Biostats lecture 1

variable

• a characteristic that is being measured can vary with different values

• ex: district, test proficiency rates in math, reading science

data

• measured values of the variable for each individual member of a study

• ex: a value of the math proficienc rate is 48% (mankato district) the collection of the values from all districts in the state are the __ of math proficiency rate

scales of measurement of a variable

• nominal

• ordinal

• interval

• ratio

nominal scale

• values are categories only

• categorize data inot mutually exclusive groups

• the actual values have no implied rank or order

• ex: male =1 and female = 0

ordinal scale

• values represent some associated order/rank

• but the distance between values may not be considered equal

• ex: pain rating scale

interval scales

• numerical data (values indicate order and have real meaning, distance between values are equal)

• has no true zero point: zero is only a reference point and does not mean absence of something

• ex: Temperature, calendar year

• can add and subtract, but ratio is meaningless

ratio scale

• numerical data (values indicate order and have real meaning, distance between values are equal)

• has true zero point

• can add, subtract, and ratio is meaningful

continuous variable

• generally measured in interval and ratio scale

categorical variable

• measured in nominal or ordinal scale

• may also be referred to as discrete

true

• T/F a continuous variable may be categorized into a categorical variable and used in analysis

continuous

• descriptive statistics describe ___ data

measures of central location

• mean

• median

• mode

measures of spread or variation

• variance and standard deviation

• range

• inter-quartile range

mean

• average, arithmetic mean

• add up all values and divide by amount of values

• affected by extreme values

• most appropriate when data is approximately symmetric and not very skewed

mean

• measure of central location when data is approximately symmetric and not very skewed

median

• 50th percentile, 2nd quartile

• order the data, if total number is an odd number, it is the middle number

• if total number of data is even, take the average of the 2 middle values

• better measure of central location when data is skewed or ordinal

median

• measure of central location when data is skewed or ordinal

mode

• most frequently occurring value

• most appropriate for categorical data

mode

• most appropriate for categorical data

variance and standard deviation

• measure of data variability around the mean

• how do individuals ina group differ from the group mean on average?

variance

• average squared difference of each value from the mean

• = SD²

standard deviation

• square root of variance (more commonly reported)

• a measure of the variability of the data values around the mean

• is used to describe the variability fo the data

• = sqrt(V)

standard error of the mean or standard error

• a measure of the precision in an estimated sample mean

• it reflects how uncertain the sample mean represents the population mean

• cannot be used to describe the variability in the data

• = SD/ sqrt n

• related to confidence interval

range

• difference between max (largest) and min (smallest)

inter-quartile range

• difference between 1st quartile and 3rd quartile

• spread/variation of the middle 50% of the data (between the 25th percentile and 75th percentile)

quartiles

• dividing the data ito 4 equal groups accoridng to the distribution values

• 1st quartile: 25th percentile

• 2nd quartile: 50th percentile (median)

• 3rd quartile: 75th

median

• 50th percentile, 2nd quartile

box and whisker plot

• also called boxplot

• line inside the box= median

• ends of the box: 1st quartile to 3rd quartile

• width (or height for a vertical plot): IQR

• whisker or tail: extends from both ends of the box, to the largest or smallest value within in 1.5 IQRs beyond the ends of the box

• circles/asterisks: outliers defined as values beyond 1.5 IQRs from the ends of the box

• the outermost circles/asterisks on either side of the box: minimum and maximum

• if there are no outliers, whiskers extend to minimum and maximum

• in literature, there are variations. pay attention to the footnote of the figure

symmetric

• mean = median

right or positively skewed

• mean > median

left or negatively skewed

• mean < median

mean and standard deviation

• if data is symmetric report these descriptive statisitcs

median, range/IQR

• if data is skwewed reprot these descriptive statistics

parametric test

• statistical test for symmetric data

• based on the assumption that observed data are distributed according to some distributions of well known forms

nonparametric test

• statistical test for skewed data

• do not assume the data follow a certain parametric distirbution

parametric distribution

• distributions of well known forms

• normal distribution

• there are numerous normal distributions, differing by their means and SDs

normal distribution

• most commonly used parametric distribution

• bell shaped

• symmetric about the mean

• mean, median, and mode are equal

• determined by 2 parameters: mean and SD

standard normal distribution

• a unique normal distribution

• mean (u)= 0: symmetric about 0

empirical rule of a normal distribution

• 68% within 1 standard deviation from the mean

• 95% within 2 standard deviations from the mean

• 99.7% within 3 standard deviations from the mean

descriptive statistics describing categorical data

• reported as n (%)

• n: number/frequency

• %: percentage/porportion of subjects in each category