lecture 1 - introduction, measurement and distributions

Question 1

why do psychologists need statistics?

Answer 1

To summarise and describe their data, to infer real differences and associations from ‘messy’ data and to generalise from samples to populations

Question 2

what is a variable?

Answer 2

anything that can be in more than one state or that can have different values

Question 3

what is a discrete variable?

Answer 3

can take a limited number of values eg university year as can segregate people on how long at uni using variable

Question 4

what is a continuous variable?

Answer 4

can take any value (as long as it is between lowest and highest points on the scale) eg time, height and can measure to infinite precision and infinitely divide.

Question 5

what is an interval variable

Answer 5

interval data - used in lots of stats test. when equal intervals on the scale represent equal differences in the property being measured.

Question 6

what is a ratio variable?

Answer 6

measurement scale needs to meet the requirement of an interval variable and the ratios along the scale need to be meaningful so the scale must have a true and meaningful zero.

Question 7

continuous variables can be continuous and discrete

Answer 7

a truly continuous variable can be measured to any level of precision whereas a discrete value can only take on certain values (usually whole numbers) on the scale. the actual values the variable takes on are limited. a continuous variable can be measured at infinite level of precision.

Question 8

what is a categorical variable ?

Answer 8

made up of categories eg species. it names distinct entities. in its simplest form it names two types of things and an entity can be placed only into one of two categories eg male or female which is known as a binary variable

Question 9

what is a nominal variable?

Answer 9

when two things are equivalent in some sense are given the same name (or number) but there are more than two possibilities. the only way nominal data can be used is to consider frequencies. its an unordered categorical variable.

Question 10

what is an ordinal variable?

Answer 10

when categories are ordered. ordinal data tells us things have occurred and the order they occurred in but tells us nothing about the differences between variables/ points on a scale.

Question 11

what is data for stats in psychology?

Answer 11

values of variables we observe and the main for of observation is measurement.

Question 12

measurement

Answer 12

data comes from measurement. type of measurement affects what we know about the world and how we treat numbers with statistics. many things in psych we want to measure we can’t see, think about how the thing we want to measure works and how the measurement works. There are four basic types of measurement (as described by S.S. Stevens, 1946) - nominal, ordinal, interval, ratio

Question 13

levels of measurement

Answer 13

the relationship between what is being measured and the numbers that represent what is being measured

Question 14

measurement error

Answer 14

measures need to be calibrated so values have some meaning over time and across situations. some variables can be measured directly eg weight but others need indirect measures eg self-report and questionnaires. measurement error is the discrepancy between the numbers we use to represent the thing we are measuring and the actual value of teething we are measuring. self-report measures will produce larger measurement error as factors other than the one your trying to measure will influence how people respond ti our measures.

Question 15

nominal

Answer 15

codes for identity/ classification
eg hair colour

Question 16

ordinal

Answer 16

represents order eg position in a race

Question 17

interval

Answer 17

reflects the difference between things eg temperature

Question 18

ratio

Answer 18

reflects the amount of a thing eg weight

Question 19

nominal scales

Answer 19

substitute for names, same/different, report only how many are the same/ different. using numbers to code for whether things are the same or different in the world.

Question 20

ordinal scale

Answer 20

More then / less than is the question here. Order is meaningful (hence the rather predictable name). Imagine four situations eg 50 y friendship, 10 y friendship, 2 y friendship, met last night. Rank from most to least “knowledge of other”. Need to preserve the order of things in the world. No assumption equal intervals - only order important. Rank ordered with no fixed gap.

Question 21

interval scale

Answer 21

No unique zero point exists
E.g. Celsius: zero = freezing point water
Fahrenheit: freezing point water = 32 degrees
Only makes sense to look at the differences between two scores not the ratio between them.
Hot day = 30°C (86°F) and cold day = 10°C (50°F)
Hot coffee = 60°C (140°F), cold coffee = 40°C (104°F)
Difference in both cases is 20°C (or 36°F) so equal differences between points means equal intervals.
Ratios say that the hot day was 3 times as hot as the cold day (1.72 using F) while the hot coffee is only 1.5 times as hot (1.346 using F)?
The ratios here are nonsense – they DO NOT make sense with interval scales!
Rank ordered with a fixed gap

Question 22

ratio scales

Answer 22

A unique zero point exists thus ratios and differences between scores make sense eg Length 2000m (2km, 1.2428 miles) to work, 200m (0.2km, 0.12428 miles) to nearest pub. No matter what unit chosen it is always 10 times as far to go to work as it is to go to the pub!

Question 23

frequency histograms

Answer 23

Data is sorted from smallest to largest eg 01, 21, 22, 26, 36, 37 …
Define bin size eg 5
Then count no of data points in bin 1, bin 2 etc
Eg bin 1 = 1 - 5 has 1 data point
Bin 2 = 6 - 10 has 0
Bin 5 = 21 - 25 has 2
Bin 6 = 26 - 30 has 1 etc
Plot count (freq) against bin

Question 24

frequency distributions

Answer 24

• The relationship between a particular value of a variable and the number of items that have that value is called a frequency distribution.
  Like the histogram, the usual way to plot a frequency distribution is to put the score on the X axis (horizontal) and the number of items having that score on the Y axis (vertical). Any plot of score against frequency will do, it is just that this conventional way of plotting things is easy to describe and analyse.

Question 25

unimodal distribution

Answer 25

only one most common score

Question 26

bimodal distribution

Answer 26

two equally common scores

Question 27

positively skewed distribution

Answer 27

ail goes towards positive end.
* Likely when there is a lower limit and people are likely to be scoring at the bottom end of the range.
E.g. reaction time, most pretty quick but some tail off.

Question 28

negatively skewed distribution

Answer 28

tail goes towards negative end.
* Likely when there is an upper limit and people are likely to be scoring at the top end of the distribution.
E.g. easy tests, most people get full marks except those that don’t study/pay attention….

Question 29

normal distribution

Answer 29

symmetrical/unimodal
f(X)=1/(σ√2π)(e)^(−(X−μ)^2/2σ^2 )

Question 30

validity and reliability

Answer 30

ensure measurement error is kept to a minimum

Question 31

validity

Answer 31

whether an instrument measures what it set out to measure

Question 32

reliability

Answer 32

whether an instrument can be interpreted consistently across different situations. to be valid the instrument must first be reliable. easiest way to test reliability is to test the same group of people twice - a reliable instrument will produce similar scores at both points in time = test-retest reliability. sometimes you will want to measure something that does vary overtime. Statistical methods can also be used to determine reliability.

Question 33

types of validity

Answer 33

if we use measurements to infer other things they are only valid if there are no other factors other than the one we’re interested in that can influence them

Question 34

what is criterion validity

Answer 34

whether you can establish that an instrument measures what it claims to measure through comparison to objective criteria eg by relating stores on your measure to real-world observations.

Question 35

what is concurrent validity?

Answer 35

when data is recorded simultaneously using the new instrument and existing criteria.

Question 36

what is predictive validity?

Answer 36

when data from the new instrument are use ti predict observations at a later point in time.

Question 37

assessing criterion validity

Answer 37

impractical as objective criteria that can be measured easily may not exist eg when measuring attitudes you may be interested in the persons perception and reality and not reality itself

Question 38

what is content validity?

Answer 38

with self-report measures/ questionnaires we can also assess the degree to which individual items represent the construct being measured and cover the full range of the construct