Quantitative Data Analysis for Social Science Rsearch

Measures of central tendency used to analyze quantitative data for basic research methods

1. Quantitative Data Analysis

2. Statistics

3. Frequency Distributions Data from one variable may be presented as counts or percentages E.g. Data from a study conducted on campus may summarize the number of respondents from each department as follows: Department No. of Students Percent_ Humanities & Ed 62 25% Social Sciences 41 16% Science & Tech 69 28% Business 78 31% TOTAL 250 100%

4. Measures of Central T endency Mean—arithmetic average Median—midpoint in a distribution Mode—most frequent score

5. MEAN What it is Arithmetic average Sum of scores _____________________________________________________________________________________________________________________________________________________________________________________________________________________________ number of scores

6. How to compute it when n is odd Order scores from lowest to highest Count number of scores Select middle score How to compute it when n is even Order scores from lowest to highest Count number of scores Compute X of two middle scores MEDIAN What it is Midpoint of distribution Half of scores above and half of scores below

7. To identify the median for the data set (with an even number of scores): 2, 5, 3, 4, 1, 6, 7, 4, 3, 2, 2, 1, 6, 5 First, arrange the set in numerical order: 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7 Find the middle position by dividing the number of scores by 2 14 ÷ 2 = 7 (There is no single middle position) The median is located between the 7 th and 8 th scores. It is calculated by adding the scores in these two positions and dividing the result by 2. (3 + 4) ÷ 2 = 7 ÷ 2 = 3.5 The median score is 3.5

8. MODE What it is - Most frequently occurring score A marketing survey asked 1000 children to identify their favourite beverage. The results are shown below.

9. Bivariate Analysis Data analysis procedures involving TWO variables are said to be bivariate. Examples of bivariate analysis procedures include: Cross-tabulation (Contingency tables)

10. Cross-tabulation An example Suppose we had data from 20 people about their preference of political party. The group, consisting of both males and females indicated whether they preferred the Here and Now Democratic Set (HANDS) or the Followers of Old Tradition Set (FOOTS). The data collected are on the next slide.

11. Cross-tabulation Sex Preference Sex Preference F FOOTS F HANDS F HANDS M HANDS M FOOTS F FOOTS M HANDS F HANDS F FOOTS M FOOTS M HANDS F HANDS F HANDS M FOOTS M FOOTS F HANDS M HANDS M HANDS F HANDS M FOOTS

12. Cross-tabulation Notice that there are TWO variables, Sex and Preference of Party. Each variable has two conditions. Sex: Male; female Preference of Party: HANDS; FOOTS We can display this data in cross-tabulation form. A cross-tabulation table is a two-dimensional grid with one variable represented on each dimension Cross-tabulations are useful with categorical data (variables measured on the nominal and ordinal levels of measurement)

13. Leacock, Warrican & Rose (2009)   Party Preference S EX   HANDS FOOTS Female     Male   *   Each respondent contributes a ‘count’ to only ONE cell. E.g. A respondent who is male and preferred HANDS would contribute a count to the cell marked by the asterisk (*) Cross-tabulation

14. This is a 2 x 2 (two by two) table because each variable has two conditions: sex – male, female; preference – HANDS, FOOTS. This is also called a contingency table . This cross-tabulation summarises that data from our example. Cross-tabulation

15. Using a cross-tabulation helps with organising the data in a manner that makes it easier to see how they are distributed over the two variables. It presents a better view of the preferences of the males and females in the group. Cross-tabulation

16. Simple Correlation Sometimes we have two continuous variables (variables on the interval or ratio levels of measurement) and we want to describe the relationship between them. To do this we may run a simple correlation. Correlation may also be used with data on the ordinal level of measurement. This procedure yields a coefficient that indicates the size of the relationship and the direction .

17. Leacock, Warrican & Rose (2009) Direction – Correlation coefficient may be positive (+) or negative (-). Positive correlation – A high (or low) score on one variable is matched by a high (or low) score on the other variable. Negative correlation – A high score on one variable is matched by a low score on the other variable. Simple Correlation

18. Size – Correlation coefficient ranges from 0 to 1. Coefficient Correlation Relationship 0.90 – 1.00 Very High Very Strong 0.70 – 0.89 High Marked 0.40 – 0.69 Moderate Substantial 0.20 – 0.39 Low Weak <0.20 Slight Negligible Simple Correlation

19. Leacock, Warrican & Rose (2009) Simple Correlation

20. Leacock, Warrican & Rose (2009) Relationships between two variables can be investigated by the application of: Pearson Product Moment correlation coefficient (interval and ratio data) Spearman Rank Order (rho) coefficient (ordinal, interval and ratio data) Cross-tabulation (nominal data) Simple Correlation