Statistics: |
a branch of mathematics that deals with collecting data and analyzing information to draw conclusions and help make decisions when faced with uncertainty. Statistics also provides a measure of confidence in a conclusion that is drawn. |
Example: |
1) Gathering data 2) Organizing and summarizing that data 3)Analyzing the data to find answers 4) Reporting the results in a way that shows how reliable those answers are |
Data |
“a fact or proposition used to draw a conclusion or make a decision.” |
Example: |
numerical; height. Nonnumerical; gender. |
Anecdotal |
The information being conveyed is based on casual observation, not scientific research. |
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—---- the misuse of data typically happens when data is incorrectly obtained or analyzed. |
Population vs. Sample |
Population: |
the entire group of items or individuals about which we want information; the entire set of objects or individuals to be studied |
Example: |
the set of all undergraduate students enrolled in Boston University as of Jan. 19, 2024. |
Sample: |
a subset of the population that is being studied. |
Example: |
part of the population of interest that we examine in order to gather information. |
Descriptive vs. Inferential Statistics |
Descriptive Statistics: |
consists of organizing and summarizing data using numerical summaries (e.g. mean, IQR, standard deviation), tables, and graphs. |
Inferential Statistics: |
uses information from a sample to make a conclusion about a larger group of items or individuals, e.g. the population. Inferential statistics are used to draw inferences about a population from a sample. |
Types of Variables |
Qualitative (or categorical) variable: |
a characteristic or attribute that places an individual into one of several categories |
Examples: |
gender; year in college –e.g. freshman, sophomore; state in which a person was born. |
Quantitative variable: |
a characteristic or attribute with numerical values for which arithmetic operations provide meaningful results (or “for which arithmetic operations make sense” |
Examples: |
How the daily weather is described - temperature, relative humidity. |
Two Types of Quantitative Variables |
Discrete variable: |
quantitative variable with either a finite number or countable number of possible values. Countable means the values result from counting, e. g. 0, 1, 2, 3 and so on. |
Examples: |
a household could have three children or six children, but not 4.53 children. |
Continuous variable: |
quantitative variable with infinite possible values which are not countable |
Examples: |
the response time of a computer could be 0.64 seconds, or it could be 0.64237123922121 seconds |
Observational Study vs. Designed Experiment |
Observational Study: |
researchers simply observe individuals or question participants without trying to influence their response. Often participants are chosen randomly. |
Designed Experiment (Experimental Study) |
Researchers setup an experiment and manipulate a variable and measure the effect of the manipulation on some outcome of interest. Often participants are randomly assigned to the various conditions and treatments. |
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Confounding: |
occurs in a study “when the effects of two or more explanatory variables are not separated.” |
Lurking variable: |
a variable that was not considered explicitly “in a study, but that affects the value of the response variable” |
Bias In Sampling |
Bias is a common problem during survey sampling. |
Selection bias (or Sampling bias): |
occurs if the method for selecting the participants produces a sample that does not represent the population of interest. |
