Mod 4 data presentation graphs bar charts tables
- 1. Data representation & analysis • Descriptive statistics: measures of central tendency – mean, median, mode, calculation of mean, median and mode. • Presentation and display of quantitative data: graphs, tables, scattergrams, bar charts. • Introduction to statistical testing: the sign test. 1
- 2. Making sense of our data Descriptive statistics refer to the central tendency Inferential statistics refer to statistical techniques Descriptive statistics The mean Standard deviation The median The mode Inferential statistics Drawing conclusions from our set(s) of data
- 3. Tables of Raw Data • Show scores prior to analysis • Hard to identify patterns in the data • Raw data cannot tell us much 3
- 4. Participant No. Score on Memory Task (Control Condition) Participant No. Score on Memory Task using Imagery (Experimental Condition) 1 15 1 18 2 11 2 24 3 13 3 16 4 11 4 24 5 14 5 17 6 16 6 29 7 17 7 20 8 22 8 25 9 15 9 18 10 14 10 27 Raw Data Table Showing Scores for Control and Experimental Conditions on a Memory Task 4
- 5. Frequency Tables • More useful than a raw data table • Can organise the values into groups when there are a large number of them, e.g., a 24- hour period could be organised into 3-hour segments of 8 values • Patterns in the data are clearer 5
- 6. Frequency Table Showing Number of Hours Spent in Day Care Total number of hours spent in day care Number of Children Percentage (%) 12 1 2.0 11 1 2.0 10 2 4.0 9 3 6.0 8 9 18.0 7 2 4.0 6 15 30.0 5 4 8.0 4 10 20.0 3 1 2.0 2 2 4.0 1 0 0 Total N = 50 100 6
- 7. Summary Tables • Include: Measures of central tendency – mean, median, mode Measures of dispersion – range, standard deviation • Provide a clear summary of data 7
- 8. Summary Table Showing Stress Scores in No Exercise and Exercise Conditions Stress Score in No Exercise Group (Control Condition) Stress Score in Exercise Group (Experimental Condition) Mode 31 15.87 Median 30 16 Mean 30.67 16 Range 34 17 SD 8.96 4.41 8
- 9. 9 The mean is the average of a set of data. It is calculated by adding up all the numbers in a set of data and then dividing them by the total number.
- 10. 1. Starts from true zero, e.g., physical quantities such as time, height, weight 2. Are on a scale of fixed units separated by equal intervals that allow us to make accurate comparisons, e.g., someone completing a memory task in 20 seconds did it twice as fast as someone taking 40 seconds The mean makes use of all the data. The mean can only be used to measure data that: The mean is also affected by extreme scores
- 11. 11 Extreme scores • Time in seconds to solve a puzzle: • 135, 109, 95, 121, 140 • Mean = 600 secs ÷ 5 participants =120 secs • Add a 6th participant, who stares at it for 8 mins • 135, 109, 95, 121, 140, 480 • Mean = 1080÷6=180 secs
- 12. 12 Median • The middle value of scores arranged in an ordered list. • It is not affected by extreme scores. • It is not as sensitive as the mean because not all scores are reflected in the median.
- 13. 13 Mode • The mode is the value that is most common in a data set, e.g.,2, 4, 6, 7, 7, 7, 10,12 mode = 7. • It is useful when the data is in categories, such as the number of people who like blue, read books, play a musical instrument. • Not useful if there are many numbers that are the same.
- 14. 14 Disadvantages of the Mode Small changes can make a big difference, e.g., 1. 3, 6, 8, 9, 10, 10 mode=10 2. 3, 3, 6, 8, 9, 10 mode=3 Can be bi/multimodal, e.g., 3,5,8,8,10,12,16,16,16,20
- 15. 15 Calculating the mean, median and mode. • Complete the worksheet for task 2.
- 16. Using Graphs to Represent Data • Graphs summarize quantitative data • They act as a visual aid allowing us to see patterns in a data set • To communicate information effectively, a graph must be clear and simple and have: A title Each axis labelled With experimental data, the IV is placed on the horizontal x-axis while the DV is on the vertical y- axis 16
- 17. Bar Chart • Used to represent ‘discrete data’ where the data is in categories, which are placed on the x-axis • The mean or frequency is on the y-axis • Columns do not touch and have equal width and spacing • Examples: Differences in males/females on a spatial task Score on a depression scale before and after treatment 17
- 18. 1 2 4 8 Without Caffeine Group With Caffeine Group Meanreactiontime(secs) Bar Chart Showing Difference in Reaction times Between Groups Given a Caffeine Drink 18
- 19. Histogram • Used to represent data on a ‘continuous’ scale • Columns touch because each one forms a single score (interval) on a related scale, e.g., time - number of hours of homework students do each week • Scores (intervals) are placed on the x-axis • The height of the column shows the frequency of values, e.g., number of students in each interval – this goes on the y-axis 19
- 20. 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7 8 9 10 NumberofStudents(Frequency) Homework (hours per week) Histogram showing number of hours spent doing homework in a survey of students 20
- 21. Frequency Polygon • Can be used as an alternative to the histogram • Lines show where mid-points of each column on a histogram would reach • Particularly useful for comparing two or more conditions simultaneously 21
- 22. 0 5 10 15 20 25 30 35 40 Week 1 Week 2 Week 3 Week 4 Number of pro- social acts observed Behavioural Observations Frequency polygon showing number of pro-social acts observed in different day care settings Adam (Child Minder) Joe (Nursery) 22
- 23. Scattergram • Used for measuring the relationship between two variables • Data from one variable is presented on the x- axis, while the other is presented on the y-axis • We plot an ‘x’ on the graph where the two variables meet • The pattern of plotted points reveals different types of correlation, e.g., positive, negative or no relationship 23
- 24. 0 10 20 30 40 50 60 70 0 50 100 150 200 Daysoffworkperyear Stress Score Scattergram showing correlation between stress and absenteeism from work 24
- 25. Exam Hints • You must be able to: State the strength and direction of a correlation, e.g., a weak negative correlation or a strong positive correlation Interpret information in tables Interpret information in different types of graphs Know the most appropriate graph to use to display a given data set Correctly label columns and rows on all tables 25
- 26. Exercise • Groups of patients with depression were assessed after six months for the effectiveness of different treatments. The higher the score the greater their improvement. • Choose an appropriate graph to display the following data: Treatment Average Improvement in Symptoms Score CBT 67 Psychoanalysis 13 ECT 30 Medication 72 26