = 5 5 / 10 = .50 9 – 1 = 8


Calculations :Calculations 85 – 80 = 5 5 / 10 = .50 9 – 1 = 8 Sqr root 8 = 2.83


Calculations :Calculations 85 – 80 = 5 5 / 10 = .50 9 – 1 = 8 Sqr root 8 = 2.83 2.83 X .50 = 1.41 = t


Go to a t table :Go to a t table Hint: use a two-tail table


Calculations :Calculations 85 – 80 = 5 5 / 10 = .50 9 – 1 = 8 Sqr root 8 = 2.83 2.83 X .50 = 1.41 = t P > .10


Calculations :Calculations 2.83 X .50 = 1.41 = t P > .10 Results not significant


Calculations :Calculations 2.83 X .50 = 1.41 = t P > .10 Results not significant Accept the null


Example :Example Norms Mean = 80 S.D. = 10


Example :Example Norms: Mean = 80, S.D. = 10 Sample mean = 92 N = 9


Calculations :Calculations 92 – 80 = 12


Calculations :Calculations 92 – 80 = 12 12 / 10 = 1.20


Calculations :Calculations 92 – 80 = 12 12 / 10 = 1.20 9 – 1 = 8


Calculations :Calculations 9 – 1 = 8 Sqr root 8 = 2.83


Calculations :Calculations 9 – 1 = 8 Sqr root 8 = 2.83 2.83 X 1.20 = 3.39 = t


Calculations :Calculations t = 3.39 P < .01


Calculations :Calculations t = 3.39 P < .01 Good significance


Calculations :Calculations t = 3.39 P < .01 Good significance Reject the null


Note :Note Some statistical programs for calculating t do not give you a t score, but just give you the p.


My verdict :My verdict Along with chi square, the t test is one of the most overused and inappropriately used inferential statistics.


non-parametric alternatives :non-parametric alternatives One sample, Kolmogorov-Smirnov


non-parametric alternatives :non-parametric alternatives One sample, Kolmogorov-Smirnov Dependent samples, sign test


non-parametric alternatives :non-parametric alternatives One sample, Kolmogorov-Smirnov Dependent samples, sign test Independent samples, Mann-Whitney, Wilcoxin, Kolmogorov-Smirnov, Pitman Exact Probability


non-parametric alternatives :non-parametric alternatives One sample, Kolmogorov-Smirnov Dependent samples, sign test Independent samples, Mann-Whitney, Wilcoxin, Kolmogorov-Smirnov, Pitman Exact Probability Correlation, Pitman Exact Probability


t scores :t scores headlessprofessor