Statistics & Research Design Test I

Central tendency & variability, Z-scores, standard deviation, normal distributions, Z-tests and (null) hypothesis testing, confidence intervals, effect size, and statistical power

Mean Definition

A measure of central tendency that represents the mathematical average of a set of scores

Mean Formula

Sum of all scores / number of scores

Median Definition

A measure of central tendency that represents the ordinal, literal middle of a set of scores

Median Formula

Number of scores + 1 / 2 (for ordinal position; if ending in .5, average the flanking scores)

Mode Definition

A measure of central tendency that represents the score(s) that most frequently appear in a set of scores

Range Definition

The difference between the largest and smallest values in a data set

Variance Definition

A measure of how far a set of numbers is spread out from the mean

Population Variance Formula

1. Calculate the differences from each score to the mean

2. Square the differences

3. Take the sum of the squares

4. Divide the sum by the number of scores in the dataset

i.e (sum of squared differences) / n

Sample Variance Formula

1. Calculate the differences between each score and the mean

2. Square the differences

3. Take the sum of the squares

4. Divide the sum by the number of scores in the dataset -1*

i.e (sum of squared differences) / n - 1

Standard Deviation Definition

The ‘average’ distance between each score and the mean

Standard Deviation Formula

1. Calculate the variance (note whether for sample or population before manipulating n)

2. Take the square root of the variance

Standard Error Definition

The standard deviation for a distribution of means, a measure of the variability of sample means across hypothetical repeated samples, compared to the population mean

Standard Error Formula

Standard deviation of sample / square root of population

Z-score Definition

A measure of how many standard deviations a specific data point lies above/below the mean of a distribution

Sample Z-score Formula

Raw score - sample mean / sample standard deviation

Population Z-score Formula

Raw score - population mean / population standard deviation

Confidence Interval Definition

A range of values that is (95%) likely to contain the true value of an unknown/unsampled population

i.e if the sampling were to be done 50 more times with 50 new scores, the mean would fall between the upper and lower bounds of the interval 95% of the time, representative of the population

Confidence Interval Formula

1. Calculate the standard error

2. Multiply the standard error by the critical value (1.96) to get the margin of error

3. Add the product to the sample mean for the upper bound

4. Subtract the product from the sample mean for the lower bound

Effect Size

The size/strength of the difference between two means

Effect Size Formula

(sample mean - population mean) / sample standard deviation

Null Hypothesis

(H₀) The default assumption of no difference/change/relationship between variables or groups

Directional Hypothesis

A hypothesis that predicts an independent variable will cause a EITHER a positive OR negative change in a dependent variable; uses a one-tailed test (5%) focusing one end of the distribution depending on the direction (increasing or decreasing)

Nondirectional Hypothesis

A hypothesis that predicts an independent variable has AN effect on a dependent variable, but does not specify whether the change will be positive or negative; uses a two-tailed test (2.5%) that accounts for both ends of the distribution

Alpha Level Definition

The likelihood that a statistical difference can be attributed to chance

i.e accepting an alpha level of .05 means there is a 5% chance the results are random, not indicative of a real effect