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Lesson 5 QUANTITATIVE DATA ANALYSIS Central tendency Which measure of central tendency should be used? 5 QUESTIONS Complete the 5 questions on the sheet Standard deviation What does this describe? How do we work this out? Step 1? Step 2? Step 3? Step 4? Step 5? Standard deviation 1. Work out the mean of the results first 2. Find this for each value 3. Sum add these numbers together 4. Divide total amount by n-1 5. Take the square root of your answer Standard deviation Score on memory test (male) 14 12 12 13 10 16 Calculate SD to 3 significant figures How can standard deviation help you understand results? Why is standard deviation used instead of the range? Better measure of spread as it less affected by extreme values Takes all of the scores into account These are scores from a memory test Comment on these results in pairs – feedback to class Female average score was higher than male Female SD higher that males – meaning their scores were more spread out than males and therefore the scores were less consistent and more varied. Normal and Skewed Distribution Normal and skewed distribution Small samples – central tendency and standard deviation useful statistics Larger samples – useful to examine overall distribution formed by the data Examining distributions can show trends in the data and we can estimate the distribution of scores in the whole population Normal and Skewed Distribution If mean, median and mode are the same/similar and focus around the middle set of scores (median) then there is normal distribution Multi-modal (more than one mode)– not normally distributed When mean, median and mode are not similar – distribution will be skewed Data is mainly above mean – negative skew – Mode> median < Mean Data is mainly below mean – positive skew – Mean> median> mode Normal Distribution Mean=Median=Mode Bell shaped curve Mean, median and mode should be aligned around the mid -point Tail ends shouldn’t meet the horizontal axis We can estimate the % of people that fall under the curve at each standard deviation 68% of the population fall between one standard deviation and 2 standard deviations etc…. Distribution – only considered for interval data (have known scores) So that mathematical calculations can be carried out Ordinal Interval Nominal Categories. This is simply putting items together without ordering or ranking them. E.g. obedient or not obedient e.g. tallies are made when observing behaviour Elements of the data describe properties of objects or events that are ordered by some characteristic (e.g. Rating on a scale of 0-10 for attractiveness where 0 is less attractive and 1- is attractive?) The order of the objects does not, however, provide any information about the distance along the continuum between any two adjacent items. Actual scores that are mathematical in having equal intervals between the so that calculations can be conducted. E.g. reaction times, number of words recalled. age, height. Ordinal. Elements of the data describe properties of objects or events that are ordered by some characteristic (e.g. Rating on a scale of 0-10 for attractiveness where 0 is less attractive and 1- is attractive?) The order of the objects does not, however, provide any information about the distance along the continuum between any two adjacent items. Interval. Actual scores that are mathematical in having equal intervals between the so that calculations can be conducted. E.g. reaction times, number of words recalled. age, height. Nominal. Categories. This is simply putting items together without ordering or ranking them. E.g. obedient or not obedient e.g. tallies are made when observing behaviour Link to other side of the course – which statistical test would you use for this type of data? Behaviour observed on bus Tally (frequency) Giving up seat 1111 Not giving up seat 11 Examples: TIME OF DAY on a 12-hour clock RELIGIOUS PREFERENCE: 1 = Buddhist, 2 = Muslim, 3 = Christian, 4 = Jewish, 5 = Other POLITICAL ORIENTATION: Left, Center, Right Examples: LEVEL OF AGREEMENT: No, Maybe, Yes MEAL PREFERENCE: Breakfast, Lunch, Dinner POLITICAL ORIENTATION: Republican, Democratic, Libertarian, Green POLITICAL ORIENTATION: Score on standardized scale of political orientation RANK: 1st place, 2nd place, ... last place Video - draw out with video and make notes https://www.youtube.com/watch?v=xpbYKaEbcPA ? Positive or negative? Why? Label where the mode median and mean would be Imagine it is a whale! Whale swimming towards vertical axis – coming home positive Away from vertical axis – leaving home negative ? Label where the mode median and mean would be ? ? ? Question 1 1. Work out the mean, median and mode for each set of scores (3 marks) 2. Is the set of scores for the ‘sound alike’ condition normally distributed? Explain your answer (2 marks) Task 2 – complete questions 1,2 and 3 of the sheet Participants in a memory study were tested on their recall of a list of 15 words. Mean number of words recalled was 10 Median was 11 And the mode was 15 a. Sketch a graph showing he most likely distribution curve for the results. b. What type of distribution is shown on your graph?