Research Methods Week 5 Descriptive Statistics Review Primary

Research Methods Week 5 Descriptive Statistics

Review: Primary Research Designs Descriptive Study - specific predictions, with narration of facts and characteristics concerning individual, group or situation Diagnostic Study - the frequency with which something occurs or its association with something else. The studies concerning whether certain variables are associated are examples of diagnostic research studies. Data collection - observation, questionnaires, interviewing, examination of records

Primary Research Designs Diagnostic Study - the frequency with which something occurs or is associated with something else – i. e. if we see X, how often do we also see Y? Data collection – Observation – count X and Y Questionnaires / interviews – ask about X & Y (but be careful of bias) Examination of records – count X & Y

Primary Research Designs Diagnostic Study - if we see X, how often do we also see Y? Practice – Do people in white cars leave work earlier than people in non-white cars? Observation – count cars and car color every five minutes – 3: 30 – 4: 15

Observation Counts Observation – count cars and car color every five minutes – 3: 45 – 4: 15 Time 3: 45 3: 50 3: 55 4: 00 4: 05 4: 10 White cars Non-white cars

Statistical Descriptions Why? We want to be able to describe a data set. It is helpful if we can summarize the data and explain its most important attributes. A common starting point is these four descriptions: � Mean � Median � Mode � Standard Deviation

Statistical Descriptions Mean – Also called “average” The most common descriptor, we use it every day to sum up a set of data. Sum of counts / number of items Example – Mean (average) temperature in January: 24 + 23 + 25 + 22 + …. / 31 days Mean height of students in this class 198 cm + …… / number of students

Statistical Descriptions Mean – Also called “average” Sum of counts / number of items Mean exit time = total white cars / 6

Statistical Descriptions Graphic Display 25 20 15 Series 1 10 5 0 1 2 3 4 5 6 Display shows how “regular” the counts are

Statistical Descriptions Graphic Display 25 20 15 Series 1 10 5 0 1 2 3 4 5 6 What if the counts are not regular, but skewed to one end? The mean in this case is misleading

Problems with the Mean The mean misleads whenever one item in the count is exceptional: Person Annual income Joe 12000 Sharma 14000 Ed 9000 Ismail 8000 Sue 9000 Donald Trump 1111000 Total income 1163000 Average income 193833 Would it be fair to say the “average” person in this company earns $193, 833?

Normal distribution 10 Axis Title For many populations we expect a standard curve – a few at each end, and most in the middle. We are used to seeing that curve in such things as intelligence measurements. In a “normal” distribution, the mean is a good reflection of the sample. 12 8 6 4 Series 2 1 Series 1 0 2 0 1 2 3 4 5

What if things aren’t “normal”? 10 Axis Title We just saw a set of incomes that did not follow that curve. Many other data sets are equally irregular. Think of things like population statistics (there are often clusters of age groups), or behaviors (people who have traveled probably cluster around “lots” and “little. ”) 12 8 6 4 Series 2 1 Series 1 0 2 0 1 2 3 4 5

Using the median The mean works well for normal distributions but misleads whenever one item in the count is exceptional. The Median defines where half of the population lies. We arrange items in an order and find the middle. Which more accurately reflects the typical employee earnings at this company, $193, 833 or $10, 500? Person Annual income Ismail 8000 Ed 9000 Sue 9000 Joe 12000 Sharma 14000 Donald Trump 1111000 Median income 10500 Mean income 193833

Practice Find the mean and median of the number of tickets issued to this set of drivers. Which number more accurately reflects the quality of Omani drivers? Person Annual speeding tickets Ismail 8 Ed 3 Sue 2 Joe 12 Sharma 14 Bill 0 Amal 0 Fatma 0

Using the mode The mode helps us describe situations where the data seem to cluster. For example, in the case off traffic violations, you may hear people talk about a “bimodal distribution. ” They mean people seem to fall into two groups – safe drivers and non-safe drivers. There is no real “average” driver. 3, 5 3 2, 5 2 1, 5 1 0, 5 0 Series 1 none to 5 more than 5

Examples of the mode Where else might there be no average? 3, 5 3 2, 5 2 1, 5 1 0, 5 0 Series 1 none Mall sizes in Nizwa Tourist season Daily rainfall Others? one to 5 more than 5

Our car sample What is the mean, median, and mode of our white cars? Excel functions – �Graphing – insert column �Statistics – Formulas, more functions, statistics � Average (mean) � Median � Mode. sngl

Our car sample �What is the mean, median, and mode of the nonwhite cars? Is their pattern normal? - graph Do the two groups differ? – compare graphs

Our car study �Compare the graphs and the mean, median, and mode of the cars? Is their pattern normal? - graph Do the two groups differ? – compare graphs

Our car sample �If you were doing a descriptive study of car patterns, how would you describe what you saw?

Our car sample �If you were doing a diagnostic study of car patterns, how would you describe what you saw?

Our car sample �If you were going to do a hypothesis testing study, what initial hypotheses could you form based on our little sample?

Next week �Test first hour �Statistics – could we show if white cars leave earlier than on-white cars?