Measurement, Sampling and Data Analysis

1. Measurement, Sampling and Data Analysis

2. Measurement – Chapter 4 • If it exists, it is measurable! • Measurement is used to gain mathematical insight into our data • Measurement is a comparison – We compare our data to a standard such as the norm, average or expected outcome • Measurement is a standard used for evaluation

3. Measurement is an essential component of quantitative research • Through measurement we can inspect, analyze and interpret our information

4. The Language of Variables • A variable is any observation that can take different values • Gender, Age, Religion, Ethnicity are variables • Attributes are specific values on a variable • Attributes of Gender = 1. Male 2. Female Are discreet values • Age (may be continuous 0-100)

5. An indicator is the responses to a single question – The main concept in the question is the variable being measured • Concept – A mental image that summarizes a set of similar observations, feelings or ideas We may not all agree on the same definition of a concept – Concepts are abstracts- binge drinking, what is it exactly? • Conceptualization – specifying the dimensions of and defining the meaning of the concept

6. We often use concepts in our theories i.e. crime, abuse, deterrence, eating disorder, substance abuse, youth gangs, poverty, What do we mean by crime? How is it measured.

7. How can we measure our concepts for research? • Devise operations that actually measure the concepts we intend to measure • Operationalization of concepts – connect concepts to observations by identifying specific observations that we will use to indicate that concept in empirical reality. The process of choosing the variable to represent the concept

8. We use variables which are derived from concepts in our hypotheses • The variables move the concepts into the realm of testability – i.e. The indicator of crime is spousal abuse • Through the indicators of a variable we are able to ascertain the characteristics, behaviors, attitudes of our subjects

9. How it Works • Define the concept We have a theory that Punishment deters criminal behavior • Choose and indicator of the concept to represent it - The concept, punishment, is operationalized by using the variable, arrest to represent it. The indicators of the variable, arrest may be 1. arrest on first offense 2. Don’t arrest on first offense

10. The concept crime is represented in our research as physical spousal abuse. • The resulting hypothesis is: If subjects are arrested on the first reported offense of physical spousal abuse then they will be less likely to offend again (recidivism) The indicators of the variable, recidivism are 1. re-offend 2. doesn’t re-offend Our concepts are now defined in measurable, testable terms

11. However, some concepts are more concrete than abstract to begin with. • Age – time elapsed since birth. • However it may need more than this…i.e. how much time? How old in hours, months, years? How will we use age?

12. Sometimes we have to use qualitative means to define a concept • What is the public’s meaning of diversity? • What are women’s meaning of rape as versus that of men?

13. Through conceptualization and operationalization, measurement becomes the process of linking abstract concepts to empirical indicants • Measurement validity – The operations we devise to measure our data must assure that we measure the variables we intended to measure

14. For the concept social class, we can use the variables: income, education and occupation. • Now we get a much clearer picture of what indicators are necessary to measure the abstract concept, social class • Income can be measured by actual income • Education can be measured by years of education • Occupation can be measured by levels from not at all professional to being very professional

15. Measuring social variables is often done through questions posed to people • A single question may not be adequate for measuring a concept. Multiple questions may be necessary • The concepts age, gender, ethnicity, religion, income, education, occupation, are what is called demographic variables. These can be measured with one question. What is your age? • But more than one question is necessary to measure Social Class, ADD, Prejudice, Nurture • May need to construct an Index of question

16. Levels of Measurement • Levels of measurement have important implications for the type of statistics that can be used in analyzing the data for a variable • 4 Levels of measurement – Nominal, Ordinal, Interval and Ratio • These levels are determined by the indicators (response/answer categories) for a variable

17. Nominal – qualitative, has no mathematical interpretation, even if numbers are attached to the value label These are called categorical variables For example, we may ask What is your gender? And the answer categories are 1. male 2. female. However, the numbers 1 & 2 do not indicate anything mathematical about the differences in the answers. Female is not more or higher of gender than Male.

18. Quantitative Levels of Measurement • Ordinal – the numbers assigned to the response categories only indicate order. 1 is lower in order than 2, and 2 is lower in order than 3. • 1. Very Unimportant is lower in order than 2. Unimportant and 2. Unimportant is lower in order than 3. Important

19. Interval – The numbers indicating values in the response categories have mathematical meaning. • They represent fixed measurement units, but have no absolute or fixed zero point. • This is important mathematically because having a fixed zero point allows us to use the highest level of statistics • Often researchers try to use ordinal level variables as interval (i.e. Likert Scales)

20. In interval level variables the numbers can be added and subtracted but ratios are not meaningful • Fahrenheit Temperature is an interval level variable. 60 degrees is 30 degrees hotter than 30 degrees. But, 60 degrees can not be said to be twice as hot as 30 degrees because Fahrenheit temperature has no absolute zero. • There are very few true interval-level measures in social science. This is why researchers use ordinal level data as interval level data and score it in ways that allow them to do so

21. Ratio – The numbers attached to these response categories represent fixed measuring units and an absolute zero point. Age is a ratio level variable. Test Scores can be ratio. i.e. 0-100

22. SamplingHow to choose survey subjects? • Sample – A subset of people (population) selected for study i.e. 100 students from Webster selected • Population – larger group from which sample comes (will infer back to this group) i.e. All Webster students participate

23. Why Sample • If can’t access entire population (too costly, too huge) Sampling Goal • Representativeness – smaller group (sample) is representative of larger group (population) • Larger the sample, more confidence in it being representative • More homogeneous the population, more confidence of sample representativeness

24. If sample is representative, findings can be generalized to population. You can infer that your sample will respond in same way as whole population • But, generalizing from sample to population involves risk • Ecological Fallacy – can’t draw conclusions about individuals from group level sample of data • Reductionist Fallacy – can’t draw conclusions about groups from individual level sample of data

25. Generalizability • Not easy to achieve in experiment • Can’t really apply findings to larger population Experiments occur in artificial setting Subjects recruited or selected, not chosen through random sampling

26. Types of Sampling Procedures • Probability – Random Sampling selects subjects out of a large population on the basis of chance ( a technique used most effectively with survey research)

27. Probability Sampling • Participants drawn by chance (random) • Every subject has equal chance of being chosen (known probability, 1:10; 1:100) How to do Simple Random Sample 1. Arbitrarily select a number from a random number table 2. Match it to number in numbered subject list for starting point 3. Continue selecting numbers and subjects Until desired number of subjects is obtained

28. Systematic Random Sample • Arrange population elements sequentially • Determine size of sample wanted • Divide sample # into # of subjects in population • Randomly select a starting point in list • Select every nth subject • If need 5 subjects and have 45 in population, select every 9th person

29. Stratified Random Sampling • Characteristics of population are known to the researcher before taking the sample • Sample is selected with mirror proportions on characteristics such as: ethnic, age, gender, religion,education level, income level etc.

30. Cluster Sampling • Unit chosen is not an individual, but is a cluster of individuals naturally grouped together such as Churches, Schools, Blocks, Counties, Businesses etc. • They are alike with respect to characteristics relevant to the study

31. Non-Probability Sampling- • Participants are not chosen by chance They are Chosen due to economical and convenience reasons • Example: Study on student attitudes. Stop students at the gym only and ask them to take the survey. They are not necessarily representative of the total student population

32. Types of Non-Probability Sampling • Accidental – just encounter a # of people and ask to be in your study It is extremely weak, but popular method Psychological research is often accidental • Convenience – Similar to accidental Individuals seek out individuals who are available Likely to be biased Not representative of any population Should be avoided

33. Snowball - used for hard to reach but interconnected populations • One person identifies and recommends another people and those people recommend other people and on and on…. • Typical subjects – drug dealers, prostitutes, practicing criminals, gang leaders, AA members

34. Data Analysis – Chapter 14

35. Why are Statistics Important • Statistics give numeric meaning to our data • Helpful tool for understanding social world and are used to: 1.describe social phenomena 2. identify relationships among them 3. explore reasons for relationships 4. test hypotheses 5. interpret cause and effect

36. Drawbacks • Can use statistics to distort reality • Lying with statistics is unethical • Easy to be careless when using statistics • Must use appropriate level of measurement for variables in our data

37. Preparing for Statistics • After data is collected it must b cleaned, checked and coded before statistics are run • There is software available to do this

38. Displaying Statistics • Graphics: Bar Charts, histograms, pie charts, frequency tables and curve graphs describe the shape of the data visually

39. Statistics for One Variable • Univariate (descriptive) - describes statistical characteristics of one variable: frequency distributions, summary statistics, measures of central tendency (mean, median mode), skewness, measures of dispersion (range, variance, standard deviation), reliability tests • Display the distribution of cases across the categories of one variable

40. Univariate Stats • Frequency distribution (1xtables) – displays the number and percentage or cases corresponding to each of a variable’s values or group of values • Shows the variation characteristics in each variable through graphs or frequency table

41. If more than 15-20 values in a variable that’s too large to show in a table i.e.AGE • The distribution of the values will be clearer in the table if the values are grouped. Age 0-10, 11-20, 21-30

42. Measures of Central Tendency – • Summarized with one of three statistics 1. Mean (arithmetic average of the values in a distribution) – sum the values of the cases and divide by the total number of cases

43. 2. Median (the point that divides the distribution in half) One in the middle 3. Mode (most frequent value in a distribution) • The Mean is the most frequently used because it is the foundation for more advanced statistics

44. Central tendency is only one measure of the shape of a distribution • Other measures of variation can also be used to give a more complete picture • Just because 3 towns have the same median income does not mean they are similar in their social characteristics due to the shape of their income distributions.

45. Picture of the data’s shape • Skewness – If there is a lack of symmetry in the data (symmetric would be Bell curve) shape of the data looks different • If data clustered to right of center- Positive skew • If data clustered to left of center – Negative or inverse skew

46. Measures of Variation or Dispersion – Are the data spread out or clustered? 1. Range- highest value minus the lowest value plus one (is influenced by outliers) 3. Variance – the average squared deviation of each case from the mean (takes into account the amount by which each case differs from the mean)

47. 4. Standard Deviation – Preferred measure of variability because of its mathematical properties ( sq. root of the variance) 5. Quartiles – points in a distribution corresponding to first 25% of cases, first 50%of cases and first 75% of cases

48. Bivariate/multivariate Analysis • Describes the association between two or more variables • Some types: Cross-tabulation, Regression, Correlation • Measures of Association- descriptive statistics that summarized the strength of an association (Variation in one variable is related to variation in another. For example Chi Sq. and Gamma are used to summarize the relationship between two or more variables in Cross-tabulation

49. CROSS-TABULATION • The tables display the distribution of one variable for each category of another variable – Gender and Party • Sex of voter determines party. • If Man then Republican

50. What to Look for The IV is Gender Do percentages and/or distributions vary at all between categories of the independent variable? By how much? (strength) (This example is nominal level data)