NSE 212 Statistical Test Formulas

Independent t test

- 2 groups, measure once

- Experimental & control group

- IV LoM: N

- DV LoM: I/R

t test

Parametric

Independent t test: df

(n1 - 1) + (n2 - 1)

Dependent (paired) t test

- Same group, measure twice

- pre/post

- IV LoM: N

- DV LoM: I/R

Dependent t test: df

n - 1

One way ANOVA

- Simple

- 2+ groups

- Measure once

- IV LoM: N

- DV LoM: I/R

Two way ANOVA

- Multifactors

- 2+ groups

- Measure once

- IV LoM: N

- DV Lom: I/R

Repeated Measures ANOVA

A one-way or two way ANOVA that involves correlated groups of participants (T1, T2, T3)

Factorial Analysis of Variance

used when an experiment involves more than one independent variable; can separate the effects of different levels of different variables

ANCOVA

- Analysis of Covariance

- Combination of ANOVA & multiple regression

- Multivariate statistical test done (test of DIFFERENCES)

ANOVA/ANCOVA: df

numerator (between groups) = # of groups - 1

denominator (within groups) = N (total sample) - # of groups

F test

Parametric

- Difference between > difference within

- Post hoc test to find source of difference

Chi-Square

- Comparison of what is observed and what is expected by chance

- IV LoM: N

- DV LoM: N

One sample Chi-Square

- Goodness of fit

Two sample Chi-Square

- Test of independence

One sample Chi-Square: df

# of rows - 1

Two sample Chi-Square: df

(# of rows - 1)(# of columns - 1)

χ2

Non Parametric

Pearson's R

- Pearson correlation coefficient

- Relationship between 2 continuous variables

- 2 groups

- IV LoM: I/R

- DV LoM: I/R

Multivariate Statistical Analysis

- Multiple Regression Analysis

- Testing RELATIONSHIPS when there are 1+ IV

- IV LoM: N/I/R

- DV LoM: I/R

Pearson's R: df

N - 2

r test

Parametric

χ2 =

(O-E)^2 / E

Normal Distribution Standard Deviation

68% = 1

95% = 2

99.7% = 3

Z score

(X-X̄)/SD

Type 1 error (alpha)

- Rejecting the null hypothesis when it is in fact true

- False positive

Type 2 error (beta)

- Accepting the null hypothesis when it is false

- False negative

alpha (α)

- Level of significance

- risk associated with not being 100% positive that what occurred in the experiment is a result of the treatment or intervention

- Commonly set at 0.05 (5%) or 0.01 (1%)

Lowering the risk of a ___ increases the risk of a ___. Why?

Type 1 error, Type 2 error

►The stricter the criterion for rejecting a H0, the greater the probability of accepting a null hypothesis when it is false (Type II error)

Null is true, Reject the null

Type 1 error

Null is false, Accept the null

Type 2 error

p ≤ α (0.05)

Reject null hypothesis, results are statistically significant

Two tailed test

Non directional hypothesis

One tailed test

Directional hypothesis

Exclusive range

h - l

Inclusive range

h - l + 1

Standard Deviation formula

SD = √ ∑ (X-X̄)^2 / n - 1

Variance formula

- Standard deviation squared

- SD^2

Pearson Product-Moment Correlation

rxy

Correlation Coefficient: 0 to 0.1

weak or no relationship

Correlation Coefficient: 0.2

weak to moderate relationship

Correlation Coefficient: 0.3

moderate relationship

Correlation Coefficient: 0.4

moderate to strong relationship

Correlation Coefficient: 0.5 to 1.0

strong relationship

Reliability Coefficient

- Cronbach's alpha

> 0.7 = considered acceptable

Positively Skewed Distribution

A distribution in which scores pile up at the low end of the scale

Negatively Skewed Distribution

A distribution in which most scores pile up at the high end of the scale.