1. Research Methods in Psychology PSY 311
Week 3: Means, standard deviations & distributions
Dr Sabahat Çiğdem Bağcı

2. Hypotheses Statements about the objective world around us
Men earn more than women
Women are more intelligent than men
As study hours increases, exam grades will get better...
Null hypothesis(H0) vs Alternative hypothesis(H1)
(H0): Men do NOT earn more than women (men and women earn equally)
(H1): Men earn more than women (men and women earn differentially)

3. Statistical significance
Psychological research – subject to probabilities
You cannot ‘prove’ something, you need to have some probabilities
a p-value of 0.05 or below indicates that a finding is significant (i.e. it is the threshold)

4. p value
p value < .05 – the likelihood that you found a relationship or difference (as you initially observed) by random chance is smaller than .05%. So you can be (at least) 95% sure that what you found is not because of random chance.

5. Type I – Type II errors

6. Session Overview Central tendency measures
Means, SD, and distributions

7. Central tendency measures
For continious data
Mean
Median
Mode
Range
For categorical data
Frequencies

8. Means
A measure of ‘central tendency’; the average = the arithmetic mean
A way of describing a sample of continuous data
Add values of each participant and divide by the sample size

9. Data Window: Data View

10. Median Median is the value that cut your sample in half
If you have a sample of 9 participants, you rank your values and the value of the 5th person – the median
1,1,2,3,4,5,5,6,7 => Median = 4
If you have a sample of 10 participants, you rank values and the average value of 5th and 6th persons
1,1,2,3,4,5,5,6,7,8 => Median = 4.5

11. Mode
Simply the most frequent value in your data set
1,1,2,3,4,5,5,6,7

12. Range Range = the highest value – the lowest value 1,1,2,3,4,5,5,6,7

13. Exercise Find mean, mode, median and range for these values
13, 18, 13, 14, 13, 16, 14, 21, 13

14. Standard Deviation (SD)
A measure of dispersion or spread of data from the mean
When values clustered around mean, SD is low
When values spread away from mean, SD is high
There is no such thing as a ‘good’ standard deviation

15. Standard deviation example
Dataset 1:
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5
Dataset 2:
3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5
Which dataset has the lower SD?

16. Normal Distribution

17. A Normal Distribution

18. Characteristics of a Normal Distribution
The distribution is bell-shaped
The curve is symmetrical around a single mid-point at which the mode, median and mean are equal to each other

19. Normal Distribution & Std Deviation

20. Research Methods in Psychology PSY 311
Week 3: Means, standard deviations & distributions
Dr Sabahat Çiğdem Bağcı

21. Normal Distribution & Std Deviation

22. Sample Size & Normal Distributions
The higher the sample size, the more the distribution gets closer to normal distribution

23. From Samples to Population
Why increasing sample size affects the distribution?
Population distribution
Sample 2
Sample 1
Sample 3
Sample 4
Population mean

24. Sampling Distributions
If you sampled a number of people from a population you could obtain sample statistics e.g. the sample mean (e.g. Mean IQ)
If you collected this mean for a number of different samples from the same population and plotted the means, you have a “sampling distribution of the means”
The more samples you obtained, the closer the mean of these sample means would be to the population mean
If you collected so many samples that you covered all people in the population, the mean of these samples would be the same as the population

25. Standard Error of the mean
A measure of dispersion (SD) of the sampling distribution of the a statistic (e.g. the mean)
The greater the standard error, the less precision of a sample statistic (i.e. how accurately any one sample represents the population)
Sample mean
Standard deviation
Sampling distribution of the means
Standard error

26. Non-normal Distributions -Skewness
Negative Skew
Positive Skew
Most people gave higher ratings, e.g. Self-esteem
Most people gave lower ratings, e.g. Aggression

27. Non-normal Distributions - Kurtosis
Leptokurtic
Platykurtic
Most people gave similar ratings around the mean, low SD
Most people gave many different ratings than the mean, high SD

28. Skewness
Skewness > 0 - Right skewed distribution - most values are concentrated on left of the mean, with extreme values to the right.
Skewness < 0 - Left skewed distribution - most values are concentrated on the right of the mean, with extreme values to the left.
Skewness = 0 - mean = median, the distribution is symmetrical around the mean.

29. Kurtosis
Kurtosis > 3 - Leptokurtic distribution, sharper than a normal distribution, with values concentrated around the mean.
Kurtosis < 3 - Platykurtic distribution, flatter than a normal distribution with a wider peak. The values are wider spread around the mean.
Kurtosis = 3 - Mesokurtic distribution - normal distribution for example.

30. SPSS Analysis
Everything works through the ‘Analyze’ menu

31. Descriptive Statistics
For counts and percentages
Analyse – Descriptive Statistics – Frequencies
For means, modes, medians and standard deviations
Analyse – Descriptive Statistics - Descriptives

32. Frequencies

33. Frequencies Output

34. Descriptives

35. Descriptives Output

36. Producing Graphs/Charts

37. Checking for normality