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