FINAL Marketing Research MKTG:3100:0EEE
Of the information management process, marketing research is involved with which of these phases?
(A) The specification of what information is needed. (B) The collection and analysis of the information. (C) The interpretation of that information with respect to the objectives that motivated the study in the first place.
Suppose that your sample size is less than 5% of the population (which is general and common). To determine the necessary sample size, you need to know how (a) big the population size is. (b) homogeneous or similar the population is on the characteristic to be estimated. (c) much precision is needed in the estimate. (d) the true mean of the population is. (e) confident you need to be that the true value falls within the precision range.
(b), (c), and (e)
Procedure for Developing a Questionnaire STEP 7: Determine Question Sequence
- Use simple and interesting opening questions (Make respondents get engaged) - Use the funnel approach - Design Branch Questions with Care - Ask for classification information last (Ask Target information first, and then Classification information like demographic breakdowns.) - Place difficult or sensitive questions late in the questionnaire
Experiments as Casual Research
- X = Independent Variable (eXposed/treatment) - Y = Dependent Variable (Observed/measure) (treatment effect is O2 - O1)
strategy-oriented problem
-Typically associated with planned change (How should we change our promotions? How should our advertising campaign change?) -Aims more directly at making decisions (selecting alternative course of action)
Define the target population
- A population is the set of all objects that possess common set of - Parameter is a characteristic or measure of a population - Researchers must be very clear and precise about defining the target population. (E.g., College students in Iowa City vs. Freshman and Sophomore who live in 15-minute walking distance to the Iowa City's downtown and consume a cup of coffee at least once a day) (These are a kind of college students who are habitual coffee drinkers and demand convenience (b/c they might not have a car).)
Nonprobability Samples
- A sample that involves personal judgment in the selection process - Impossible to evaluate the degree of sampling error (No Inference; Not generalizable)
Procedure for Developing a Questionnaire Step 6: Prepare dummy tables
- A table used to show how the results of an analysis will be presented - Preparing a complete set of dummy tables forces you to think carefully about each piece of information to be collected
Place difficult or sensitive questions late in the questionnaire
- After the respondents get involved in the study, they are less likely to refuse to answer - EX: "We want to investigate people's snack consumption" DON'T Q1. What is your income level? Q2. Which snack do you like the most? Q3. Please rank your preference among the following snacks DO Q1. Which snack do you like the most? Q2. Please rank your preference among the following snacks ... Q10. What is your income level?
Focus Groups
- An interview conducted among a small number of individuals simultaneously; the interview relies more on group discussion than on directed questions to generate data. - Need a highly skilled moderator (ensures the group does not wander too far from the key issues.) - Participants are homogenous within group; heterogenous across groups
Why should you conduct exploratory research?
- Develop hypotheses (desired outcome IS the hypothesis) - Better formulate the manager's decision problem (better define the issue if you know more about the industry) - Increase researcher's familiarity with the problem (Clarify concepts)
Procedure for Developing a Questionnaire Step 10: Reexamine steps 1-9, pretest questionnaire, and revise if necessary
- Ensure every question is not confusing, ambiguous, offensive, sensitive, or leading Run Two Pretests: (1) personal interviews (close friends/family) - obtain comments, any problems (2) Run a small survey (n < 25) - see any issues from the results
Case Analysis
- Intensive study of selected examples of the phenomenon of interest. - Examine existing records, observe the phenomenon, conduct interviews, etc. - Analyze what is happening in a given situation- Extreme cases (much more beneficial to look into these) vs. moderate cases
Identify the sampling frame
- Sampling frame is a list of population elements from which a sample will be drawn. - Commonly used sampling frames: Customer database, Telephone directories, Lists developed by data compilers - The characteristics of the population should remain the same in the sampling frame. E.g., gender ratio
Three types of Market Testing
- Standard Test Market (most real, least favorable) The company sells the product through its normal distribution channels. - Controlled Test Market An entire test program conducted by an outside service in a market in which it can guarantee distribution. - Simulated Test Market (most unreal, most favorable) Consumer ratings as well as (likely or actual) purchase data obtained in a simulated store environment EX: Generate a shelf for Ketchup in a virtual store to see which brand or type people will choose (had to do online because people don't buy ketchup that often)
Discovery-oriented problem
-Associated with unplanned change (Revenues dropped by 10% What happened? Why is it happening?) -Goal is to provide good information to give management some insight into what they should do next
Procedure for Developing a Questionnaire Step 5: Determine Wording of Each Question
-use simple words +DON'T "Do you think the current distribution of soft drinks is adequate?" +DO "Do you think soft drinks are readily available when you want to buy them?" "Do you think you can find soft drinks easily when you want to buy them?" -avoid ambiguous words and questions +DON'T "How often do you watch movies online using the Netflix online service?" Answers: Never, Rarely, Occasionally, Sometimes, Often, Regularly, Frequently, Always +DO "Over the past two weeks, how many movies have you watched online using the Netflix online service?" Answers: None, 1, 2, 3, 4, 5, more than 5 -avoid leading questions (A question framed to give the respondent a clue as to how s/he should answer, happens a lot in the political world) +DON'T "Are you more inclined to invest in the stock market now that interest rates on savings accounts are so low compared to last year?" DO "Are you more inclined to invest in the stock market compared to last year?" -avoid unstated alternatives +DON'T "Would you like to have an end-of-year bonus, if this were possible?" +DO "Would you prefer to have an end-of-year bonus, or do you prefer to increase your individual retirement contribution for next year?" -avoid assumed consequences (A problem that occurs when a question is not framed so as to clearly state the consequences, and thus it generates different responses from individuals who assume different consequences) +DON'T "Do you favor a 5% increase in state taxes?" +DO "Do you favor a 5% increase in state taxes to repair aging bridges?" -avoid generalizations and estimates Don't make your respondents work too hard! (ask how much coffee drank in a week, not in a year) -avoid double-barreled questions (A question that calls for two responses and creates confusion for the respondent) +DON'T "How satisfied are you with the price and quality of the service you received?" +DO "How satisfied are you with the price of the service you received?" "How satisfied are you with the quality of the service you received?"
Necessary conditions for Causality
1. Consistent Variation (X and Y always occur or vary together) (Positive and Negative Relationships) 2. Time Order (of occurrence) (X should occur before or simultaneously with Y.) 3. Elimination of Other Explanations (The occurrence of Y is because of X only.) (hard to prove this one!!!)
sampling procedure steps
1. Define the target population (Who?) 2. Identify the sampling frame (How to find?) 3. Select the sampling plan (How to select?) 4. Determine sample size (How many?) 5. Select the sample elements 6. Collect the data from the designated elements
two-tailed test
A hypothesis test in which rejection of the null hypothesis occurs for values of the test statistic in either tail of its sampling distribution. (will/will not)
Branch Question
A question that routes respondents to different survey items based on their responses to the question
Filter Question
A question used to determine if a respondent is likely to possess the knowledge being sought, and if a respondent qualifies as a member of the defined population
Types of Probability Samples: Stratified
1) The population is divided into subgroups using a relevant variable - (e.g., # coffee consumption per day: bedtime) 2) Randomly select some members from each group • Subset are homogeneous within each group, but heterogeneous between with respect to key variables.
Procedure for Developing a Questionnaire Steps
1. Specify what information will be sought 2. Determine method of administration 3. Determine content of individual questions 4. Determine form of response to each question 5. Determine wording of each question 6. Determine question sequence 7. Determine physical characteristics of questionnaire 8. Develop recruiting message or script 9. Reexamine steps 1-8 and revise if necessary 10. Pretest questionnaire and revise if necessary
Multivariate Analysis: Correlation
A statistic that measures the degree of linear relationship between two continuous variables Two variables: - Variable 1 (IV): Continuous - Variable 2 (DV): Continuous Measuring - Association (linear relationship) between Variable 1 and 2 (UNDERSTANDING THE CORRELATION BETWEEN THINGS) - The magnitude and the direction (positive or negative) of the association
Multivariate Analysis: Regression
A statistical technique used to derive an equation representing the effect of a single or multiple independent variables (IVs) on a continuous dependent variable (most flexible)
Split-ballot technique
A technique for combatting response bias; multiple versions of the questionnaire are produced and distributed
Recall Loss
A type of error caused by a respondent's forgetting that an event happened at all (e.g., satisfaction survey after a month of the visit)
Telescoping Error
A type of error resulting from the fact that most people remember an event as having occurred more recently than it did (e.g., Number of chocolates consumed prior 7 days)
Three basic factors affect the sample size when working with a probability sample
Amount of Variation (𝝈) Degree of Precision (𝑯) - Half of Sampling Error Degree of Confidence (𝒛)
Use r-squared for simple regression....Use Adjusted r-squared for multiple regression
Adjusted R Square - What it indicates: what percentage of the variation in the dependent variable is explained by the model - Interpretation: The model account for 11% of the variation in revenues
funnel approach
An approach to question sequencing, starting with broad questions and narrowing down the scope
Response order bias (position bias)
An error that occurs when the response to a question is influenced by the order in which the alternatives are presented (Options presented earlier > later)
Response rate serves two important functions
Assessment of the potential influence of nonresponse error on the study's results Indicator of the overall quality of a data collection effort
Paired Sample T-Test
COMPARING two means of two variables e.g., importance of visits by various reasons
one sample t test
Compare a mean against a specific number e.g., average #visits = 6 (nation average)
Independent Sample T-Test
Compare means of one variable across two groups e.g., average #visits by pool users {0 = N, 1 = Y}
Suppose your friend, Billie, wonders whether having a significant other (0 = no girlfriend/boyfriend, 1 = have a girlfriend/boyfriend) depends on a student's year-in-college. Since you take the Marketing Research course, she asks you whether there is any way of testing her hypothesis. What statistical analysis/test should you explain to her?
Cross-tabulation
Amount of Variation (𝝈)
Degree of random error in observed responses Higher the variation, larger sample size is required (all else being equal). How to guess the amount of variation? - Use a sample standard deviation as a proxy for the amount of variation (of the population, σ) - The rules of thumb: +For continuous variable: use Maximum and Minimum. 𝜎 = (𝑀𝑎𝑥 - 𝑀𝑖𝑛) / 6 +For binary variables: use Proportion (𝑝 = % "𝑌𝑒𝑠") 𝜎 = SQRT(𝑝*(1 − 𝑝))
Probability Samples
Each member of target population has known, nonzero chance of being included in the sample Possible to estimate the amount of sampling error (Inference can be made; Generalizable)
sampling error
Error due to the act of sampling Related to the random error. If the researcher uses the probability sampling, the magnitude of sampling error is quantified. The difference between results obtained for a sample and the results from the whole population Usually less troubling than the other sorts of errors - Can reduce the sampling error by increasing the sample size - The degree of sampling error can be estimated if probability sampling is used (i.e., what we learned in Ch 14, the equation to find ±H)
Non-sampling Error
Error due to the way that sampling is done. Related to the systematic error. Includes noncoverage error, nonresponse error, response error, recording error, and office error
Nonresponse Error
Error from failing to obtain information from some elements of the population that were selected and designated for the sample. - Those who responded to the survey are systematically different from those who didn't respond (e.g., WP 2018). - e.g., A university wants to assess the success of its graduates based on their annual salaries five years after graduation. Which graduates are more (less) likely to return their survey? Those who are happy (unhappy) with their salaries. Two methods for diagnosing nonresponse error - Contact a sample of nonrespondents - Compare respondent demographics against known demographics of the population.
noncoverage error
Error that arises because of failure to include qualified elements of the defined population in the sampling frame. It is basically a sampling frame problem. Can be reduced, although not necessarily eliminated, by recognizing its existence and working to improve the quality of sampling frame. - E.g., Change of address, phone number, email address, etc.
Response Error
Error that occurs when an individual provides an inaccurate response, consciously or subconsciously, to a survey item. Possible ways to have response error include: - Does the respondent understand the question? - Does the respondent know the answer to the question? - Is the respondent willing to provide the true answer to the question? - Is the wording of the question or the situation in which it is asked likely to bias the response?
Data Analysis: Key Considerations
First, do we analyze the variable by itself or in relationship with other variables? Univariate Analysis - Analysis of an individual variable Multivariate Analysis - Analysis involving multiple variables Second, what level of measurement scale was used? Categorical Variables - Nominal and ordinal scales yield categorical variables Continuous Variables - Interval and ratio scales yield continuous variables
Types of Nonprobability Samples: Judgement
Handpick samples based on the researcher's judgement (i.e., those who are expected to serve the research purpose). - Snowball (an initial set based on the judgement sampling and then gets bigger by asking the initial set to help identify others with the desired characteristics.) Main problem - No way of knowing if/how the sample is representative of the population
Hypothesis Testing
How can we tell whether a particular result obtained from a sample would be true for the population as a whole (and not just for the sample)? Through hypothesis testing, we can establish standards about whether to accept sample results as valid for the overall population.
Procedure for Developing a Questionnaire Step 1: Specify what information will be sought
Hypotheses, dummy tables, etc., make it clear what information is needed.
Hypothesis Testing: Correlation
Hypothesis testing: need to get a T statistic (T value)
The response rate calculation for online/mail surveys is
RR = UQR / (CA - BA) RR = Response Rate UQR = Number of Usable Questionnaire Returned CA = Number of Contacts Attempted BA = Number of Bad Addresses (invalid/wrong address)
Recording Error
Recording error is the mistakes made by humans or machines in the process of recording respondents' response (i.e., during the survey/interview). - by the respondent/observer/interviewer
Which one of the following about the regression analysis FALSE?
Regression analysis explores the effect of the dependent variable(s) on the independent variable.
A brand product manager wants to know if men and women have different purchase intentions about a product. The manager plans to measure the purchase intention in a 1-7 Likert Scale (1 = definitely not buy, 7 = definitely buy). What statistical test should the manager use?
Independent sample t-test
normal thinking
It is observed that managers or employees that have been working for long in an organization have a normal approach to a problem. They do not see the problem as an opportunity. EXAMPLE Many managers, particularly those who have been with a company for a long time, are afflicted with "____________", which can get in the way of understanding the true nature of a problem.
nominal scale, ordinal scale, interval scale, ratio scale
NOMINAL: numbers assigned to object/words, mode (ex: gender, social security number) ORDINAL: Rank Objects, median and mode (ex: Assessing preference for soft drinks) INTERVAL: how you feel about something, Mean, Median, and Mode (ex: indicate you liking for each soda) RATIO: comparison of absolute magnitudes (actual amount) of the numbers, Geometric & Harmonic Means, Mean, Median, Mode (ex: How many times have you gone to java house in the past week?)
Suppose the owners of Tru Coffee plan to measure consumer awareness of the cafe and use the local landline telephone directory to draw a sample from which to survey the people in Iowa City. However, some people do not have a landline telephone. This represents ________ error.
Noncoverage
H0 vs. Ha
Null Hypothesis (H0) - The hypothesis that a proposed result is not true for the population. - What researchers want to reject. - e.g., the number of males is the same as that of females. Alternative Hypothesis (Ha) - The exact opposite of the H0 (The hypothesis that a proposed result is true for the population) - e.g., the number of males is different from that of females. Based upon what rule do we reject (or not reject) H0? - It's based on whether I make errors if I reject H0 and how big the error would be if I reject H0.
Office Error
Office error is the error due to data editing, coding, or analysis error - by the coder/researcher/analyst - Most office error can be reduced, if not eliminated, by proper control over data processing
A store manager wonders whether there exists a significant relationship between the customers' disposable income (measured in dollars) and their shopping time (measured in minutes). What statistical analysis/test should the manager use?
Pearson correlation
Procedure for Developing a Questionnaire Step 2: Determine Method of Administration
Personal Interview Telephone Interview Mail Questionnaire (most private) Online Survey
What type of new-to-the-world data that is collected to address a current problem?
Primary data
The response rate calculation for telephone surveys (assuming no eligibility requirement) is
RR = CI / (CI + R + NAH) RR = Response Rate CI = Number of Completed Interviews R = Number of Refusals NAH = Number of Non-At-Homes
The general response rate calculation is
RR = CI / E RR = Response Rate CI = Number of Completed Interviews with responding units E = Number of Eligible responding units in the sample
Exploratory Research Design
Research conducted to gain ideas and insights to better define the problem or opportunity confronting a manager. (does not involve probability sampling plans.)
Descriptive Research Design
Research in which the major emphasis is on describing characteristics of a group or the extent to which variables are related. (NOT productively used to clarify concepts)
Procedure for Developing a Questionnaire Step 3: Determine Content of individual questions
Research objectives are translated into information requirements. How many questions? (Collect the needed data using as few questions as possible) (Yet, if necessary, ask several questions than ask one with confusions.) Make sure that you collect single piece of information from one question EX: question asked to the Crest toothpaste consumers (Instead of... "Why do you use Crest toothpaste? Ask... "How did you first happen to use Crest?" AND "What is your primary reason for using it?")
Which of the following is TRUE about hypothesis testing?
Researchers want to reject the null hypothesis.
Types of Nonprobability Samples: Convenience
Select samples simply based on convenience. - Sample elements are chosen because of being in the right place at the right time. Main problem - No way of knowing if/how the sample is representative of the population
A researcher wants to assess the amount of "sampling error" associated with an estimate. Which of the following sampling methods would you recommend the researcher use?
Simple random sampling
Degree of structure of the questions
Structured (fixed-alternative, close-ended, or multiple-choice question) or Unstructured (open-ended question)?
Researchers must strive to achieve the high response rates
Survey length Guarantee of confidentiality Interviewer characteristics and training Personalization Response incentives Follow-up surveys and reminder
AFC survey results show that the mean number of visits per month is 10. However, according to the fitness industry report, the typical member of a fitness club visits 8 times per month on average. The AFC manager wonders whether the population of AFC members visits AFC more often than the national average. Which of the following is NOT true?
The appropriate method of hypothesis test is the chi-square goodness-of-fit test.
Degree of Confidence (𝒛)
The more confidence we want to be, the larger the sample we need e.g., We need our estimate to fall into this precision range 95% of times
Degree of Precision (𝑯) - Half of Sampling Error
The more precision we need, the larger the samples we require (the smaller precision is, the less error you allow) EX: We need the estimate to be ±0.01 the true value in the population (need more samples
Types of Probability Samples: Cluster
The population is divided into clusters using less relevant variable (e.g., # coffee consumption per day: Season of the birth) Sample in which (1) the population is divided into MECE subgroups (NS), (2) randomly choose subgroups (one or more), and use all individuals in the subgroup (one-stage) or (3) randomly select a few individuals (two-stage) from the chosen subgroups. (heterogenous within) Most appropriate when subset are heterogeneous within, so that each cluster reflect the diversity of the whole population. - e.g., Assuming you drinks coffee mostly during the group work (homogeneous within the group), dividing clusters by locations (area sample) or season of the birth (each subgroups less than 10).
Question order bias
The tendency for earlier questions on a questionnaire to influence respondents' answers to later questions
Simple Regression: when there is only one IV
Two Purposes: 1. Explaining and Understanding: Relationship between X and Y: 𝑎 =? 𝑏 =? e.g., 𝑎 = 1, 𝑏 = 2 2. Predicting 𝑌 =? (if X is given) e.g., 𝑌 is predicted to be 5 when 𝑋 = 2
Multiple Regression: when there are multiple IVS
Two Purposes: 1. Explaining and Understanding: Relationship between Xs and Y: 𝑎 =? 𝑏1 =? , ... , 𝑏𝑘 =? e.g., k = 2: 𝑎 = 0.5, 𝑏1 = 1, 𝑏2 = 0.5 2. Predicting 𝑌 =? (if Xs are given) e.g., 𝑌 is predicted to be 3 when 𝑋1 = 2, 𝑋2 = 1 (i.e., 𝑌 = 0.5 + 𝑋1 + 0.5 ∙ 𝑋2)
Basic Univariate Statistics: Continuous Measures
Two-box technique converts an interval-level rating into a categorical measure for presentation purpose.
Casual Research Design
Type of research in which the major emphasis is on determining cause-and-effect relationships. (typically concerned with the determination of causal relationships)
Procedure for Developing a Questionnaire Step 3: Determine Content of individual questions: Is this question "Answerable"?
Unable to answer? - No proper answers given - Use a filter question to ensure this won't happen (screening question) Unwilling to answer? - When a sensitive question is asked OR when it is too effortful to answer - Place difficult/more sensitive questions later in the survey
Confidence Intervals for Means
When interval and ratio scales are used in the question, it gives the continuous variable. - Mean is the main statistics of interest (e.g., average number of visits to the store). Sampling error for mean = Z * (s/SQRT(n))
Confidence Intervals for Proportions
When nominal and ordinal scales are used in the question, it gives the categorical variable. - Proportion is the main statistics of interest. (e.g., proportion of males/females) Confidence Intervals for proportions are: 𝑝 − 𝑠𝑎𝑚𝑝𝑙𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟 ≤ 𝜋 ≤ 𝑝 + 𝑠𝑎𝑚𝑝𝑙𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟 𝑝 = the relevant proportion obtained from the sample 𝜋 = population proportion
communication vs observation
Which of the following is an advantage of the observational method over the communication method of gathering primary data? Objectivity
Histogram
a bar chart on which the values of the variable are placed along x-axis and the frequency of the values is shown on y-axis Histogram allows a condensed picture of the distribution Can detect the outlier - an observation so different in magnitude from the rest of the data
one-tailed test
a hypothesis test in which the research hypothesis is directional, positing either a mean decrease or a mean increase in the dependent variable, but not both, as a result of the independent variable (most likely, not likely)
Analysis of Variance (ANOVA)
analysis of variance test used for designs with three or more sample means
Among the four measures we have learned (nominal, ordinal, interval, and ratio), frequency analysis can be used for
any measures
Validity of measures is
concerned with the extent to which differences in scores reflect true differences in the characteristic.
A common use of demographic and socioeconomic data in marketing is
delineating market segments. (data is raw facts, Hispanic population is growing in the US)
Types of Nonprobability Samples: Quota
e.g., Male : Female ≈ 40 : 60 → 4 Males, 6 Females One or more characteristics of the population are represented in the sample. - To build a sample that looks like the larger population of students. Main problem - The specific sample elements in a quota sample are left to the discretion of the researcher (e.g., why Gender is used?)
Types of Probability Samples: Simple Random
e.g., Randomly select 10 students from the student list Everyone has a chance to be selected with 𝑝 = 1/N - Recall the Excel functions to conduct simple random sampling (e.g., the winner for a chocolate. See the Student dataset) Each population member has an equal probability of being selected. Main problem - Depends mainly on having a good sampling frame (cf. if what if we do not have a list of population?)
Types of Probability Samples: Systematic
e.g., Randomly select the starting point from the first k, and select students by adding every k from the student list (to simplify, if we have 30 students and want to sample 10 of them, then k = 3) A probability sampling plan in which every kth element in the population is selected for the sample pool after a random start. - Since the start was random, each name after the first is a function of the random choice (i.e., the first choice), and hence is random. Main problem - How can we ensure the total sample numbers as we planned? Not reachable (e.g., absence), not eligible (e.g., who does not in this course, yet name is on the list), refused to answer, not contacted after all. Steps to achieve - Arrange the sample frame to n - Select the sample N - Compute the sample interval k = N/n - Continue the process until you select the amount needed for the sample
cross-tabulation
most commonly used for studying the relationship between two or more categorical variables (i.e., nominal or ordinal scales) - cf. correlation: between two continuous variables. (just used to give correlation) Examine whether one variable (the independent or predictor variable) has an influence on another variable (the dependent or outcome variable) Yet, NO causality can be established!! EX: Does the doctor's referral have any effect on therapy pool usage? (promotion strategies) Null Hypothesis (H0 ) - Therapy pool usage is not related to Doctor's recommendation Alternative Hypothesis (Ha ) - Therapy pool usage is related to Doctor's recommendation
descriptive statistics
numerical data used to measure and describe characteristics of groups. Includes measures of central tendency and measures of variation. Most commonly used descriptive statistics are: - Mean, median, and mode (measure of central tendency) - Min, max, standard deviation (measure of dispersion)
Frequency analysis
organizes data into groups and shows the number of observations that fall into each group
p-value vs. 𝛼
p-value - The probability of obtaining a proposed result if in fact H0 is true in the population - e.g., p-value = 0.03 - "If we reject H0, such conclusion could be wrong three times out of one hundred." 𝜶 (significance level) - The acceptable level of error selected by the researcher (usually 0.05), where the level of error refers to the probability of rejecting H0 - e.g., a = 0.05 "When I reject H0, if such a rejection decision is wrong no more than five times out of hundred, I am willing to reject H0" Reject H0 when p-value < a
Suppose a researcher is interested in people's mobile data plan choices. Based on the assumption that people who consume more (less) data choose more (less) expensive mobile data plans, the researcher divides the population of T-Mobile consumers into heavy and light users. The researcher then uses a simple random sampling to draw samples for each group. This is an example of ________ sampling.
stratified
Confidence Intervals
the range on either side of an estimate that is likely to contain the true value for the whole population All we need to do is to calculate the degree of sampling error.
Three methods of ethical reasoning
utility- do benefits exceed costs? rights- are human rights respected? justice- are benefits and costs fairly distributed?
Calculating Sample Size
𝐻 = 𝑧 * (𝜎 / SQRT(𝑛)) OR 𝑛 = 𝑧 2 ∙ 𝜎 2/𝐻 2
