Measurement and statistics in research

where can statistics commonly be found

newspapers, advertisements, financial news, sports, weather, and journal articles

how are statistics used in journal articles

to measure relationships between variables, summarize and depict data, and evaluate experimental results

what is the goal of learning statistics in this context

to understand simple calculations, evaluate statistical use, and interpret results correctly

what do we usually work with in research—samples or populations

samples

what is a population

larger group from which a sample is drawn

what type of letters are used to describe sample values

latin

what type of letters are used to describe population parameters

greek

what is a variable in measurement

a defined phenomenon that is being measured

what does measurement involve

assigning values to outcomes

what are objective measures

measurements of physical quantities and qualities using equipment

are objective measures usually numeric

yes

what are subjective measures

ratings or judgments made by humans about quantities or qualities

what are examples of subjective measures

pain, quality of life, patient satisfaction

what are some categorical subjective variables

gender, religion, blood type

what are the four categories of measurement scales

nominal, ordinal, interval, and ratio

how are the four measurement scales ordered

in order of increasing complexity

why does the type of measurement scale matter

because certain types of statistics are best used with specific types of data

which scale type is the simplest

nominal

which scale type is the most complex

ratio

what is the origin of the term "nominal"

it comes from the Latin nomin, meaning "name”

what do nominal scales do

they place variables into categories using labels

do nominal categories differ in quality or quantity

quality

what comparisons can be made with nominal data

A = B or A ≠ B (equivalence or non-equivalence)

can someone belong to more than one nominal category at the same time

no

what are examples of nominal variables

diagnosis, gender, religion, blood type, political preference

how useful are nominal scales for statistical analysis

not much can be done

what do ordinal scales measure

variables ordered along a continuum (rank order)

what does ranking in ordinal scales tell us

whether one observation is above or below another

can ordinal data show how large the differences are between ranks

no

what are examples of ordinal variables

pain scale, satisfaction levels, and height ranked

how useful is ordinal data for statistical analysis

not much can be done

what does "interval" in interval scales mean

it refers to equal spaces between measurement units

what is a key feature of interval scales

they have equal intervals between values

do interval scales have a true zero point

no

what does an interval scale allow you to identify

equal intervals between any two measurements

what are examples of interval scales

fahrenheit and celsius temperature

what can be concluded from interval-scale temperature differences

whether something is warmer or colder, but not true ratios

can interval data be used for statistical analysis

yes

what does "ratio" in ratio scales mean

it comes from the Latin ratio, meaning calculation

what is the defining feature of ratio scales

they have equal intervals and an absolute zero

what does an absolute zero mean

the complete absence of the variable

why are ratio scales the most precise

they include all characteristics of nominal, ordinal, and interval scales plus a true zero

what does an absolute zero allow you to do

make true ratio statements (twice as much)

what is an example of a ratio vs. interval scale

interval: 0°C (arbitrary zero).
ratio: 0 Kelvin (absolute zero, no heat)

what does a nominal scale show

how many cases are in each category

what does an ordinal scale show

the relative position of things on a continuum

what does an interval scale show

how many points units one measure is greater or less than another

what does a ratio scale show

how many times larger or smaller one is to another with the chance of absolute zero

what happens if measurement tools are faulty

it is difficult to accept or reject a research hypothesis

what should good measurement do

minimize error

what are the two qualities any assessment tool must have

reliability consistency and validity does what it should

what is test-retest reliability

same measurement twice on the same participant to test stability over time and correlate the two tests

what is the ideal correlation coefficient for test-retest reliability

aim for plus 0.8

what is inter observer reliability

two or more clinicians independently assess the same patient to check consistency from rater to rater and correlate results

what is internal consistency

the extent that results on different items correlate with each other

how is internal consistency measured

using cronbach alpha aim for alpha above 0.8

give an example of internal consistency

exams on a topic in a class should show consistency on how different questions are answered

what is measurement validity

the test does what it is supposed to do accuracy of the test

does validity refer to the test or the results

validity refers to the results of the test not the test itself

can test results be partially valid

yes

what is content or face validity

how well items represent the entire universe of items for an exam ask an expert if items assess what you want low content validity means test did not reflect material presented

what is predictive or criterion validity

how well a test predicts a criterion predicts future values

what is construct validity

verified by comparing the test to other tests measuring similar qualities to see correlation often difficult to establish

what is the purpose of a screening test

identifying the presence of disease or not

what are the four possible outcomes of a screening test

true positive, false positive, false negative, true negative

what is sensitivity

proportion of people who test positive who really have the condition true positive

what is specificity

proportion of people who test negative who really do not have the condition true negative

what does sensitivity of 1 and specificity of 1 mean

perfect valid test

what is the purpose of descriptive statistics

organizing and summarizing raw data to get an accurate look at what the data looks like

what are examples of descriptive statistics

frequency distribution average score degree one score varies from another tables graphs histograms polygons

what does central tendency measure

the most typical or representative scores in a group of data

what does variability measure

the extent to which scores are spread out

what are parametric tests

assume samples are drawn from a normal distribution and have the same variability use interval or ratio data

what are non parametric tests

do not assume normal distribution or homogeneity use ordinal or nominal data

what is the first step with a set of data

find an average

what are the three commonly used averages

mean, median, mode

what is the mean

arithmetic center of gravity

what is the median

middle score

what is the mode

the most common score

what does the mean describe

the center or balance point of a frequency distribution

how do you calculate the mean

sum of scores divided by number of cases sigma over n

what is the median

the middle value of a set of ordered numbers with 50 percent of scores on each side

how do you calculate the median for an even number of cases

take the two middle values and find their average

how do you calculate the median for an odd number of cases with no duplicates

select the middle value

does the median change if data at the center repeats

yes

how do you calculate the median with repeating data

first divide n by 2 to find the middle position count cases from the left use lower limit of repeated number then go fraction of the way needed between lower and upper limits

what is the mode

the most frequent value or category in a distribution

what is the mode used for

most frequently occurring value used for nominal ordinal and sometimes interval ratio data

what is the median used for

exact center of rank ordered data when odd or average of two middle values when even used for ordinal and interval ratio data particularly when skewed

what is the mean used for

arithmetic average sum of xs divided by n used for interval ratio data

why should measures of variability be reported

reporting only an average without variability may misrepresent a set of data two datasets can have the same average but different variability

what are three measures of variability

range, variance, standard deviation

what is the range

difference between the highest and lowest score

why can the range be unreliable

if the high or low is an outlier

what is the most important measure of variability

standard deviation

what is the variance

the average of the squared deviations from the mean divided by the number of cases

what is the standard deviation

the square root of the variance

what is the range

difference between the highest and lowest score easy to calculate but highly unstable

why do we square deviations when calculating variance

the sum of the average deviation about the mean is zero squaring makes all positive

how is sample variance calculated

sum of squared differences between observations and their mean divided by n minus 1