# t test

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Published on November 14, 2008

Source: authorstream.com

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

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