Data analysis LO: Identify and apply different methods of measuring central tendencies and dispersion

Data analysis and Presentation (AQA Classification) Candidates should be familiar with the following features of data analysis, presentation and interpretation: Analysis and interpretation of quantitative data. Measures of central tendency including median, mean, mode. Measures of dispersion including range and standard deviation. Presentation and interpretation of quantitative data including graphs, scattergrams and tables. Analysis and interpretation of correlational data. Positive and negative correlations and interpretation of correlation coefficients. Presentation of qualitative data. Processes involved in content analysis.

Results of a word recall test from a list of 25 words: Central Tendency “General term for the midpoint or typical value of a distribution”. The ‘average’ value/score for each condition group on the DV measurement. Three main ways of measuring C.T: Mean, Mode, Median Results of a word recall test from a list of 25 words: 8, 10, 10, 10,10, 11, 11,12, 14, 25

[if two values are equally frequent, it is a bimodal dataset] MEAN: The sum total of the individual scores in the group divided by the number of people in it. 8+10+10+10+10+11+11+12+14+25= 121/10 = 12.1 MEDIAN: The numeric value separating the higher half of a sample from the lower half. So with numbers arranged in order, it is the middle value. 8, 10, 10, 10, 10, 11, 11,12, 14, 25  Median is MODE: The most frequent value in the dataset. 8, 10, 10, 10, 10, 11, 11,12, 14, 25  Mode is [if two values are equally frequent, it is a bimodal dataset] 10.5 10

MEAN: Uses all the values in the set, so is most ‘sensitive’ to variations in the data. BUT affected by atypical, extreme values. Used when data are normally distributed, unskewed and there are no outliers. MEDIAN: Less ‘sensitive’. BUT not affected by atypical, extreme values. Used when you can’t use the mean because of Skew or outliers. MODE: Does not give any information about other values. For many data sets there is no meaningful modal value, or their may be several. Only used when dealing with frequency data.

Organised List Random List 20 15 15 13 18 19 45 14 24 20 23 10 28 21 21 6 25 22 30 25 Exam Question: a) Identify a suitable measure of central tendency that could be used with these data. Justify your answer. (2 marks) Identification of the mean or median. There are no repeated scores in either list, so the mode would not be appropriate. Justification for the mean could be that it used all of the available data, that it is a powerful/sensitive measure or that it is suitable for use with interval/ratio data. Justification for using the median is that it is relatively unaffected by outlying scores.

Dispersion The variability or spread of scores within a data set (away from the mean). Range: - A simple measure showing the ‘total’ spread of data. Difference between highest and lowest scores in a set of data: top value minus bottom value. Affected by atypical, extreme values. 8, 10, 10, 10,10, 11, 11,12, 14, 25 (25 – 8) = 17 [(25 - 10.5) + (10.5 – 8)] = 14.5 + 2.5 = 17]

Standard Deviation: Considers the ‘distance’ of each measurement from the mean, the most accurate measure of dispersion. Thus gives the ‘average’ distance of any given measurement away from the mean. Standard Deviation = [Square root] of [sum of all squared deviations from the mean], [divided by N] (8-12.1)2 +(10-12.1)2 +(10-12.1)2 +(10-12.1)2 +(10-12.1)2 +(11-12.1)2 +(11-12.1)2 +(12-12.1)2 +(14-12.1)2 +(25-12.1)2 = 206.9 (root square that) = 14.4 / 10 = 1.44

Exam example (June 2011)

Presentation Quantitative Data Tables: need clear headings with the units of measurement. Number of Organised Words Recalled Number of Random Words Recalled 8 11 10 14 17 16 15 18 12 25 MEAN 12.1 16.1

Graphs: Bar chart: Discrete categories, bars 14 Graphs: Bar chart: Discrete categories, bars separated. Uses conditions’ Means for comparison. Histogram: X axis has continuous data, no gaps between bars. DV on X axis, frequency on Y axis. Scattergram: Continuous data on both X & Y axes. Showing the individual points of one variable plotted against the other variable. Used for correlation. 12 10

‘Conceptual’ Content Analysis A frequency analysis of the number of times certain words, concepts, themes, phrases, behaviours sentences, etc within text or during observation. Process of Analysis: - Sampling: The researcher must first decide which material to use in study (or Who to observe and How). - Pilot: Before actual analysis the researcher must become familiar with the types of material likely to be encountered - Framework: Deciding on the ‘Coding units’ and ‘Categories’ of those units to construct a system for categorising the data. - Procedure: Record the number of occurrences of a particular coding category.