RMA: WEEK 8

Question 1

Measures of spread

Answer 1

• Measures of spread look at how much scores vary in terms of distribution (are they far apart or squashed)
• Measured by
  1. Range
  2. Interquartile range
  3. Standard deviation

Question 2

Range

Answer 2

• Difference between smallest value and biggest value > smallest N - biggest N
• Does not tell us about scores/dataset between the minimum and maximum just the smallest + biggest

Question 3

Interquartile range

Answer 3

• Measures spread of results of the middle 50% of scores > this is in between first quartile (Q1) and third quartile (Q3)
• Q1 - Q3 = interquartile range
• IQ range tells us about range between quartiles + median is found in Q2

Question 4

Standard deviation

Answer 4

• Measures variation from the mean > if data is more spread out (varying more), SD is bigger > smaller when data is less spread out (varying less)
• Larger SD = larger spread of results

Question 5

How to calculate standard deviation

Answer 5

1. calculate mean (+ all N then divide by amount of N)
2. Once we know the mean, we can plot how far other scores deviate from the mean > e.g: if mean is 15, 16 would be +1 SD and 14 = -1SD
   - We want the average of how much scores deviate, cannot do normal mean as it cancels out > square all data points + find sum = SD (but will be a squared answer)
3. Find difference between actual data point and the mean (if mean=15 and actual data point is 11 the diff= -4)
4. Square this result (makes dataset positive) and add all the squared scores up
5. Do normal mean > sum of squared scores divided by the amount of scores > this value = variance (S²)
6. SD is too big bc we squared it > square root the variance result = SD > can compare SD across samples

Question 6

Graphs

Answer 6

• Visual method of representing data
• Indicates pattern of data like spread of data, type of correlation
• Graphs can help decide how to analyse data (e.g: lots of outliers suggest to avoid mean or bimodal data indicates to look for confounds like gender)
• Graphs can illustrate findings
• is best to plot data before using statistical analysis to identify trends

Question 7

Bar graphs

Answer 7

• can be used for ordinal + nominal data
• can see trends + outliers very easily due to the visual format
• Horizontal bar graphs > same as normal bar graph but the bar does not go upwards against x axis but horizontal towards y axis
• Stacked bar graphs > can incorporate different information but is split into different sections separated by colour e.g (e.g: graph on a whether a person spends time clubbing, at a restaurant or pub)
• Histogram > shows data which is in a certain range

Question 8

Bar graph: Histogram

Answer 8

• area covered on graph represents frequency (how often a certain value comes up
• e.g: how often the score 15 comes up like once
• histograms help understand frequency of particular values
• can see potential outliers
• no gap between bars

Question 9

Stem-and-leaf plots

Answer 9

• shows data in compact form
• helps see under which stem most subsets fall under
• shows size of data subsets > e.g: shows sizes of values between 10 and 9 or 10-19
• Stems refer to tens and leaves refer to units
  e. g: stem of 0 (1 ten) means the leaves (units) must be numbers under the value of 10 such as 4 and 8 (1-9) > this is recorded as 48 (not forty-eight but four,eight)
• when the stem is 1 (goes to 10 or over), the leaves are only counted using the units so 12 is referred to as 2, 10=0, 15=5
• can easily see where most data is + can use hundreds

Question 10

Box plots

Answer 10

• Summarises lower quartile (Q1) + upper quartile (Q3), median (Q2), minimum, maximum + outliers
• Median value is always indicated by the bar in the middle of the box (identify N on Y axis using bar)
• Q1 is lower down and Q3 is higher up and Q2 is in between > when we know Q1 + Q3 we can draw the box plot (Q1=bottom of box, Q3=top of box)
• Maximum value + minimum can be seen on highest and lowest score/data
• the minimum may not be the actual min as if outliers have been removed, the actual min from original data would be gone + min would be the smallest score which does not count as an outlier
• Can see outliers > analysis software removes outliers > do this by 1.5 x interquartile range above Q3 to see high outliers or 1.5 x IQ range below Q1 to see low outliers
• Distance between Q1 + Q3 = Interquartile range > can help when comparing box plots to see difference

Question 11

Scatterplots

Answer 11

• Can easily see if there is a relationship between variables > trends + patterns can be identified
• Random looking plots = data which is probably not correlated
• Positive correlation or negative correlations can also be seen.