RMA: WEEK 10

Question 1

Shape of normal distribution + SD

Answer 1

• shape can vary a bit depending on x axis and y axis figures but should have a general identifiable shape > the bigger the SD, the more spread out the data
• can compare SDs across different normal distributions

Question 2

Mean + SD symbols

Answer 2

• Mean of sample = x̅ (x bar)
• Mean of population = μ (mu)
• Standard deviation of sample = S
• SD of population = σ (sigma)

Question 3

Characteristics of normal distribution

Answer 3

• Normal distribution is described by a normal curve.
• Symmetrical.
• Single-peaked.
• The tails meet the x-axis at infinity > never really touch x axis > never get value of 0
• Location determined by its mean.
• Shape determined by SD.
• Statistical tests assume the data is normally distributed.

Question 4

What we can do with mean and SD in normal distribution

Answer 4

• When we know the mean + SD we can compare values from different data sets (only when we know the mean + SD of whole population not when taking samples)

Question 5

Standard scores (Z-scores)

Answer 5

• number of SDs by which values of raw score is above or below the mean value
• Z scores can be taken from any distribution of data then compare
• Distribution of Z score = difference between observed x and mean divided by SD

Question 6

Calculating Z scores

Answer 6

• Z scores look at distribution of difference between the score we are observing and the mean > takes every value in distribution + look at difference between this value + mean (these values are given in exam)
• This difference is then plotted in a separate normal distribution > standard(ised) normal distribution
• calculate by picking the observed value, see how many SDs they are away from the mean (given data in exam)
• Z score = observed X - mean = ? divided by SD

Question 7

Standard normal distribution

Answer 7

• Standardising all the values on a normal distribution using Z scores = standard normal distribution
• This is where μ = 0 and σ = 1
• This ND allows us to work out proportion of scores above or below a certain point as total area under the curve is 100%

Question 8

Calculating proportions in standard normal distribution

Answer 8

• Work out z score of observed value then work out % of the proportion you want > depends on whether you want to know the percentage of scores above (right) or below (left) a certain point
• On SPSS, table entry gives area to the left of Z score selected
• E.G: what proportion of women are taller than 182cm? work out Z score > 182-164=18 divided by 12.9 = 1.4 > Z=1.4
  Table entry gives are to left of Z= 0.9192 (those shorter than 182cm) > % of women taller than 182cm = 1 - 0.9192 (we minus the amount from the left from 1 because we know the area is 1 or 100% of scores) = 0.0808 x 100 = 8.08%