# t test

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Category: Education

## Presentation Description

How to use t tests and interpret a t table.

## Presentation Transcript

### 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