STAT 1350 MIDTERM

margin of error

"if we took many samples using the same method we used to get this one sample, 95% of the samples would give a result within plus or minus number of percentage points of the truth about the population" -we need a margin of error to tell us how close our estimate comes to the truth -takes variability into account -if the sample is not random, the margin of error may not mean what we think it means

all students in STAT 1350 are asked to complete a survey in which they are asked to indicate their major, their age, the number of credits they are enrolled in, the name of their hometown, and the distance they live from campus. of these five variables, how many are categorical?

2 - major and hometown

which principle of experimental design reduces bias?

2. randomization

which principle of experimental design reduces chance variation?

3. use enough subjects in each group -the number of subjects that is "enough" depends

when asked, as part of a national poll, what they would do if they won the mega millions lottery, 65% of a random sample of 350 adults said they would quit their jobs. what is the approximate margin of error for this poll?

5.3%

dr. grey has developed a new acne medication called "pimple pulverizer." she claims this medication will dramatically lessen the severity of acne. she recruits 60 teenagers who are suffering from acne to take part in her study. all 60 of these teenagers use "pimple pulverizer" for one month, and at the end of the one-month period, they all report an improvement in their acne. a critic of dr. grey's study points out that we cannot trust the findings of the study because there was no control group. why would it be important to have a control group?

a control group will allow dr. grey to better assess whether improvement in acne might be due to the placebo effect

variability

a description of how spread out or how different the values of sample statistics are when we take many samples -large variability means that result of sampling is not repeatable -unaffected by population size as long as its at least 20x larger than the sample size -determined by sampling design and sample size n

imagine taking many different simple random samples from the same population. we expect what?

a different value of the statistic for each sample

control group

a group of people who take part in every part of the experiment except the treatment -randomization produces groups of subjects that should be similar, on average, in all respects before we apply the treatments -comparative design exposes all groups to similar conditions, other than the treatments they receive -controls for lurking variables

sampling frame

a list of individuals from which we will draw our sample

table of random digits

a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these two properties: 1. each entry in the table is equally likely to be any of the 10 digits 0 through 9 2. the entries are independent of each other; knowledge of one part of the table gives no information about any other part -as long as all labels have the same number of digits, all individuals will have the same chance to be chosen

nonsampling processing error

a mistake in mechanical tasks such as doing arithmetic or entering responses into a computer -technology and attention to detail can minimize processing errors

statistic

a number that describes a sample; the value of a statistic is known when we have taken a sample, but it can change from sample to sample -we often use a statistic to estimate an unknown parameter

parameter

a number that describes the population; a parameter is a fixed number, but the actual value of this number is unknown in practice

sample

a part of the population from which we actually collect information and is used to draw conclusions about the whole -to make sense of any sample result, we must know what population the sample represents -most statistical samples are used in a broad sense -a sample can produce more accurate data than a census -the size of the sample matters; larger samples are more representative (no number to describe how big is "big enough") -ideally, we want a sample that is representative of the population of interest; if our sample is not representative, we need to be cautious in terms of the conclusions we draw about the population

probability sample

a sample chosen by chance; not always random

census

a sample survey that attempts to include the entire population in the sample -even if you take a census, there is always the possibility you will make errors and draw the wrong conclusions -depending on the size of a population and the resources you have, taking a census can be expensive and time-consuming

biased sampling method

a sampling method that produces data which systematically favors certain outcomes

there are 100 students in Dr. Varma's anatomy course. one day, Dr. Varma writes the name of each student on a slip of paper, puts all 100 slips of paper into a box, mixes the box well, and then draws 10 slips from the box. she does this in order to choose a group of students to participate in a class demonstration. we would consider this group of 10 students to be what?

a simple random sample of the class

observational study

a study in which the researcher observes individuals and measures variables of interest but does not attempt to influence the responses -explanatory variable is not manipulated -example: survey

placebo

a treatment with no active ingredients within an experiment

lurking variable

a variable that has an important effect on the relationship among the variables in a study but is not one of the explanatory variables studied

response variable

a variable that measures an outcome or result of a study; dependent variable

explanatory variable

a variable that we think explains or causes changes in the response variable; independent variable

Logan has to conduct an experiment for his psychology course. in order to get participants to take part in his experiment, he posts a flyer on the bulletin board in Thompson Library. the flyer includes Logan's email address, and the first 50 OSU students who send an email message to Logan about their interest in being in the experiment are selected to serve as subjects in the experiment. what type of sample would these 50 students comprise?

a voluntary response sample

suppose in a recent survey of a simple random sample of 150 OSU undergraduates, it was found that 35% of these undergraduates were born and raised in Ohio. what is the population for this example?

all OSU undergraduates

why is random assignment necessary?

allows us to draw cause-and-effect conclusions

why is random sampling necessary?

allows us to generalize the results beyond the sample

sampling error

an error caused by the act of taking a sample; they cause sample results to be different from the results of a census

nonsampling error

an error not related to the act of selecting a sample from the population; they can be present in a census

double-blind experiment

an experiment in which neither the subjects nor the researchers know which treatment each subject is receiving

completely randomized design

an experiment in which we randomly assign individuals to treatment groups and compare the results of the different groups; also called randomized comparative experiment -can have any number of explanatory variables

clinical trial

an experiment that studies the effectiveness of medical treatments on actual patients

"one-track" design

an experimental design in which only a single treatment is applied

sample survey

an important kind of observational study in which only some members of a group of individuals are studied -selected because they represent the larger group -manageable and can lead to a good estimate of what is actually going on in the population

nonsampling response error

an incorrect response given by a subject -skilled interviewers can reduce response errors

statistical significance

an observed effect of a size that would rarely occur by chance -depends on the number of subjects involved -not the same as practically significant (meaningful)

variable

any characteristic of an individual -can take different values for different individuals

treatment

any specific experimental condition applied to the subjects; if an experiment has several explanatory variables, a treatment is a combination of specific values of these variables

a particular set describes college athletes and includes information about each athlete's age, sport played, year in school, and grade point average. who are the individuals in this data set?

athletes

when a sampling method systematically favors certain outcomes, we say that method is what?

biased

what combines when creating control group in an observational study?

comparison and matching

experiment

deliberately imposes some treatment on individuals in order to observe their responses

how do you take a stratified random sample?

divide the individuals in the population into groups based on some characteristic; then take simple random samples within each of those groups and combine all those samples into one big sample

when we take a census, we attempt to collect data from who?

every individual in the population

how does a placebo aid an experiment?

helps us better assess whether it's the ingredients in the treatment that is affecting the response and not the placebo effect

what is a common misconception about sample size?

if the size of a sample is relatively small compared to the population, the sample cannot accurately reflect the population -in reality, if we have sampled randomly, we can be confident the results of the sample reflect the population, even if the sample is only a small fraction of the population

data

information from which conclusions can be drawn; information gathered with a particular context -without knowing the context, it becomes harder to interpret and understand the data -reflect society

going to a wedding can be expensive! according to a national survey conducted in 2018, close friends and family of those who are getting married spend an average of $627.72 on each wedding-related event they attend. if you learn that some of the adults who participated in the survey did not give accurate responses because they did not correctly remember how much they actually spent on wedding-related expenses, this would be considered to be what kind of error?

nonsampling error

where does the best data about cause and effect questions come from?

observational studies -more impressive if they compare matched groups and measure as many lurking variables as possible to allow statistical adjustment

undercoverage

occurs when some groups in the population are left out of the process of choosing the sample

systematic sample

order the individuals in the population and then select every nth individual to be in the sample

categorical variable

places an individual into one of several groups or categories

what kind of error does the margin of error cover?

random sampling error -undercoverage, nonresponse, and other practical difficulties can cause large bias that is not covered by the margin of error

can a census or sample provide more accurate data?

sample

simple random sample

sample which allows impersonal chance to do the choosing; every individual in the population has an equal chance of being included in the sample and every sample size of n has an equal chance of being chosen -ideal, but very hard to get -easy way to find the average -avoids bias

voluntary response sample

sample which consists of people who choose themselves by responding to a general appeal -can be problematic because people with strong opinions are most likely to respond; sometimes the only ethical choice for experiments using people

stratified random sample

sample which divides the individuals in the population into groups based on some characteristic and then uses a simple random sample

every week, the college of arts and sciences at OSU sends out an email message called "News and Updates." one week, the message begins with the following: "we want your feedback! if you've got a minute or two, please take this survey to let us know what you think of News and Updates. We're always on the lookout for ways to make this useful and relevant to you, and we welcome your input." Since this method of sampling relies on voluntary response, we would consider it to be source of what type of error?

sampling error

what does a good sampling method have in regards to bias and variability?

small bias and small variability

how do you take a simple random sample?

start with a list of the whole population, then use a random method (such as a random number table or software) to select n of those individuals, with each individual having an equal chance of being chosen

what do Ohio residents think of the recent decision by the government to raise the gas tax in Ohio? to find out, a polling company wants to survey Ohio residents, and they want their sample to include residents from each of the 88 counties in Ohio. to ensure that members from each county are represented in the sample, the polling company should take what type of sample?

stratified random sample

dropouts

subjects who begin the experiment but do not complete it -if subjects drop out because of their reaction to one of the treatments, bias can result

nonadherers

subjects who participate but do not follow the experimental treatment -can cause bias

numerical variable

takes numerical values for which arithmetic operations such as adding and averaging make sense; sometimes referred to as a quantitative variable

bias

the consistent, repeated deviation of the sample statistic from the population parameter in the same direction when we take many samples; a systematic overestimate or underestimate of the population parameter

random sampling error

the deviation between the sample statistic and the population parameter caused by chance in selecting a random sample -the margin of error in a confidence statement only includes random sampling error -sampling frame

population

the entire group of individuals about which we want information in a statistical study -the size of the population does not matter if the sample is representative

nonsampling nonresponse error

the failure to obtain data from an individual selected for a sample -most serious problem

subjects

the individuals studied in an experiment

a manufacturer of table saw blades is interested in determining whether a narrower blade will cause less burning of wood when cutting very hard woods, such as maple. to answer this question, engineers obtain 100 similar one-inch-thick hard maple boards. half of the boards are sawed using the new, narrow-style blade, and the other half of the boards are sawed using the standard-width blade. all cuts are done at the same feed rate. the engineers then measure the amount of burning on each board. who are the individuals in this experiment?

the maple boards

what does statistical significance depend on?

the number of subjects involved

individuals

the objects described by a set of data -sometimes called subjects, participants, or cases

placebo effect

the response to a placebo/dummy treatment -says that people tend to respond to any treatment

texas and ohio have both enacted a new law that raises the minimum legal age to purchase tobacco products to 21. how do residents of each state feel about this new law? a simple random sample of 1000 adults is taken from Texas, and a separate simple random sample of 1000 adults is taken from Ohio. the population size of Texas is approximately 28.7 million people and the population size of Ohio is approximately 11.7 million people. if we use the quick method to estimate the margin of error for each sample, the margin of error for the Texas sample would be what compared to Ohio?

the same as the margin of error for the Ohio sample because the two random samples are the same size

statistics

the science of data

convenience sample

the selection of whichever individuals are easiest to reach -quick and easy method, but the sample might not be representative of the population

why do we select a sample?

to get information about some population

what is the purpose of an experiment?

to study whether the treatment causes a change in response

one of the principles of experimental design is to randomize. what does this mean?

to use impersonal chance to assign subjects to treatments in an experiment

Sawyer Technical College is a two-year college attended by both full-time and part-time students. Because parking conditions are not very good at STC, a survey is administered to students in order to find out more about how parking conditions might be improved. After survey data is collected, it is discovered that the survey was only sent out to full-time students; part-time students, who are also an important part of the population, were accidentally left out of the process of choosing the sample. we would refer to this as what?

undercoverage

how can you reduce the variability of a simple random simple?

use a larger sample

how can you reduce bias in a sampling method?

use random sampling

what decreases confounding?

using a randomized comparative experiment: comparing two or more treatments

what is the most common weakness in experiments?

we cannot generalize the conclusions widely

how might we eliminate or reduce the placebo effect?

we don't want to

when are two variables confounded?

when their effects on a response variable cannot be distinguished from each other -may either be explanatory or lurking variables

to see if eating just before bed causes nightmares, a sample of participants is recruited to spend the night in a sleep laboratory while being connected to machines that monitor their sleep patterns. participants are randomly assigned to be given a meal before bed or not, and the numbers of nightmares are recorded and compared for the two groups. what is the explanatory variable in this study?

whether a meal is eaten before bed or not

what are the types of error in estimation?

1. bias 2. variability

what makes a good observational study?

1. comparative 2. matching 3. measures and adjusts for confounding variables

what are the principles of experimental design?

1. control the effects of lurking variables on the response by ensuring all subjects are affected similarly by these lurking variables; then compare two or more treatments 2. randomize: use impersonal chance to assign subjects to treatments so treatment groups are similar, on average -reduces bias 3. use enough subjects in each group to reduce chance variation in the results

what are the types of biased sampling methods?

1. convenience sample 2. voluntary response sample

what are the advantages of random samples?

1. eliminates bias 2. if we take lots of random samples of the same size from the same population, the variation from sample to sample will follow a predictable pattern; this predictable pattern shows that results of bigger samples are less variable than results of smaller samples

which principle of experimental design controls the effects of lurking variables?

1. ensuring all subjects are affected similarly

what does a confidence statement consist of?

1. margin of error: says how close the sample statistic lies to the population parameter 2. level of confidence: says what percentage of all possible samples satisfy the margin of error -the conclusion of a confidence statement always applies to the population, not the sample -conclusion is never completely certain -95% confidence is usual, but another percentage can be chosen

what are the types of nonsampling error?

1. processing error 2. response error 3. nonresponse error -other nonsampling errors could arise if the questions are slanted to favor one response over others

how are random sampling and random assignment different?

1. random sampling deals with how subjects are chosen to be a part of a study 2. random assignment deals with how subjects are put into groups or allocated to treatments at the start of a study

what are the types of sampling errors?

1. random sampling error 2. undercoverage

what are the types of random sampling?

1. simple random sample (of size n) 2. stratified random sample

what is the margin of error for 95% confidence?

1/square root of n -because the sample size n appears in the denominator, larger samples have smaller margins of error -to cut the margin of error in half, we must use a sample 4x as large (because of the square root)