PSY300: Advanced Methods in Psychology
Lecture 1
Revision: Means, Means and More Means!
Two Types of Data
- Ratio and interval scale parametric data
- Ordinal and nominal non-parametric data
- This distinction determines the types of statistical analyses that may be applied to the data
Parametric: Centrality and Spread
M = (ΣX)/N
2 2
SD = (Σ(X-M) )/N
SD = √
Z Scores
- A Z score is the number of standard deviations a score is above or below the mean
- Formula to change a raw score to a Z score: Z = (X-M)/SD
- Formula to change a Z score to a raw score: X = (Z) (SD) + M
The Normal Distribution
- “If you get 8/10 on a Wordsum, and it was normally distributed, what top % of the distribution
would you occupy?”
- “If we wanted to contact „at risk‟ individuals, defined as the lowest 2% (Z < -2), what Wordsum
score would we use as a cutoff to recognise such individuals?”
Independent Samples t-Test
- Shape: t-distribution with df based on two samples: df Total df1+ df 2
- Observed t-score for the difference between the two actual means: t = (M – 1 )/S 2 Difference
- If the observed t-score above is larger than the critical value of t for p = .05, the null hypothesis is
rejected
Theory of ANOVA
- Total SS: We calculate how much variability there is between scores (total sum of squares; SS ) T
- Between SS: We then calculate how much of this variability can be explained by the model we fit to
the data; ho

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