Lecture 3

Question 1

Variable

Answer 1

It can very or change. Math - a quantity during a clacl that is assumed to vary or can vary. Computing - data item that can take on more than one value during the runtime of a program.

Question 2

Scales of measurement

Answer 2

Measure a variable.

Question 3

Nominal variable -

Answer 3

Measured by categories. Measurement scale based on the classification of an observation according to a group it belongs. Examples - gender, political party, marital status.

Ex: Heart rate after oseous injection during endo appt (epinephrine keeps anesthetic close to nerve). Use anesthetic without epinephrine - doesn’t last as long.

They took 48 people, each person received 2 injections (anesthetize both sides, operate on 1). Measured how long before things got numb. They are their own control. They measured pulse before and after interoseous injection.

HOE - 2 - clinical trial. Data presented as “anesthetic success or failure” for each type. This group type is our nominal variable.

Question 4

Ordinal

Answer 4

Like nominal, but we can categorize it by logical rating system (good/bad, poor-fair-good). We now have added information about this variable. This is a classification of observation. Heart example.

Numbers do not represent normal number line as well, as you can space them differently in depiction of the data. This is the problem with the ordinal data, as you don’t know the relationship between different variables.

Question 5

Continuous

Answer 5

Interval:
Measurement scale characterized by equal units of measurement - distance between any two numbers is of known size - zero point is arbitrary. EX: fahrenheit and centigrade. We know that 10 degrees is more than 0 degrees. So we have equal intervals.

Ratio:
Measurement scale characterized by equal units of measurement and a true zero point at its origin. Example - mass and time.

Question 6

Gender/sex

Answer 6

Nominal

Question 7

Marital status

Answer 7

Married - widow - other - nominal.

Question 8

Education level

Answer 8

Ordinal if more than 2 categories.

Question 9

Living situation

Answer 9

Ordinal

Question 10

Cognitive status

Answer 10

ordinal

Question 11

Dental care utilization - 2 categories

Answer 11

Nominal

Question 12

Age in years

Answer 12

Continuous

Question 13

Average number of teeth

Answer 13

Continuous

Question 14

Summarizing variables

Answer 14

Population vs Samples
Populations - greek symbols mew, delta. These are not variables.
Samples - roman characters Xbar S - variables.

Question 15

Measures of central tendency

Answer 15

Mode - avg. value (most useful for nominal scale). Most commonly occuring value. It is possible that there is more than one mode.

Mode- “good” common dental health.

Question 16

Median

Answer 16

Most useful with ordinal scale, also can be used for higher order scales - continuous. Cannot be used for nominal variables.

Insensitive to extreme values, which is why it is occasionally used on continuous variables.

If you have an even number of variables, you average the two.

Question 17

Mean

Answer 17

Measure of center of continuous variable. Sum of measurements divided by number of measurements.

Sensitive to extremes. Used for most of physical properties (materials). Can be used for ordinal variables if they are turned into numbers (poor fair good best = 1 2 3 4).

Question 18

Variance

Answer 18

s^2 - MS mean square. Average of the square of the deviations of the measurements about their mean.

Subtracting this sample mean from each of the measurements and squaring the result to eliminate negative numbers. The sum of these squared deviations is called the sum of squares and is an important measure of variability. Sums of squares divided by degrees of freedom - 1 (n-1).

Question 19

Standard deviation

Answer 19

Positive square root of variance.

Question 20

Measures of variability

Answer 20

range, interquartile range, variance, standard deviation, coefficient of variation.

Question 21

Coefficient of Variation

Answer 21

CV - measures the percentage of spread around mean. Unitless. Allows for comparisons - 100*SD/Xbar

Question 22

Standard error of the mean

Answer 22

Most confusing. Very special kind of standard deviation. Theoretical standard deviation. What if we took lots of samples from a theoretical pop, and took mean? We also calculate standard deviation for these means. If you then take all of the mean values from a different sample, you have a new variable for the means - this has an average value and a standard deviation. SE is SD/sqrt(N). Mean is the same as population, SD is not. SD is how certain we are that the mean measures the population.

Question 23

SD vs SE

Answer 23

Standard deviation - lets us make inferences about a population: EX heights, you get an SD and mean. Mean value is the best guess of what the height value for the population is. The SD allows you to infer about the spread and scatter around mean.

SE Used to assess how accurately a sample mean reflects population mean.