1. Frequency distributions and graphing data: Levels of Measurement Frequency distributions Graphing data

2. Stages in scientific investigation: Obtain your data: Usually get data from a sample, taken from a population. Descriptive statistics: Reveal the information that's lurking in your data. Inferential statistics: Use data from a sample to reveal characteristics of the population from which the sample data were presumably selected.

3. Levels of measurement: 1. Nominal (categorical or frequency data): When numbers are used as names. e.g. street numbers, footballers' numbers. All you can do with nominal data is count how often each number occurs (i.e. get frequencies of categories).

4. 2. Ordinal: When numbers are used as ranks. e.g. order of finishing in a race: the first three finishers are "1", "2" and "3", but the difference between "1" and "2" is unlikely to be the same as between "2" and "3". Many measurements in psychology are ordinal data - e.g., attitude scales.

5. 3. Interval: When measurements are made on a scale with equal intervals between points on the scale, but the scale has no true zero point. e.g. temperature on Celsius scale: 100 is water's boiling point; 0 is an arbitrary zero-point (when water freezes), not a true absence of temperature. Equal intervals represent equal amounts, but ratio statements are meaningless - e.g., 60 deg C is not twice as hot as 30 deg! Many measurements in psychology are interval data - e.g., IQ scores. -4 -3 -2 -1 0 1 2 3 4 1 2 3 4 5 6 7 8 9

6. 4. Ratio: When measurements are made on a scale with equal intervals between points on the scale, and the scale has a true zero point. e.g. height, weight, time, distance. Measurements in psychology which are ratio data include reaction times, number correct, error scores.

7. Frequency distributions: 50 scores on a statistics exam (max = 100): 8482727072 8062968668 6887898582 8785848889 8686787081 7086887969 7961687577 9086788981 6791827377 8078768683

8. Raw (ungrouped) Frequency Distribution: ScoreFreqScoreFreqScoreFreqScore Freq 961866761660 950852751650 940842740640 930831731630 920823722621 911812710611 901802703 893792691 882783683 872772671

9. Class interval width = 3 ScoreFrequency 94-961 91-931 88-906 85-8710 82-846 79-816 76-786 73-752 70-725 67-695 64-660 61-632 Class interval width = 5 ScoreFrequency 95-991 90-942 85-8915 80-8410 75-799 70-746 65-695 60-642 Grouped Frequency Distributions:

11. ScoreRaw Freq. (=total in each cell) 94-961 91-931 88-906 85-8710 82-846 79-816 76-786 73-752 70-725 67-695 64-660 61-632 Cumulative Frequency Distributions: Cumulative freq. (=each cell total + all preceding cell totals) 50 49 48 42 32 26 20 14 ( = 2+5+5+0+2) 12 ( = 5+5+0+2) 7 ( = 5+0+2) 2 ( = 0+2) 2 ( = 2) Cumulative freq. (= cum. freq. as % of total) 100 98 96 84 64 52 40 28 ( = (14/50)*100 ) 24 ( = (12/50)*100 ) 14 ( = (7/50)*100 ) 4 ( = (2/50)*100 )

13. Relative Frequency Distributions: Useful for comparing groups with different totals. Group A: N = 50 ScoreRaw Freq. 96-1003 91-954 86-9011 81-8515 76-808 71-754 66-702 61-653 Total:50 Group B: N = 80 ScoreRaw Freq. 96-1003 91-954 86-9018 81-8524 76-8011 71-759 66-705 61-656 Total:80 Rel. Freq. 6 % 8 % 22 % 30 % 16 % 8 % 4 % 6 % 100 % Rel. Freq. 3.75 % 5.00 % 22.50 % 30.00 % 13.75 % 11.25 % 6.25 % 7.50 % 100 % Relative frequency = (cell total/overall total) x 100

14. Raw Frequency and Relative Frequency Distributions: Only the scale of the graph changes - not the pattern of frequencies.

16. Effects of aspect ratio and scale on graph appearance: (a) A graph aimed at giving an accurate impression...

17. (b) A tall thin graph exaggerates apparent differences...

18. (c) A low wide graph minimises apparent differences...

19. (d) Starting the scale at a value other than zero can also exaggerate apparent differences.