S2 Research methods - 1

Introduction central tendency z-scores

Schedule:

Lecture 1:

• Frequency distributions
• Normal (gaussian) distribution
• Central tendency
• Z Scores

Frequency distributions - describe the pattern of observations in a data set

E.g how many times does each observation appear in my dataset?

Central tendency - a value that represents the typical average or centra; value in a dataset

Mean: sum of all data points divided by number of observations

Mean = sum of all data/number of data points (∑/n)

Median: middle data vale when assorted from ascending to descending order

Mode: data value that occur with the greatest frequency

In a perfect distribution the mean, median and mode are the same value

Normal distribution

• Symmetrical
• Unimodal
• Mean, median and mode at the centre of peak
• 68% of scores fall between 1 SD and 95% between 2SD

Kurtosis

Collective intelligence

• Vox populi (galton, 1970)
• Guess the weight of the ox
• 787 guesses of experts and non experts
• Mean guess - 1207
• Real weight - 1198

Z-scores (standard scores)

Z score- Standard normal distribution : the same as the normal distribution but always has a mean of zero and SD of 1)

• 68% scores within +/- 1SD
• 95% scores within +/- 2 SD
• 99.7 Scores within +/- 3SD

Z scores are standardised scores - a group of data points transformed to have a mean of 0 and a SD of 1 just like the standard normal distribution

A Z score is expressed in standard deviation units

• Z score of 1 is 1SD above the mean
• Z score of -1 is 1SD below the mean

𝘟−𝝻/𝞂 = Individual score-mean score/standard deviation

M=20/5=4

SD=1.41

Using Z score

Daria scored 90 on a maths test and 65 on a spelling test did she perform better at maths or spelling to compare her score in these 2 tests we need to standardise the units, so we convert the scores to Z scores (expressed in SD Units)

Overall class distributions

Maths test: mean=100 and SD =10

Spelling test: mean=70 and SD=10

Maths test: mean=100, SD=10, Score of 90

Spelling test; mean =70, SD=10, Score of 65

Important values of Z scores

A Z score of 1.96 is the cutt off for the top 2.5% of the distribution

Z score of -1.96 is the cut off for the bottom 2.5% of the distribution

Together they amount to 5% of the distribution

So 95% of the z scores lie between -1.96 and 1.96

We say that ‘95% of scores lie between +/- 2SD. That's just because it's easier to remember we are rounding for brevity. The exact figure is +/- 1.96SD

Finding raw scores from Z scores

X = 𝝻 + Z𝞂

• X - Raw score, individual score or test results
• 𝝻 - the mean
• Z - z score
• 𝞂 - the SD

Multiply the Z score by the SD then add the mean

Things to do:

• Weekly homework
• Reading - bourne ‘starting out in methods and statistics for psychology 51-59 -> 283-317

Revision guide

1. What is a frequency distribution
2. What does a normal distribution look like whats its properties
3. Why do we care about distribution of data
4. What is central tendency
5. What are the 3 common measures of central tendency
6. Properties of Z scores
7. Why do we love them so much (aka how do you use them)
8. How do you calculate a z score (what's the mformula)

Assessments

• Final exam (40%)
• Research report (35%)
• Weekly homeworks (20% total)
• Sona (5%)