Section 4: How to Analyse Quantitative data? What is statistics? Factors affecting how data are analyzed Sampling and Statistical Significance 2015 Research Methods (HK)

What is statistics? A statistics is a summary statement about a set of data; statistics as a discipline provides techniques for organizing and analyzing data. 2015 Research Methods (HK)

Factors affecting how data are analyzed Whether to use the data for descriptive or inferential purpose Univariate, bivariate and multivariate The level of measurement of the variables: nominal, ordinal, interval and ratio 2015 Research Methods (HK)

Descriptive Statistics Descriptive Statistics is concerned with organizing and summarizing the data at hand to make them more intelligible. (易領悟) For e.g. The highest and lowest scores and average score on an exam are descriptive that summarize a class’s performance in the examination. 2015 Research Methods (HK)

Inferential Statistics Inferential statistics deals with the kinds of inferences that can be made when generalizing from data, as from data to the sample data to the entire population. It is based on probability theory, inferential statistics may be used for 2 district purposes: **to estimate population characteristics from sample data; **to test hypotheses 2015 Research Methods (HK)

Univariate Analysis What is univariate analysis? The five aspects to be determined in preparing a univariate analysis. 2015 Research Methods (HK)

What is univariate analysis? Definition of univariate analysis “It is an examination of the distribution of cases on only one variable at a time.” Babbie (2005) The analysis of a single variable for purposes of description. The aim is to get a clear picture of the data by examining one variable at a time It is useful to see there is sufficient variation between the findings of the values The less variation, the more difficult in detecting how differences in one variable are related to differences in another variable 2015 Research Methods (HK)

Distribution Frequency Distribution e.g. Out of the 120 students; 65 of them are male and while 55 are female Percentage Distribution e.g. Out of the 120 youths; 54.2% of them attended some type of protest and while 45.8 have no experience of political participation 2015 Research Methods (HK)

Central tendency Mode (most frequent) An average representing the most frequently observed value. Median (midpoint) An Average representing the value of the ‘middle’ case in a rank-ordered set of observations. Mean (arithmetic average) An average computed by summing the values of several observations and dividing by the number of observations. See Babbie (2004) pp404 for the diagram 2015 Research Methods (HK)

Dispersion Range Standard Deviation The distance separating the highest and lowest values. It is the simplest way to detect dispersion. Standard Deviation The standard deviation is an index of the amount of variability in a set of data. A higher SD means that the data are more dispersed; a lower SD means that they are more bunched together. 2015 Research Methods (HK)

Standard Deviation (SD) II E.g. Here is the hypothetical mean & SD on an index of Life Satisfaction in 4 Western countries: Country Mean SD England 6.7 1.0 Germany 6.7 1.2 Italy 6.6 3.2 U.S.A. 6.5 1.3 2015 Research Methods (HK)

Standard Deviation (SD) III What conclusion can we make out of this set of data?? The mean scores are almost identical, implying that satisfaction with life is similar in the countries studies. However, there are differences in the standard deviations in England, Germany, & U.S.A. indicated that these countries are homogenous as far as satisfaction is concerned. Italy, however, the dispersion is greater, suggesting that the degree of satisfaction reflected by the mean is not common to all the Italians in the group studies. 2015 Research Methods (HK)

Bivariate Analysis What is Bivariate Analysis? Crosstabulation and Chi Square Association between Variables Note on Sampling & Statistical Significance 2015 Research Methods (HK)

When to use Crosstabulation? Xtab tables are useful to illustrate relationships between variables, but require that the variables be expressed in only a few categories. The larger the table, the more difficult it is to interpret. 2015 Research Methods (HK)

Crosstabulation I A way of displaying data in order to readily detect association between 2 variables. e.g.: Smoking* by Marital Status* Marital Status Married Never Married Smoking___________________________________ Yes 21.5% 56.5% No 78.5% 43.6% TOTA L 100% 100% 2015 Research Methods (HK)

Let’s look at the following example: There are 2 variables that the researcher want to examine: Marital status is put across the top and yes/no for smoking in rows, each are having 2 categories. The crosstabulation table will have 2 columns and 2 rows; the so-called 2X2 table. There are 2 ways of presenting the crosstab table. The choice can either depend on what question is put and which set of data will give a more meaningful interpretation. 2015 Research Methods (HK)

Table 2a Smoking. by Marital Status Table 2a Smoking* by Marital Status* (Here we ask what is the smoking situation among the sub-groups of the married and the never married Married (N=130) Never Married(190) Smoking_______________________________________ Yes 50 (38.5%) 90(47.5%) No 80 (61.5%) 100(52.5%) TOTAL 100% 100% Analysis: Among the married, those who don’t smoke are far more than those who do. The difference is 23%. However, for the never married sub-group the difference is much more smaller: 5%. Discussion: It seems the married are more careful with their health. It is quite widely known that smoking is damaging to health. 2015 Research Methods (HK)

Married Never Married TOTAL Table 2b Smoking* by Marital Status* (Here we ask the marital status of the smoke and not smoke respondents) Married Never Married TOTAL Smoking______________________________________ Yes (N=140) 50 (35.7%) 90(64.3%) 100% No (N=180) 80 (44.4%) 100(55.6%) 100% Analysis: Among those who smoke, the never married sub-group has a much higher percentage (64.3%); while the married 35.7%. The difference is big: 28.6. For those who do not smoke, both sub-groups have a narrower difference:11.2% 2015 Research Methods (HK)

When to use Chi Square? (1) Chi Square Tests can answer two types of question: --about the sample --about the relationship of the selected variables http://www.youtube.com/watch?v=WXPBoFDqNVk 2015 Research Methods (HK)

Measures of Association I Measures of association is also know as correlation coefficients. A measure of association is a single number that expresses the strength, and often the direction, of a relationship. That is to say an index which provides a concise description of the character of the relationship between 2 variables. There are 5 measures of association: Lambda Gamma Tau Rho Chi-square 2015 Research Methods (HK)

Measures of Association II Summary of Measures of Association Measure Type of Data High Association Independence* Lambda Nominal 1.0 0____ Gamma Ordinal +1.0, --1.0 0____ Tau Ordinal +1.0, --1.0 0____ Rho Interval, ratio +1.0, --1.0 0____ Chi-square Nominal, ordinal Infinity 0____ *Independence means that knowledge of one variable does not reduce the chance of errors on the other variable. Means of association=0 if the variables are independent (no relationship). http://www.youtube.com/watch?v=cNrnSEWKJgg 2015 Research Methods (HK)

The character of relationships: Strength Direction Nature If there are large differences between subgroups, there is a strong relationship. 2015 Research Methods (HK)

Strength If there are large differences between subgroups, there is a strong relationship If the subgroup to which people belong makes a big difference to their characteristics on the DV, then the 2 variables are strongly related. 2015 Research Methods (HK)

Direction When dealing with ordinal or internal variables can describe direction of relationship: positive & negative +ve relationship: one in which people who score high on one variable are more likely than others to score high on the other variable & vice versa. Those with low education are most likely to be low income earners. -ve relationship: one in which people who are high on one scale tend to be low on the other & vice versa. 2015 Research Methods (HK)

Nature Association of ordinal or interval variables can be either linear or curvilinear. Linear—Percentages change in a consistent direction Curvilinear---Percentages change from high to low, then to high 2015 Research Methods (HK)

How to interpret Correlation Co-efficient The figure computed is also between –1 and +1. (Except the data obtained from nominal measurement, which can only be +1) The higher the figure the stronger the association; 0=no association; 1.00=perfect association Co-efficient for ordinal & interval data can have a minus sign in front which means the association is negative. The sign means nothing about the strength of relationship. --0.75 & 0.75 are equally strong relationship. The closer the co-efficient to 0, the weaker association there is. –0.15 & 0.15 are equally weak relationship. 2015 Research Methods (HK)

Note on Sampling & Statistical Significance I Researchers always aim at obtaining a representative sample. That is, a sample that can be treated as through it were the population. It is rare to have a perfectly representative samples, but the chance of forming a representative one can be considerably enhanced by probability sampling. 2015 Research Methods (HK)

Note on Sampling & Statistical Significance II *The topic of statistical significance examines the issue of how confident we can be that findings relating to a sample of individuals will also be found in the population from which the sample was selected. *In statistics, the word ‘significance’ does not mean ‘important’. Being significant in statistical sense refers to that the results are not due to chance. A statistical difference is that one which is not attributed to chance. *3 levels of significance are often used in research reports: 0.05, 0.01 & 0.001. These mean, respectively, that the chance of getting the measured association as a result of sampling error are 5/100, 1/100 & 1/1000. 2015 Research Methods (HK)

Summary of Section 4 You should have learned: ..what statistics is and how it relates to quantitative research ..univariate analysis ..bivariate analysis ..sampling and level of significance

Readings Babbie, E. Chapter 16: Statistical Analyses (Please cover INTRODUCTION, DESCRIPTIVE STATISTICS and INFERENTIAL STATISTICS only) 2015 Research Methods (HK)

One Big Reminder before I stop Please always refer to the published works of other social science scholars. Read on how they have conduct their researches and also on how they present their works. Good luck! THANK YOU! 2015 Research Methods (HK)