Stages in scientific investigation: Frequency distributions and graphing data: Levels of measurement:

Transcription

1 Frequency distributions and graphing data: Levels of Measurement Frequency distributions Graphing data 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. Levels of measurement: 1. Nominal (categorical or frequency data): When numbers are used as names. e.g. street numbers, footballers' numbers.. Ordinal: When numbers are used as ranks. e.g. order of finishing in a race: the first three finishers are "1", "" and "3", but the difference between "1" and "" is unlikely to be the same as between "" and "3". All you can do with nominal data is count how often each number occurs (i.e. get frequencies of categories). Many measurements in psychology are ordinal data - e.g., attitude scales. 1

2 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: is water's boiling point; 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., 6 deg C is not twice as hot as 3 deg! 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 Many measurements in psychology are interval data - e.g., IQ scores. Measurements in psychology which are ratio data include reaction times, number correct, error scores. Frequency distributions: Raw (ungrouped) Frequency Distribution: f f f f f f f f f RM1 exam scores, in order of size.

3 Grouped Frequency Distributions: Grouped Frequency Distributions: Class interval width = Frequency Class interval width = Frequency Frequency Raw frequency of exam scores (class interval =) Frequency Raw frequency of exam scores (class interval = ) Cumulative Frequency Distributions: Raw Freq. (=total in each cell) Cumulative freq. (=each cell total + all preceding cell totals) ( = ) 3 ( = ) 6 ( = 1++3) 3 ( = 1+) 1 ( =1) % cumulative freq. (= cum.freq. as % of total) ( = (6/46)* ) 1. ( = (3/46)* ).4 ( = (1/46)* ) Cumulative frequency (%) Cumulative frequency of exam scores % of students scored or less in the exam Exam score 3

4 Relative Frequency Distributions: Useful for comparing groups with different totals. Group A: N = Group B: N = 8 Raw Freq. Rel. Freq. Raw Freq. Rel. Freq % % % % % % % % % % % % - 4 % % % % Total: % Total: 8 % Relative frequency = (cell total/overall total) x Raw frequency Raw Frequency and Relative Frequency Distributions: Only the scale of the graph changes - not the pattern of frequencies. Raw Frequencies of s (N = ) Relative frequency (%) Relative Frequencies of s (N = ) Scatterplots and correlations: Useful for exploring relationships between variables. 15 students' coursework marks and exam marks: Effects of aspect ratio and scale on graph appearance: (a) A graph aimed at giving an accurate impression... coursework mark Correlation between coursework and exam marks 6 8 exam mark Each point represents one student's performance (exam mark and cwk mark). Pearson's correlation =.. Correlations range from +1 (perfect positive correlation) to -1 (perfect negative correlation).. is close to - i.e. no relationship between coursework and exam performance. 3 4

5 (b) A tall thin graph exaggerates apparent differences.. (c) A low wide graph minimises apparent differences.. 3 No. of accidents per year 3 (d) Starting the scale at a value other than zero can also exaggerate apparent differences. 3 5