EBP Chapter 6: Descriptive Statistics

define raw data

data collected from each measured variables

-must be aggregated and transformed in order to be meaningfully interpreted

techniques of raw data

-frequency distributions

-descriptive statistics

-measures of central tendency

-measures of dispersion

define frequency distributions

a table that indicates how many individuals (and the %) in the sample fall into each set of categories

-categorical (nominal) variables

what is a bar chart used for?

a visual display of a frequency distribution

-bars not touching = nominal categories

define grouped frequency distributions

shows the frequency of a subset of scores by combining adjacent values into a set of categories

-approach to summarizing continuous variables

what is a histogram used for?

visual display of a grouped frequency distribution

-bars touching = continuous variables

define frequency curve

-basically a grouped frequency distribution indicated by lines instead of bars

-useful for displaying trend data

define descriptive statistics/ distribution variable

numbers that summarize the data pattern of scores observed on a measured variable

-this pattern is called the distribution variable

what are 3 measures of central tendency

-mean

-median

-mode

what are 3 measures of dispersion (spread)?

-range

-variance

-standard deviation

which is the most commonly used measure of central tendency?

mean

how many means can there be per distribution?

only ONE mean per distribution

another name for mean

average

what is the mean influenced by?

extreme scores (outliers)

define median

score in the center of the distribution

-only ONE value per distribution

-NOT influenced by outliers

-used with distributions that are not "normal" (skewed)

define mode

value that occurs most frequently in a distribution

-can have more than one more

-not influenced by outliers

-gives the least information in terms of description of the data

define distribution

the pattern of scores observed on a measured variable

what is a normal distribution?

data distributions that are shaped like a bell

where do measures of central tendency fall on a curve?

all three measures of central tendency fall at the same point on the distribution

-mode is always at the top

-median is always in the middle

-mean is always the tail

skewed distributions (outliers)

-extreme scores in a distribution

-results in distributions that are not symmetrical

-can either be positively or negatively skewed

positively skewed distribution

negatively skewed distribution

define dispersion

aka the "spread" of data

-the extent to which scored are tightly clustered around or spread out away from the measures of central tendency

what are the 3 values of dispersion?

-range

-variance

-standard deviation

define range

-simple measure of dispersion, and is least useful

-calculated as the maximum observed score minus the minimum observed score

what is the most common measure of dispersion reported?

standard deviation

define standard deviation

useful for describing how much the scores in a set of data vary

what does a large standard deviation indicate?

a large standard deviation in relation to the value of the mean indicated a large spread of scores in the data set

how is dispersion symbolized?

dispersion = s

what ways is dispersion calculated? (4)

-mean deviations

-sum of squares

-variance of s^2

-standard deviation or s

define mean deviations

computing each score minus the mean of the variable

define sum of squares

squaring the mean deviations and summing them

define / equation variance or s^2

dividing the sum of squares by the sample size, N

define (rlly caluate) standard deviation or s

taking the square root of the variance

characteristics of range

-simplest

-computation includes only the highest and lowest scores in the distribution of scores

characteristics of variance

-more sophisticated

-computation includes all scores in the distribution

characteristics of standard deviation

-square root of the variance

-has same characteristics of the variance

-commonly reported in oral health research reports

-is associated with the normal curve

standard deviation and the normal curve

standard deviation and the normal curve'

assuming a normal distribution, we can estimate the percentage of subjects who obtain certain scores just by knowing the mean and standard deviation of the data

the empirical rule

approx. 68% of the scores will fall in the range defined as +/- 1 standard deviation

-approx 95% of the scores will fall bw +/- 2 standard deviations from the mean

-approx 99% of the scores will fall between +/- 3 standard deviations from the mean

what is the ultimate purpose of descriptive stats?

make inferences about the population

define margin of error

because of random error, sample characteristics will most likely not be exactly the same as the population.

how to minimize margin of error (3):

-increase the size of a sample (N)

-this makes it more likely the sample will be representative of the population

-provides more precise estimates of population characteristics