Phil 105 Generalization

"What is the main idea of 'Generalizations and Statistical Evidence'?"

Main idea is to reason well with generalizations

"What is 'Statistical generalization'?"

Creating general claims about a population from a sample

"What is 'Statistical Instantiation'?"

Creating a specific claim about a sample from a general claim

"What does 'Sample as Evidence' include?"

Good and bad ways to collect samples; Not all samples do not always support the hypothesis directly and strongly

On what is the strength of evidence dependent?

Strength of evidence is dependent on probabilities; Probability of e given H; Probability of e given Not H

What affects the accuracy of probabilities?

Accuracy of probabilities; Sample size

Example: In Phil 105, two students are sampled and both are right-handed — what question is asked?

Knowing how many people in Phil 105 are right-handed; Two students are sampled; Both are right-handed

If two students sampled are both right-handed: how likely is this if everyone in the class is right-handed?

1

If two students sampled are both right-handed: how likely is this if at least one person in this class is left-handed (as a way of implying the opposite claim)?

>1 (such as 0.8)

How can the result be analyzed quantitatively in the example?

Can also be analyzed by using strength factor; Strength factor = 1.25; Very weak support

What ratio quantifies the amount of strength to support the hypothesis?

E if H is true / E if H is not true; Quantifies the amount of strength to support the hypothesis

What about instances of selection effects?

Any instances of selection effects

Why do sample sizes matter?

Small sample sizes provide insufficient or weak evidence

How big of a sample size is necessary?

Depends on how precise your conclusion is to be; Rule of thumb is the law of large numbers

Raven Mutation Hypothesis example — what is H in Example 1?

H: All ravens on the island have the mutation

Raven Mutation Hypothesis Example 1 — probability if H is true?

1 (Because you couldn’t see anything else wrong with the ravens)

Raven Mutation Hypothesis Example 1 — if Not H: 80% of ravens have the mutation, what is the probability of two sampled ravens both having the mutation?

Roughly 0.33 = 0.8^2

Raven Example 1 — what is the strength factor roughly?

Strength factor is roughly around 3

What is a rule of thumb sample size to obtain significant strength factor?

10 is a rule of thumb to obtain significant strength factor

Raven Mutation Hypothesis Example 2 — what is the strength factor when Not H probability is roughly 0.01?

Strength Factor is 100; Really strong suppositional strength

What are the upshots about sample size and representativeness?

A larger sample is more representative of population; Unrepresentative samples are the cause from small sample sizes

How big of a sample do we need (summary)?

An appropriate sample size to get the accuracy of conclusion you want

What is the status quo for Confidence Interval?

Status quo is 95%; A range of values that supports your hypothesis based on specific ranges to get one of those values

What is the status quo for Margin of Error and what does it represent?

Status quo is 3%; A range of values outside of the confidence interval; Doesn’t support your hypothesis

What are types of Selection Effects leading to Sampling Biases — Geographical?

Geographical: More independent, locally owned restaurants are in the downtown area; Sample is not reflective of everyone in that area

What are types of Selection Effects — Socioeconomic?

Socioeconomic: Neighbours with more wealth are more likely to have intendent, flashy restaurants; Sample is underrepresented; From focusing on one instance

What selection effect can Time of Day cause?

Time of Day: Some restaurants, diners, and other businesses depend on the daytime to accommodate for their targeted audience; Causes sample to not be reflective of what’s available in that area

What selection effect can Type of Cuisine cause?

Type of Cuisine: Family run restaurants are often chosen depending on type of cuisine; The chosen participants reflect their preference of cuisine

What is an appropriate sampling method to reflect the entire population?

Appropriate proportion of subgroups that reflect the entire population; Refers to stratified sampling method; Also, a criteria of a representative sample

What are common survey pitfalls relating to participation biases?

Participation biases: Rate my prof has extreme data from both ends; Either extreme love or hate for the prof; Selectively targeting a specific demographic; Being anonymous or not dictates how comfortable you feel to share your information

Give an example of response bias mentioned in the notes.

Response bias: Using ChatGPT to generate answers to your assignments

How does the use of language influence bias in surveys?

Use of language also influences the amount of bias from participants; Negatively structured questions; Double barrelled questions; Overwhelming pieces of information in the question

What is the role of summary statistics in analyzing data?

Summary statistics: criterion of summarizing the statistical data to convey the most important information; Two Questions: What features of the data are most important? What is the most appropriate way to present the data?

When is the median particularly helpful?

Median is helpful with outliers in a data; Using the arithmetic mean distorts the true reality of the data set

When is the mode helpful?

Mode is helpful to find what’s most common of a product or service

What is a truncated mean?

Truncated mean

What is the geometric mean and how is it calculated?

Geometric Mean: A type of mean calculation for calculating the average of growth rates; Nth root of the product of those values; Multiply those values and put it in a root of how many values is present