Research Methods and Statistics

Mean

- the average of all the raw scores
- Equal to the sum of the observations divided by the number of observations
- Interval and ratio data (when normal distribution)
- Point of least squares
- Balance point for the distribution
- susceptible to outliers

Median

– the middle score of the distribution
- Ordinal, Interval, Ratio
- for extreme scores, use median
- Identical for sample and population
- Also used when there has an unknown or undetermined score
- Used in “open-ended” categories (e.g., 5 or more, more than 8, at least 10)

- For ordinal data

- equal to the square root

Mode

- most frequently occurring score in the distribution

- Bimodal Distribution

- Not commonly used distribution and their

- Useful in analyses of qualitative or verbal nature
- For nominal scales, discrete variables

- value of the mode gives an indication of the shape of the distribution as well as a measure of central tendency

Range

- equal to the difference between highest and the lowest score
- Provides a quick but gross description of the spread of scores
- When its value is based on extreme scores of the distribution, the resulting description of variation may be understated or overstated

Interquartile Range

difference between Q1 and Q2

Semi-Quartile Range

interquartile range divided by 2

Standard Deviation

- approximation of the average deviation around the mean
- gives detail of how much above or below a score to the mean

- equal to the square root of the average squared deviations about the mean
- Equal to the square root of the variance
- Distance from the mean

Variance

- equal to the arithmetic mean of the squares of the differences between distribution and their mean
- average squared deviation around the mean

Percentile or Percentile Rank

- not linearly transformable, converged at the middle and the outer ends show large interval

- expressed in terms of the percentage of persons sample who fall below a given score
- indicates the individual’s relative position in the standardization sample
- essential in creating normalized standardized scores

Quartile

- dividing points between the four quarters in the distribution
- Specific point

Decile/STEN

- divide into 10 equal parts
- a measure of the asymmetry of the probability distribution of a real-valued random about its mean

Pearson R

- interval/ratio + interval/ratio

Spearman Rho

- ordinal + ordinal

Biserial

- artificial Dichotomous + interval/ratio

Point Biserial

- true dichotomous + interval/ratio

Phi Coefficient

- nominal (true dic) + nominal (true/artificial dic.)

Tetrachoric

- Art. Dichotomous + Art. Dichotomous

Kendall’s

- 3 or more ordinal/rank

Rank Biserial

- nominal + ordinal

T-test Independent (Unpaired T-test)

- two separate groups, random assignment

T-test Dependent (Paired T-test)

- one group, two scores

One-Way ANOVA

- 3 or more groups, tested once

One-Way Repeated Measures

- 1 group, measured at least 3 times

One-Way ANOVA

- 3 or more groups, tested once

One-Way Repeated Measures

- 1 group, measured at least 3 times

Two-Way ANOVA

- 3 or more groups, tested for 2 variables

ANCOVA

- used when you need to control for an additional variable which may be influencing the relationship between your independent and dependent variable

ANOVA Mixed Design

- 2 or more groups, measured more than 3 times

MANOVA

- used to test the differences between the means of multiple dependent variables across two or more independent groups

Mann Whitney U Test

- t-test independent

Wilcoxon Signed Rank Test

- t-test dependent

Kruskal-Wallis H Test

- one-way/two-way ANOVA

Friedman Test

- ANOVA repeated measures

Lambda

-for 2 groups of nominal

Goodness of Fit

- used to measure differences and involves nominal data and only one variable with 2 or more categories

Test of Independence

used to measure correlation and involves nominal data and two variables with two or more categories

Regression

used when one wants to provide framework of prediction on the basis of one factor in order to predict the probable value of another factor

Linear Regression of Y on X

- Y = a + bX
- Used to predict the unknown value of variable Y when value of variable X is known

Linear Regression of X on Y

- X = c + dY
- Used to predict the unknown value of variable X using the known variable Y

Test for Normality

data are drawn from a population that has normal distribution

Kolmogorov-Smirnov

More than 50 sample size

Shapiro-Wilk

Less than 50 sample size