Quantitative Research Methods PDF

Quantitative research design Quantitative Research Design Study design Study population Sample size determination Sampling method Data collection procedure(tools to be used for data collection, method of data col...

Quantitative research design Quantitative Research Design Study design Study population Sample size determination Sampling method Data collection procedure(tools to be used for data collection, method of data collection) Quality assurance procedure (description of procedure to maximize validity and reliability of data[pre-testing questionnaire, supervision, re-interviewing of a subgroup of respondents, training, coding, data entry, editing, plan for data control, indicate multiple sources of data collection, other data quality checks etc) Data analysis Ethical considerations 4/23/21 2 Study design Observational studies Descriptive - case reports/case series - cross- sectional descriptive studies - ecological/correlational studies Analytic studies - cohort studies - case- control studies Experimental studies - clinical trials - field trials -community trials 4/23/21 3  According to Uma Sekaran in Research Method for Business 4th Edition, Roscoe (1975) proposed the rules of thumb for determining sample size where sample size larger than 30 and less than 500 are appropriate for most research, and the minimum size of sample should be 30% of the population.  The size of the sample depends on a number of factors and the researchers have to give the statistically information before they can get an answer. For example, these information like (confidence level, standard deviation, margin of error and population size) to determine the sample size. Determining sample size ⚫ What do you need to consider ⚫ Variance or heterogeneity of population ⚫ Previous studies? Pilot studies? ⚫ Level of precision ⚫ Confidence level ⚫ Generally, we need to make judgements on all 3 variables Sample size determination ⚫ 4 basic techniques ⚫ Using a census for small populations ⚫ Using a sample size of a similar study ⚫ Using published tables ⚫ Using formulae to calculate sample size Using formulae  Study populations and sampling 4/23/21 14 Sampling Techniques & Samples Types Sampling Techniques & Samples Types Sample definition Purpose of sampling Stages in the selection of a sample Types of sampling in quantitative researches Ethical Considerations in Data Collection The process of selecting a number of individuals for a study in such a way that the individuals represent the larger group from which they were selected  STUDY POPULATION SAMPLE TARGET POPULATION 4  A sample: “a smaller (but hopefully representative) collection of units from a population used to determine truths about that population” (Field, 2005) The sampling frame A list of all elements or units in a population from which a sample is taken. Population & Sample ⚫ A population is a complete set of people or objects(e.g clinics, neighborhoods) with a specifies set of characteristics - clinic - demographic - geography - period of time ⚫ A sample is a subset of the population 4/23/21 20  To gather data about the population in order to make an inference that can be generalized to the population Stages in the Define the target population Selection of a Sample Select a sampling frame Determine if a probability or nonprobability sampling method will be chosen Plan procedure for selecting sampling units Determine sample size Select actual sampling units Conduct fieldwork  Purpose – to identify participants from whom to seek some information  Issues ◦ Nature of the sample (random samples) ◦ Size of the sample ◦ Method of selecting the sample  Important issues ◦ Representation – the extent to which the sample is representative of the population ◦ Generalization – the extent to which the results of the study can be reasonably extended from the sample to the population ◦ Sampling error The chance occurrence that a randomly selected sample is not representative of the population due to errors inherent in the sampling technique  Non- Probability probability samples samples  Known as probability sampling  Best method to achieve a representative sample  Four techniques 1. Simple random 2. Stratified random 3. Cluster 4. Systematic 1. Random sampling Selecting subjects so that all members of a population have an equal and independent chance of being selected ❖ Advantages 1. Easy to conduct 2. High probability of achieving a representative sample 3. Meets assumptions of many statistical procedures ❖ Disadvantages 1. Identification of all members of the population can be difficult 2. Contacting all members of the sample can be difficult  Random sampling (continued) ◦ Selection process  Identify and define the population  Determine the desired sample size  List all members of the population  Assign all members on the list a consecutive number  Select an arbitrary starting point from a table of random numbers and read the appropriate number of digits 2. Stratified random sampling ◦ The population is divided into two or more groups called strata, according to some criterion, such as geographic location, grade level, age, or income, and subsamples are randomly selected from each strata.  Stratified random sampling (continued) ◦ Advantages  More accurate sample  Can be used for both proportional and non- proportional samples  Provides for representation of subgroups in the sample ◦ Disadvantages  Identification of all members of the population can be difficult  Identifying members of all subgroups can be difficult  Stratified random sampling (continued) ◦ Selection process  Identify and define the population  Determine the desired sample size  Identify the variable and subgroups (i.e., strata) for which you want to guarantee appropriate representation  Classify all members of the population as members of one of the identified subgroups 3. Cluster sampling  The process of randomly selecting intact groups, not individuals, within the defined population sharing similar characteristics  Clusters are locations within which an intact group of members of the population can be found  Examples  Neighborhoods  School districts  Schools  Classrooms  Cluster sampling (continued) ◦ Advantages  Very useful when populations are large and spread over a large geographic region  Convenient and expedient  Do not need the names of everyone in the population ◦ Disadvantages  Representation is likely to become an issue  Cluster sampling (continued) ◦ Selection process  Identify and define the population  Determine the desired sample size  Identify and define a logical cluster  List all clusters that make up the population of clusters  Estimate the average number of population members per cluster  Determine the number of clusters needed by dividing the sample size by the estimated size of a cluster  Randomly select the needed numbers of clusters  Include in the study all individuals in each selected cluster 4. Systematic sampling ◦ Selecting every Kth subject from a list of the members of the population ◦ Advantage  Very easily done ◦ Disadvantages  subgroups  Some members of the population don’t have an equal chance of being included  Systematic sampling (continued) ◦ Selection process Identify and define the population Determine the desired sample size Obtain a list of the population Determine what K is equal to by dividing the size of ⚫ the population by the desired sample size Start at some random place in the population list Take every Kth individual on the list  Example, to select a sample of 25 dorm rooms in your college dorm, makes a list of all the room numbers in the dorm. For example there are 100 rooms, divide the total number of rooms (100) by the number of rooms you want in the sample (25). The answer is 4. This means that you are going to select every fourth dorm room from the list. First of all, we have to determine the random starting point. This step can be done by picking any point on the table of random numbers, and read across or down until you come to a number between 1 and 4. This is your random starting point. For instance, your random starting point is "3". This means you select dorm room 3 as your first room, and then every fourth room down the list (3, 7, 11, 15, 19, etc.) until you have 25 rooms selected. 1. Convenience sampling 2. Purposive sampling 3. Quota sampling 1.Convenience sampling: the process of including whoever happens to be available at the time …called “accidental” or “haphazard” sampling …difficulty in determining how much of the effect (dependent variable) results from the cause (independent variable)  2. Purposive sampling: the process whereby the researcher selects a sample based on experience or knowledge of the group to be sampled …called “judgment” sampling …potential for inaccuracy in the researcher’s criteria and resulting sample selections 3. Quota sampling the process whereby a researcher gathers data from individuals possessing identified characteristics and quotas …people who are less accessible (more difficult to contact, more reluctant to participate) are under-represented Data Collection Questionnaire design : Objectives of the session is to understand ❑ Objectives of questionnaires ❑ Advantages and disadvantages ❑ Design of questionnaires ❑ Type of questions used ❑ Common problems and pitfalls  1.1 What is a questionnaire ❑ A series of written questions/items in a fixed, rational order ❑ A questionnaire is an instrument (form) to: ❑ Collect answers to questions ❑ Collect factual data ❑ Gathers information or measures ❑ A well designed questionnaire: ❑ Gives accurate and relevant information to your research question ❑ Minimises potential sources of bias ❑ Will more likely be completed  1.2 Advantages /disadvantages ❑ Can reach a large number ❑ Provides only limited of people relatively easily insight into problem: and economically ❑ Limited response ❑ Provide quantifiable allowed by questions ❑ Maybe not the right answers questions are asked ❑ Relatively easy to analyse ❑ Varying response: ❑ Misunderstanding/misint erpretation ❑ Need to get it right first time: ❑ Hard to chase after missing data  1.3 Types of questionnaires Interviewer-administrated Vs Self-administrated ❑ Face to Face: ❑ By post: ❑ Telephone: ❑ Email/internet:  1.4 Advantages /disadvantages ❑ Self-administered questionnaire: ❑ Advantages: ❑ Disadvantages: ❑ Cheap and easy to administer ❑ Low response rate ❑ Preserves confidentiality ❑ Questions can be misunderstood ❑ Completed at respondent's convenience ❑ No control by interviewer ❑ No influence by interviewer ❑ Time and resouces loss ❑ Interview-administered questionnaire: ❑ Advantages: ❑ Disadvantages: ❑ Participation by illiterate people ❑ Interviewer bias ❑ Clarification of ambiguity ❑ Needs more resources ❑ Quick answers ❑ Only short questionnaires possible ❑ Especially on telephone ❑ Difficult for sensitive issues  1.5 Choice of the type of questionnaire ❑ Choice of the questionnaire type will depend on several factors such as: ❑ Speed ❑ Cost ❑ Internet Usage ❑ Literacy Levels ❑ Sensitive Questions Training questionnaire design II: Stages for design  2.1 Stages in designing the questionnaire I ❑ Design your survey plan: ❑ Decide on goals: ❑ Identify your specific research objectives ❑ Know the subject: ❑ Lessons learnt, secondary data review ❑ Formulate a hypothesis (if appropriate) ❑ Define information needed to test hypothesis:  2.2 Stages in designing the questionnaire II ❑ Determine study population: sampling ❑ Know the respondents: ❑ Occupation ❑ Special sensitivities ❑ Education ❑ Ethnicity / Language Questionnaire needs to be adapted to your population, not the opposite! ❑ Design variables and questions: ❑ Content of the questions ❑ Format of the questions ❑ Presentation and layout ❑ Coding schedule (if appropriate) ❑ Pilot and refine questionnaire Training questionnaire design III: Presentation and layout  3.1 Presentation and layout ❑ Clear consistent layout: ❑ Adequate space to answer / Large font size ❑ Appropriate page breaks ❑ Avoid ❑ experimental layouts ❑ fancy logos ❑ printed on recycled paper/is an equal opportunity employer etc ❑ Using colour or printing questionnaire on coloured paper may help ❑ Use filter questions, if necessary ❑ Give clear instructions about how to answer the questions (design guideline if necessary)  3.2 Good practice for layout ❑ Good appearance / easy on the eye ❑ Short and simple ❑ Relevant and logical ❑ High response rate ❑ Easy data summarisation and analysis  3.3 Organizing questions ❑ Decide on order of items/questions : ❑ Easy → difficult ❑ General → particular ❑ Factual → abstract ❑ Where to place sensitive questions? Be aware of ordering effects! ❑ Group questions by topic/ response options ❑ Starting questions: ❑ Simple ❑ With closed format ❑ Relevant to main subject ❑ Non-offending ❑ Neither demographic nor personal questions Don’t put most important item last!  4.1 Contents of questions ❑ Clear focus on research question ❑ Avoid sidetracking ❑ Avoid unnecessary information ❑ Demographic information ❑ Contact information (if non-anonymised)  4.2 Format of questions ❑ Adjust to responding audience: ❑ Professionals vs. public ❑ Middle class vs. prisoners ❑ Keep sentences simple and short ❑ Define key words (“fully vaccinated”) ❑ Remember option “don’t know” Do you own cattle or have frequent ❑ Ask for one information at a time: contacts with cattle? Yes  No  ❑ Use mutually exclusive and exhaustive answer options ❑ Vertical order of answer options  4.3 Be accurate ❑ Do you often touch cattle? Yes  The range of error due to use of imprecise words may be as high as 20 to 30 No  percent. ❑ How often did you touch a cattle during the past 3 months? Once  Twice  Three times or more  Not at all  Don´t know   4.4 Be objective ❑ Did you drink the strange brownish drink in Zimbabwe? Yes  No  ❑ Which beverage did you consume? Water  Beer  Wine  Burkutu  None of them  Don´t know   4.5 Be simple ❑ Did you smoke not less than a mean amount of 7 cigarettes/2 days from 2013 onwards? Yes  No  ❑ Did you smoke an average of 2 pack of cigarettes/week for the last 5 years? Yes  No  Don´t know  4.7 Format of questions Two main question formats: Closed format → forced choice: Open format → free text: ▪Yes ▪Why do you feel concern about food ▪No accessibility during the next month? ▪Don’t know Please describe: ______________________________ ______________________________ ▪Always ______________________________ ▪Sometimes ______________________________ ▪Never ______________________________ ____ ▪ Multiple choice ▪ Numeric open end ▪ Text open end ▪ Rating scale ▪ Agreement scale  4.8 Closed or Open questions? ❑ Advantages: ❑ Advantages: ❑ Simple and quick ❑ Not directive ❑ Reduces discrimination against less ❑ Allows exploration of issues literate to generate hypothesis, qualitative ❑ Easy to code, record, analyse research, focus groups, trawling ❑ Easy to compare questionnaires ❑ Used even if no comprehensive range ❑ Easy to report results of alternative choices ❑ Good for exploring knowledge and attitudes ❑ Disadvantages: ❑ Detailed and unexpected answers ❑ Restricted number of possible possible answers ❑ Loss of information ❑ Disadvantages: ❑ Interviewer bias ❑ Possible compromise: ❑ Time-consuming ❑ Insert field “others“ ❑ Coding problems ❑ Difficult to analyse! ❑ Difficult to compare groups  5.1 Closed questions Straightforward response: What is your age in years? ___ years How long have you owned a car? ___ years What is your sex (gender)? Male Female Did you stay in your house when the earthquake occurred? Yes No Don’t know  5.2 Closed questions Checklist: Which of the following agricultural activities did you do last week? ❑ Buying seeds ❑ Preparing your field ❑ Planting ❑ Harvesting  5.3 Closed questions Rating scale - Nominal: Did you do use soap during the following domestic activities during the past six months? Always Sometimes Seldomly Never ❑ Cooking ❑ After toilets ❑ After fieldwork ❑ Indicate your sex: ___Male ___Female  5.4 Closed questions ❑ Rating scale – Numerical: How useful would you think that information on the risk of being strike by earthquake? (please circle) 1 2 3 4 5 6 7 Not at all useful Very useful ❑ Analogue: How much is your food insecurity severe (put the tick on the line) 0 10  5.6 Closed questions Scales for measuring attitude (Lickert) Stray dogs carry a higher risk of rabies?: ⚫ No, I strongly disagree ⚫ No, I disagree quite a lot ⚫ No, I disagree just a little ⚫ I’m not sure about this ⚫ Yes, I agree just a little ⚫ Yes, I agree quite a lot ⚫ Yes, I strongly agree  5.7 Coding schedule ❑ Questionnaire can be pre-coded ❑ Quicker and easier data entry ❑ Examples: ❑ Male 1 ill 1 ❑ Female 2 Not ill 0 ❑ Don’t know 3 Don’t know 9 ❑ Single 1 Separated 3 ❑ Married 2 Divorced 4 ❑ Widowed 5 Don’t know 9 Problems and pitfalls  6.1 Problems and pitfalls ❑ Avoid questions that ask two things at once - you won’t know which ‘bit’ people are answering: ❑ Have you ever had stomach ache and diarrhoea? ❑ Avoid ambiguity..... ❑ Do you go to the woods a lot? ❑ Avoid jargon/abbreviations/slang: ❑ How often do you get up at night to PU? (pass urine) ❑ Should IVDUs be treated in the community?  6.2 Problems and pitfalls ❑ Avoid not mutually exclusive options: What age are you? ❑ 16-20 ❑ 20-25 ❑ 25-30 ❑ 35-40 ❑ Avoid leading questions Do you think that the food in the hotel made you sick? Did the hotel staff seem unhygenic to you? Do you agree that the hospital staff were close to exhaustion? ❑ Typographical / spelling errors  6.3 Length of a questionnaire ❑ Sufficient to capture needed data ❑ Short enough to hold participants’ attention ❑ Type of survey affects length ❑ Types of questions affect length ❑ Quantitative/Qualitative/Mixed approach affects length ❑ Participant characteristics affect length  validation ❑ Use or adapt existing questionnaires ❑ Validated (and possibly harmonised) ❑ New questionnaires ❑ Not validated ❑ Needs to be tested (pilot) ❑ Pilot with a similar group of people to your intended subjects ❑ Highlights problems before starting ❑ Effects of alternative wording ❑ Overall impression on respondents and interviewers ❑ Final polishing after several amendments  6.4 Questionnaire introduction ❑ Covering letter/ interview introduction: ❑ Who you are/ you work for ❑ Why you are investigating (purpose of the survey) ❑ Why it is important to hear from the respondent ❑ What may be done with the results and what possible impacts may occur with the results. ❑ Where you obtained the respondent’s name ❑ How and where you can be contacted ❑ Guarantee of confidentiality ❑ Length of interview (be honest) ❑ Due date for response Usefulness of study should be clear to all respondents Summary  7.1 Designing a questionnaire ❑ It’s all about the questions… ❑ Effect of a given word ❑ Balance in question wording ❑ Don’t know answers – offered or volunteered? ❑ Using scales ❑ Question order ❑ Pre-testing  7.2: Designing questions ❑ When devising your questions consider the following: ❑ What is essential to know? ❑ What would be useful to know? ❑ What would be unnecessary? ❑ Retain the former, keep the useful to a minimum and discard the rest  7.3 Best practices A well designed questionnaire: ❑ Will give appropriate data which allow to answer your research question ❑ Will minimise potential sources of bias, thus increasing the validity of the questionnaire ❑ Will much more likely be tested and completed ❑ FINALLY, keep your questionnaire short and the questions simple, focused and appropriate It is the researcher’s ethical responsibility to safeguard the story teller by maintaining the understood purpose of the research… The relationship should be based on trust between the researcher and participants. Inform participants of the purpose of the study.  Being respectful of the research site, reciprocity, using ethical interview practices, maintaining privacy, and cooperating with participants. Patton (2002) offered a checklist of general ethical issues to consider, such as: ❖ reciprocity ❖ assessment of risk ❖ confidentiality, ❖ informed consent ❖ and data access and ownership. Qualitative researchers must be aware of the potential for their own emotional turmoil in processing this information During the interview process, participants may disclose sensitive and potentially distressing information in the course of the interview.. ✔ Creswell, J., W. (2012) Educational research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research, 4th ed. ✔ Patton, M.Q. (2002). Qualitative Research and Evaluation Methods. Thousand Oaks, CA: Sage. Outline ⚫ Introduction ⚫ Variables & scales of measurements ⚫ Dealing with Data: Coding, Entering, and Cleaning ⚫ Descriptive Statistics ⚫ One Variable ⚫ Two Variables ⚫ More than Two Variables ⚫ Inferential Statistics ⚫ Conclusion Variables ⚫ As Katzenellenbogen et al put it, variables are “the characteristics which one measures, and about which data are collected …” (1997: 101). ⚫ 2 broad categories: ⚫ Quantitative (numerical) ⚫ Discrete ⚫ Continuous ⚫ Qualitative (categorical) ⚫ Norminal ⚫ dicotomous Variables c’td Discrete quantitative (numeric) variables – take on only whole numbers (integers) – unit of measurement cannot be subdivided, e.g. numbers of teeth in a mouth = 24, number of people at Olympics Opening Ceremony = 79 251 Continuous quantitative (numeric) variables – infinite numbers of possible values such as fractions and the basic unit of measurement can be subdivided, e.g. weight = 63.59 kg, distance from Zaria to Kaduna = 359.69 km. Qualitative (categorical) variables – non-numerical, without any magnitude, e.g. gender (male/female), type of tooth (incisor/molar). – However in reporting variables, a number can be used to describe a quality, e.g. gender. For example, 1 = male and 2 = female. It is extremely important to understand the types of variables you are going to analyse, as the types of statistical analyses carried out will depend on the type of variable Scales of measurement A nominal scale : Objects or observations are categorised or placed into classes, e.g. diabetic or non-diabetic. The characteristic of a nominal scale is that the attributes do not have a quantitative value. The assigned value is qualitative. An ordinal scale is used to express the ranking of a characteristic in some empirical order, e.g. ranking of students in class or people by income level. The data may be discrete or continuous, and may be either qualitative or quantitative. An interval scale includes quantitative characteristics that yield continuous units of measurements, and equal intervals between points on a scale, e.g. age or height. An interval scale does not have to begin with absolute zero, e.g. body temperature in F degrees. A ratio scale involves measurements that indicate intervals on a continuous scale e.g Temperature in Kelvin(zero degree is absolute 0) Gender Type Age Exam Income Variable Type of (yrs) Mark Group House (%) (N/mon Gender Nominal th) Type of House Nominal or M Brick 13 79.67 1000+ Ordinal F Wood 11 79.59 500-999 Age (yrs) Interval F Mud 12 78.65 0-499 Exam Mark (%) Ratio Income Group Ordinal  Types of variables and measurement scales Nominal and dichotomous Qualitative Ordinal Variables Interval (continuous) Quantitative Ratio Rational variables had a zero at the end of the scale. De: Goldim JR. Manual de Iniciação à Pesquisa em Saúde. 2a edição. Porto Alegre: 66 Dacasa Editor, 2000. Dealing with data ⚫ Data collected in quantitative research is in the form of ⚫ Numbers ⚫ To use this data, researchers: ⚫ Reorganize it for computer analysis ⚫ Analyse the data ⚫ Summarize the data in tables, charts or graphs ⚫ Interpret or give theoretical meaning to it Dealing with Data ⚫ Coding - reorganizing raw data into a format that ⚫ is easily entered into a computer ⚫ or is machine-readable. ⚫ Entering data – statistical packages(Excel; SPSS, STATA; typically: ⚫ each row is a case ⚫ each column is a variable ⚫ Cleaning data ⚫ checking the accuracy of coding and data entry. Levels of analysis Data analysis at 3 levels – one variable at a time (univariate) – two variables at a time (bivariate) – or more than two (multivariate) Basic analysis: Univariate analysis ⚫ Calculate descriptive statistics for each variable ⚫ Number of observations ⚫ Categorical variables: ⚫ proportions ⚫ For continous variables ⚫ Mean, median, mode ⚫ Standard variation Frequency Distributions Summarizing information Using tables – including counts and percentages Using graphic representations – Histogram – bar chart – pie chart Example of a histogram (showing two variables – each bar would be a univariate histogram) Example of a Pie Chart Measures ⚫ Mode of Central Tendency ⚫ the most common or frequently occurring number. ⚫ Median ⚫ the middle point or 50th percentile ⚫ Mean ⚫ the arithmetic average used with interval or ratio level data ⚫ very sensitive to extreme values Example of mean vs. median We survey seven people and ask each how many alcoholic drinks he or she consumed in the past month. The results are Person 1 2 3 4 5 6 7 Drinks 0 1 3 4 5 6 80 The median number is 4 – three people consumed fewer, and three people consumed more The mean is 14.14: the total number of drinks is 99, divided by 7 people is 14.4 From this example, you can see how ‘outliers’ – extreme values – affect the mean much more than the median. Measures of Variation ⚫ Variation is ⚫ the spread, dispersion, or variability ⚫ around the center of the distribution ⚫ Range ⚫ the distance between smallest and largest scores ⚫ e.g. ages might vary from a range of ages 21–59. ⚫ Percentiles ⚫ scores at a specific place within the distribution ⚫ if someone age 26 is at the 25th percentile, that means that 25% of the respondents were under age 26 ⚫ Standard deviation ⚫ an average distance of each score from the mean Results with Two Variables ⚫ Bivariate statistics ⚫ indicate whether there is a statistical relationship between two variables ⚫ There are two possible relationships: ⚫ Covariation ⚫ two variables are associated statistically. ⚫ Independence ⚫ there is no association between two variables Bivariate Contingency Table ⚫ Cross tabulation of two variables at the same time. ⚫ Shows how the pattern of distribution of one variable is “contingent” on the other variable Test for association between two variables The strength of the association between two variables e.g (disease and exposure) can be assessed using significance tests In 2 X 2 tables (qualitative data),you test the significance of the association by carrying out a Chi-Square test with an attached p-value For quantitative data, the mean scores between two groups can be tested for significance using statistical tests such as the t-Test, again with an attached p-Value For both the Chi-Square and t-Tests, commonly a p-value of less than 0.05 is considered a significant association between the disease and the exposure. More than Two Variables: Statistical Control ⚫ A way to test whether an observed relationship between two variables is spurious, which means: ⚫ Caused by a third variable ⚫ that separately affects the two variables we had been examining ⚫ Like in the examples we’ve seen: ⚫ Ice cream consumption, short-sleeve shirts ⚫ warm weather ⚫ Use of night light, nearsightedness in children ⚫ nearsightedness in parents Multiple Regression Analysis ⚫ A statistical technique for variables measured at interval or ratio levels ⚫ Results in a measure called R2 (R-squared), which measures the combined influence of multiple independent variables on one dependent variable ⚫ Regression also shows the independent effect of each variable, controlling for the other variables ⚫ The effect on the dependent variable is measured by a standardized regression coefficient: beta (ß)