Chapter 1: Statistics, Data, & Statistical Thinking

Question 0

What is statistics made up of?

Answer 0

Data

Question 1

Define (Statistics)?

Answer 1

The science of collecting, organizing, analyzing, raw data, then presenting it so that it can be used to make predictions, decisions, or draw conclusions.

Question 2

Explain the four step process of statistics.

Answer 2

1) Identify what you want to research: To do this a researcher must decide what questions they want answered, questions must be specific, this helps determine what population they will use to get their answers.
2) Collect data needed to answer questions: Samples are often used because populations are to big, if data is not collected probably conclusions drawn from data will be flawed.
3) Describe the data: Once the data is collected and analyzed it must be presented to others, the two ways of doing this is (Graphically or Numerically).
4) Perform Inference/ Draw Conclusions : Accurate results should be able to be extended to the entire population with a high level of confidence.

Question 3

What is (Data)?

Answer 3

Info. that describes characteristics of an individual, can be (Numerical or Non-Numerical), eg gender is a variable, but the information that the gender is male or female are data.

Question 4

What do we use data for.

Answer 4

We use data to draw conclusions, make decisions predictions, etc.

Question 5

What is a (Data Item)?

Answer 5

One particular piece of data.

Question 6

What is the difference between (Data & Information)?

Answer 6

1) Data: A collection of raw facts or numbers.

2) Information: Analyzed data, that holds a particular meaning.

Question 7

What is a (Data Set)?

Answer 7

A collection of counts, measurements, etc. that’s collected while performing a study.

Question 8

Describe the difference between (Descriptive and Inferential) statistics?

Answer 8

1) Descriptive: The use of (Tables/Graphs), to summarize data.
2) Inferential: Taking the results of a (Sample), & implying them to the (Entire Population).

Question 9

What are the different types of data?

Answer 9

There are different types of data for each type of variable, thus qualitative variable corresponds with a qualitative data, the same is so for quantitative, discrete, or continuous data.

Question 10

What is the (Probability Theory) based on?

Answer 10

(Inferential Statistics).

Question 11

What is a (Population)?

Answer 11

The collection of all outcomes being studied, eg. all counts, measurements, etc. a population does not have to be large, eg. all the people in a city, everyone in a 20 member class, or all the corvettes made last year are all populations.

Question 12

What is a (Parameter)?

Answer 12

A numerical measurement that describes a characteristic of a population, eg. 30% of Americans are overweight, 30% describes a characteristic of a population, thus it’s a (Parameter).

Question 13

Why do we study populations?

Answer 13

To look for characteristics in the elements that make up the population, theses characteristics are called variables, eg. we may be interested in the average age, & education of all the women in a small town.

Question 14

What is a (Sample)?

Answer 14

A part of a whole population, most populations are large, thus you can’t measure everyone or everything in a population, instead you measure a smaller piece, or sample.

Question 15

What is a (Statistic)?

Answer 15

A numerical measurement that describes a characteristic of a sample, eg. 30% of the 400 people participating in the study were considered overweight.

Question 16

What is the importance of a (Measurement)?

Answer 16

It assigns a value to a variable, eg. a group of male workers makes up a population, the variable is they are all male, if we want to assign a value to the variable, we take a measurement, for eg. age, height, weight, how fast they run a .25/mile, etc. then we assign a number/value to the variable.

Question 17

What is a (Variable)?

Answer 17

Characteristics of an individual that is part of a population or sample, variables often change between individuals, eg. gender, height, age, etc.

Question 18

What is one of the main goals of a researcher?

Answer 18

To help determine why certain variables are so different between individuals.

Question 19

Name the 2 types of variables?

Answer 19

1) Quantitative: A variable that has a (Quantity), thus it consists of numbers, eg. tempt, weight, height, etc.

There are 2 types of (Quantitative Variables).

a) Discrete: Variables that have a definite value that can be counted, eg. number of children in a family, students in classroom, etc.
b) Continuous: Variables that have an infinite number of values, variable must be measured, eg. temp, height, weight, etc.
2) Qualitative: A variable having to do with (Qualities), thus it consists of words, eg. short, tall, male, female, etc. but if variable is presented as people who are 5’6” or under, it becomes (Quantitative Data).

Question 20

Name the 4 levels of measurement that a variable can be measured in?

Answer 20

1) Nominal: A variable is nominal if it names, labels, or categorize data, nominal variables have no specific value, thus they can’t be ordered or ranked, eg. political parties, religions, marital status, etc.
2) Ordinal: An ordinal variable is the same as a nominal variable except it can be ordered or ranked, eg. letter grades, evaluations, etc.
3) Interval: Data with precise value, even if data lies between 2 measurements it’s exact value can be found, data can be ordered or ranked, this measurement has a zero, but it’s not a true zero, eg. IQ scores, temp, on a cold day a thermometer might read zero, but that doesn’t mean there is no temperature, thus it’s not a true zero.
4) Ratio: Has a true zero, true ratio is difference between the same variable of 2 different values, data can be ordered or ranked, eg the difference between 2 people’s weight, age, or height, eg. if one person is 3 feet tall and another is 6 feet tall the (Ratio) is the person that’s 6 feet tall is twice as tall as the 3 foot tall person.

Question 21

What is a measure of (Reliability), & why is it important?

Answer 21

A statement that describes (Uncertainty) found in inference statistics, the only way to be 100% sure of a measure is to measure entire population, in most cases this can’t be done, thus there is always a (Degree of Uncertainty) when measuring a sample of a large population, eg. 60% of 1000 people sampled preferred Coke or Pepsi, the 60% doesn’t mean 60% of entire population prefers Coke, but 60% is within a certain range of entire population, let’s say 5%, thus (60% +/- 5%) is the number of reliability for the inferred stat.

Question 22

What is a (Constant Sample)?

Answer 22

A sample that has all the same elements, eg. a sample of all women, men, lawyers, etc.

Question 23

What type of variable are these level of measurements?

Answer 23

Both nominal and ordinal are qualitative variables, while interval and ratio are quantitative variables.

Question 23

Where are some places that you can collect pre-existing data.

Answer 23

1) Governmental Sources: The government collects all types of data, eg. crime, obesity, poverty rate, census, etc.

Question 24

Describe the 4 methods used to collect data.

Answer 24

1) Observational Study: Research performed while observing characteristic of individuals researchers want to study, the major difference between observation and experimentation is the variable being studied can't be manipulated in any way, observational studies only determine relationships between variables, not cause and effect. 2) Experimental Study: Researchers manipulate the variable they want to study with goal of predicting outcome, variable in experimental group is manipulated, variable in control group is not, thus any change in experiment is due to variable manipulation. 3) Simulation: A physical model of a real life situation, simulations allow us to study situations that may be dangerous to researchers if they tried to re-create them, eg. car crash dummies. 4) Survey: Used when studying one or more characteristics about a population or sample, when conducting survey researcher must be careful how questions is worded, could lead to bias answer.

Question 26

Describe the three different types of (Observational Studies).

Answer 26

1) Cross-sectional studies: Collects info. about individuals at either specific, or over short period of time, advantages studies are cheap and easy to perform, disadvantages don't always tell whole story. 2) Case-control studies: Requires individuals to remember past events, or researchers to depend on past documents/records, individuals with certain characteristics are matched with individuals who don't share similar characteristic, advantages cheap/easy to perform, disadvantages researchers must count on individuals to remember past events accurately, & truthfully. 3) Cohort studies: Identify group that share common characteristic, aka (Cohorts), observe over time, usually long period of time, some cohorts may have been exposed to (Explanatory) variable while, others may not, due to data collected over long time this is called a (Prospective Study), advantages most powerful of all observational studies, disadvantages performed over long time, individuals drop out could lead to flawed outcome.

Question 27

Which is better observational or experimental studies?

Answer 27

While experimental studies determine cause-and-effect observational studies are important in research also, they are usually performed when experimental studies are not possible.

Question 28

What is a confounding variable, what type of experiments are they usually found in?

Answer 28

A variable that was not accounted for, thus it could affect the outcome of the study/experiment, usually happens during observational studies.

Question 29

In regards to an experiment what does (Blinding) mean?

Answer 29

It's when the participants of an experiment don't know if they are part of the experimental group, or the control group.

Question 30

What does the info. from a sample of a population tell us?

Answer 30

If the sample size is large enough it can infer the characteristics of the entire population.

Question 31

What are some of the ways stats. can be misleading?

Answer 31

1) Sample Size/Selection: If the sample size isn't big enough, or selection random enough, the results could be misleading. 2) How was stats/results averaged, aka (Ambiguous Average). Which method used to find average; mean, median, mode, or midrange, using one or the other can help support your agenda. 3) What value is attached to stat: Spending is up 3% is better than saying its up 6/million, even though both might be true. 4) Detached Stats: When a comparison is made via a stat, what is the stat being compared to, eg. Brand a is 5x better; better than what is what you should ask yourself. 5) Implied Connection: A connection maybe implied that really doesn't exist, be careful not to draw conclusions were none exist. 6) Be careful of graphs, they can be misleading. 7) If survey is used to obtain stats, how were questions phrased, phrasing could effect outcome.

Question 32

Describe the 4 basic sampling methods used to obtain a population or sample, explain each method?

Answer 32

1) Simple Random Sampling: Every member in population has equal chance being selected, eg. like picking random numbers out of a hat. 2) Systematic Sampling: No (Frame) needed, individuals of population selected at regular intervals until sample size is reached, eg. we decide to survey every eighth individuals in a population, we randomly choose number between 1 & 8, eg. 5, start with 5th person, this is first person in sample size, then add 8 to 5 to get 13, then add 8 to 13 & get 21, we continue adding 8 to last number until sample size is filled. 3) Stratified Sampling: Population divided into 2 or more subgroups called (Strata) based on (Homogeneous) or similar characteristics, eg. sex, ethnicity, age etc. a sample is obtained randomly from each strata, advantages, don't have to interview as many people as you do in simple random sample, yet get same if not more information, eg. establish similarities or differences based on like characteristics such as age, race, gender, etc. 4) Cluster Sampling: Population divided into subgroups, groups could have either similar/dissimilar characteristics, sample obtained by surveying all members of simple randomly selected clusters, disadvantages outcome not as precise, advantages cost-effective.

Question 33

What is a simple random sample, what is key to accomplish it, & what is the goal of every simple random sample?

Answer 33

The process by which chance dictates an individual from a population being chosen to take part in a study, randomness is key in accomplishing this, eg. we want to select five from a population of 30, thus we put all 30 in a hat and randomly select five, the goal of every random sample, is for it to be representative of the entire population.

Question 34

How does one obtain a simple random sample?

Answer 34

Assign individuals in population a 2 digit number starting with 01, end with total amount of population, choose simple random sample from 01, & last number of total population.

Question 35

Why does inference in a simple random sample vary?

Answer 35

Because numbers in simple random sample vary, thus the numbers pick in one simple random sample will most likely not be duplicated in a second random sample.

Question 36

Explain the (Convenience Sampling Method), what are the disadvantages of convenience sampling?

Answer 36

Sampling done with no randomness, based on convenience, eg. Individuals in close proximity during time of sample, disadvantage may not represent entire population, not random, instead individuals are self-selected.

Question 37

Explain the difference in using a seed for a simple random sample versus a stratified sample.

Answer 37

In a simple random sample you only need one seed, in a stratified sample you need a new seed for each stratum.

Question 38

What is a (Double Blind Experiment)?

Answer 38

It's when the researcher as well as the participants don't know if they are part of the experimental or control group, this design is the preference of most researchers

Question 39

What are the 3 key elements of a well designed experiment?

Answer 39

1) A control 2) Random Assignment 3) The outcome must be able to be replicated

Question 40

In statistics what does the word (Individual) mean?

Answer 40

An individual is a person or an object that is part of a population that we want to gather information on.

Question 41

What is the difference between an (Explanatory, Response, & Lurking Variable)?

Answer 41

1) Response Variable: A particular (Situation or Quantity) that a researcher is interested in studying. 2) Explanatory Variable: Anything that could influence response variable. 3) A Lurking Variable: An exploratory variable not considered in an experiment, yet it can affect response variable, thus any relationship between exploratory and response variable may be caused by this lurking variable.

Question 42

What is a (Census), how often is it taken?

Answer 42

A list of individuals in a population including certain characteristics about each individual, mandated by the Constitution, the census must be taken every 10 years.

Question 43

Why is a census important, and is the U. S. successful at taking it.

Answer 43

1) Census helps determine number of representatives in House of Representatives. 2) It helps determine how governmental funds are distributed, eg medicaid. 3) It helps plan for the construction of schools and roads. No certain members of the population go uncounted, eg. those who are illiterate, can't speak the language, the homeless, are here illegally, etc.

Question 44

When was the first census taken.

Answer 44

In 1790 under the presidency of Thomas Jefferson.

Question 46

What is the difference between (Sample Without Replacement vs Sample With Replacement)?

Answer 46

Sample without replacement means what's your name has been selected from the population your name does not go back in the population, thus you can't be chosen a second time, sample with replacement means your name does go back in the population once chosen, thus you can be chosen a second time.

Question 47

In statistics what is the difference between little n, & big N?

Answer 47

Little n is the sample size, which are pulled from big N which is the population size.

Question 48

What is the goal in sampling a population?

Answer 48

To obtain info. about the population, with the least amount of expense.

Question 49

In statistics what causes a sample to be (Bias)?

Answer 49

A sample is biased when it does not represent the population.

Question 50

What are the three sources of bias while sampling a population?

Answer 50

1) Sampling Bias: Methods used to obtain individuals for sample favors some in a population over others. 2) Non-Response Bias: 3) Response Bias:

Question 51

What is a (Frame)?

Answer 51

A list of all individuals in a population being studied.