STATS Lecture 1

Levels of Measurement

levels of measurement are essentially the rules for assigning numbers to objects

• nominal

• ordinal

• interval

• ratio

Nominal - lowest level

data categories must be exclusive (each datum fits only on category)

• the date categories must be exhaustive (each datum will fit into at least one category)

• Ex: Gender, Race/Ethnicity, Box method

Ordinal (order)

includes categories that can be rank ordered

• categories must be exhaustive and mutually exclusive

• each category must be recognized as higher or lower or better or worse than another category

• you do not know exactly how much higher or lower one subjects score is in relation to another subject’ score

• - do not have continuum of values with equal distances between them

• ex: pain scale, rank top 10, severity scale, likert scale

Nonparametric or distribution-free analysis tech.

used to analyze nominal and ordinal level variables to examines relationships

• assumptions:

• values need not be normally distributed

• this level of measurement is usually ordinal or nominal

Measurement of Central Tendency

• nominal level data: MODE (most frequently occurring in data set)

• ordinal level data: MEDIAN (middle value in a data set)

measurement central tendency - descriptive statistical analyses such as frequencies and percentages are…

used to describe demographic variables

measurement central tendency - range is used to…

determine the dispersion or spread of values of a variable measured at the ordinal level

analysis from book examples

chi-square (E:19) - NOMINAL variables (yes/no, smoker non smoker)

spearman rank-order correlation coefficient (E:20) - ORDINAL variables (placement for “how well done”)

Mann Whitney U and Wilcoxen Signed Ranked (E:21,22) - conducted to determine differences among groups when measure at ORDINAL level

Interval

(ALWAYS NUMBERS)

distance between intervals of the scale are numerically equal

• no absolute zero

• score of zero does NOT indicate that property being measured is absent

• continuous variable e

• EX: temperature, number ranges not starting at zero, calendar days

Ratio

highest form of measurement

• numerically equal intervals of a scale

• there IS an absolute zero (baseline)

• continuous variables

• EX: pulse, BP, age

Parametric Statistics

powerful analysis techniques conducted on interval and ratio levels of data to describe variables, examine relationships among variables and determine difference between groups

Parametric Statistics - ASSUMPTIONS

• distribution of scores is expected to be a normal distribution or approximately normal

• variables are continuous, measured at INTERVAL or RATIO level

• data can be treated as though they were obtained from a random sample

Parametric Statistics Examplesss

• Means and Standard Deviations (E:8, L:9) - use INTERVAL or RATIO levels

• Pearson’s correlation coefficient (E:13) - determines relationships between variables

• T-test (E:18) and ANOVA (E:18) - calculated to determine significant differences between groups

Significant Results

Those results that keep with the outcomes predicted by the researcher and their team

significant results are usually identified by * or p values less than or equal to 0.05

p≤0.05

(0.06 no no, 0.001 is ok)