1.3 Data Recording, Analysis and Presentation Design of raw data recording tables Use of raw data recording tables Standard and decimal form Significant figures Estimations from data collected

This is raw data >>> Psychological investigations that collect quantitative data tend to generate quite a lot of results – one or more scores for each ppt This is raw data >>> Unprocessed In purest form

Psychologists may wish to present raw data in a number of ways: Fractions Decimal form Standard form Percentage Ratio Significant figures

Fractions

Decimal form

Standard form

Percentage

Ratio

Significant figures

In psychology, we take the raw data found and can run… Descriptive statistics Inferential statistics

1. Descriptive statistics Descriptive statistics are broken down into two categories: Measures of central tendency Measures of dispersion

Measures of central tendency There are different measures of central tendency: The mean The mode The median

The mode The mode is the most frequent score in a set of results EXAMPLE: 1 5 6 7 7 7 11 18 Note; you should always write the numbers in order to see the most frequent number with ease

The mode If two or more scores are equally common there will be two or more modes EXAMPLE 1 1 1 2 5 7 7 7 11 11 11

THE MODE A researched asks participants to decide whether their last dream was active, inactive, or mixed. The researcher found out of 50 people 12 said active, 36 said inactive, and 2 said mixed. The mode would be 36/50 inactive

The mode Summary: MOST COMMON Effective when data is nominal Categorises only – does not describe accurately when there are more than one mode Very unrepresentative of data

Both medians are similar The median To calculate the median you need to present the data in order from smallest to largest. You then select data in the middle of the list Scores with an even number of data? There will be two middle numbers. These should be added together and divided by two Example Bus drivers: 11 12 13 20 22 25 26 28 30 20+22=42 42/2=21 so the median is 21 Non bus drivers: 1 4 9 15 20 24 25 30 37 39 20+24=44. 44/2=22. so the median is 22 Both medians are similar This suggest there is nondifference between intelligence of bus drivers and non bus drivers

The median Summary: MIDDLE MOST NUMBER Not affected by extreme scores Value may not actually appear in data set More tedious than mode and mean

The mean Usually called the 'average’ The mean is calculated by adding up all the scores in the data set by dividing the total number of scores. This does include any 0’s

The mean Summary: THE AVERAGE  Makes use of all the values in the data set  If extreme values are included it can distort results

What types of data can be used? The mode can be used with any type of data. It is the only measure of central tendency that can be used with nominal data The median cannot be used with nominal data, but can be with any other type of data The mean can only use interval or ratio data

Graphs and tables A3 handout LINE GRAPH BAR GRAPH PIE CHART SCATTER DIAGRAM HISTOGRAM

What is your favourite Psychologist? Freud? Milgram? Bandura? Sperry? Loftus? Tally up the number of responses for each psychologist

You should now convert these numbers into decimals You should divide the value by the total number of values Example: Freud… 8 people out of 20 8/20 =0.4

Now convert these into percentages Times the decimal by 100 EXAMPLE: Freud 8 people out of 20 8/20 = 0.4 0.4 x 100 = 40%

Let’s create a pie chart To draw a pie chart you will need a protractor. Firstly draw a circle, then each portion of the pie can be worked by the percentage of the 360 degrees of a circle. This done by multiplying the decimal x 360 Freud 8 people out of 20 8/20 = 0.4 0.4 x 360 = 144

http://www.ocr.org.uk/Images/266938-descriptive-statistics-teacher-guide.pdf

The second component of descriptive statistics is… MEASURES OF DISPERSION Range Variance Standard deviation

The range Identify the largest and smallest value Remember with this example the medians were similar In this case, the ranges are quite different This tells us about the diversity of ability amongst bus drivers Identify the largest and smallest value Subtract the smallest value from the largest value Then add 1 Example Bus drivers: 11 12 13 20 22 25 26 28 30 30 – 11 = 19, 19+1 = 20… Range = 20 Non bus drivers: 1 4 9 15 20 24 25 30 37 39 39 – 1 = 38, 38+1 = 39…. Range = 39

The range Not representative of data set when there is extreme scores – one really large number or really small number (ie an outlier) Fails to take into account quantity of numbers involved

The variance Just as the mean can tell us more than the mode, the measurement ‘variance’ tells us more than the range Rather than looking only at extreme scores of the data set, the variance considers the difference between each data point and the mean – this is called the deviation

The variance These deviations are then squared Added together Then the total is divided by the number of scores in the data set And then minus one This is represented by the formula

Variance Before we begin to calculate, note you always do the parts of the sum in brackets first EXAMPLE DATA SET BUS DRIVERS: 2, 15, 6, 8, 14, 19, 9, 4, 8, 13

Variance Step 1: calculate the mean (x̄) Add all the numbers together: 98 Divide the total by the total number in data set: 10 98+10 = 9.8 Therefore, mean (x̄) = 9.8

Variance Step 2: Write down the number of scores (n) In this case n=10

X X - (x̄) (X-x̄)² 2 15 6 8 14 19 9 4 13 Variance Step 3: Draw a table with 3 column and write the scores (values of X) down in the first column

X X - (x̄) (X-x̄)² 2 7.8 15 5.2 6 3.8 8 1.8 14 4.2 19 9.2 9 0.8 4 5.8 13 3.2 Variance Step 4: Work out the difference between each score Remember: X-x̄ 2-9.8 = 7.8 15- 9.8 =5.2

Variance Step 5 Square each of these differences X X - (x̄) (X-x̄)² 2 7.8 60.84 15 5.2 27.04 6 3.8 14.44 8 1.8 3.24 14 4.2 17.64 19 9.2 84.64 9 0.8 0.64 4 5.8 33.64 13 3.2 10.24 Variance Step 5 Square each of these differences

Variance Step 6 Add together the column of differences X X - (x̄) 2 7.8 60.84 15 5.2 27.04 6 3.8 14.44 8 1.8 3.24 14 4.2 17.64 19 9.2 84.64 9 0.8 0.64 4 5.8 33.64 13 3.2 10.24 225.6 Variance Step 6 Add together the column of differences

Variance Step 7 Take the total (255.6) and divide this by n-1 (10-1) 225.6 + 9 = 28.4

Variance The variance tells us about the dispersion of a group (how varied the results are)

Standard deviation If the mean is 3.08 and the SD is 0.64 This means the data on average is 0.64 above (3.72) or below (2.44) the mean

Standard deviation The variance is always written squared. If you find the square root of 28.4 = 5.33 (SD) . Each data point is on average 5.33 away from the mean (9.8) SD = 5.33