Lecture 2: describing data with numbers

Question 1

discrete

Answer 1

• levels of the variable can only be described as different types of categories
• measuring somethings in separate categories

Question 2

continuous

Answer 2

• levels of the variable can take on a range of values that are not restricted to a list of simple categories
• take on any value along a range

Question 3

nominal scale

Answer 3

• levels represent different categories or groups
• most basic
• discrete categories and count how many people fit into that category
• assign numbers to objects where different numbers indicate different objects

Question 4

ordinal scale

Answer 4

• minimal qualitative distinctions
• rank order in terms of some quantity
• there is now an ordering element of the different categories
• assign numbers to objects but now that number has meaning (ex 1st place and 2nd place in a race)

Question 5

interval scale

Answer 5

• quantitative properties
• intervals between levels are equal in size
• can be summarized using means
• no absolute zero
• tells you the difference between 1st and second pace weather it was 20 minutes or 4 seconds
• numbers have order but there are also equal intervals between adjacent categories (difference in height will be one inch throughout)

Question 6

ratio scale

Answer 6

• detailed quantitative properties
• equal intervals
• absolute zero can be summarized using mean
• differences are meaningful plus ratios are meaningful and there is a true zero point (ex weight in pounds: 10lbs is twice 5lbs and zero pounds would mean no weight)

Question 7

frequency distributions

Answer 7

• the most basic form of data analysis
• can be in tabular or graphical format
• indicated how often different values are present in a data set
• think of a table for a cladogram

Question 8

derive a frequency distribution (group frequency distribution)

Answer 8

• raw scored are transformed into a tally by counting the number of cases for each value
• instead of making a cladogram think of tallying up the results rather than displaying what percent no one got

Question 9

central tendency of a distibution

Answer 9

• most representative score or value
• where the average is on a graph
• vertical measurement on a graph

Question 10

dispersion

Answer 10

• extent of deviation from central tendency
• how spread out are the scores
• a horizontal measurement on a graph

Question 11

Skewness

Answer 11

• asymmetry in distribution
• positive skew: long tail in positive direction
• negative skew: long tail in negative direction

Question 12

Σ

Answer 12

• sigma
• sum of all values

Question 13

disadvantages of mean

Answer 13

• subject to distorting effects of outliers

Question 14

median

Answer 14

• point that divides the distribution into two equal parts

Question 15

mode

Answer 15

• the most frequently occurring score

Question 16

what is variability

Answer 16

• how close to the center of the distribution are the scores

Question 17

variance

Answer 17

• (Σ(X-M)^2)/N-1
• N = number of values
• X = any given distribution
• M = mean
• the sample variance formula uses N-1 in the denominator because sample information is being used to estimate a population characteristic
• the sample must be squared to avoid negative numbers

Question 18

standard deviation

Answer 18

• removes the squared components of variance by taking the square root of the variance
• calculates how spread out each measure is from the mean
• greater accuracy since all values are included

Question 19

range

Answer 19

• the difference between the smallest (minimum) and the largest (maximum) values

Question 20

correlation

Answer 20

• correlation coefficient: a statistic that indicates the strength and direction of the relationship between two variables
• PPMCC = “r”
• 0 = no correlation
• -1 = negative correlation
• +1 = positive correlation
• r indicated the degree of linear relationship between two variables the data may have a strong nonlinear relationship that r does not reveal

Question 21

effect size

Answer 21

• a general term for the strength of relationship between variables; r is one indicator of effect size; when used this way r is usually squared to produce r squared
• r squared can be interpreted as the proportion of variability in one variable accounted for by variation in another variable

Question 22

type I error

Answer 22

• a false positive
• results are just due to chance
  when the threshold is set to 5% which is the convention, then the researcher as a 5% chance or less of making a type I error

Question 23

type II error

Answer 23

• a missed opportunity
• more likely to occur when the threshold is set too low and or when the sample was too small
• when the researcher is actually right but throws the findings away since they seem to be due chance