Quiz Two - Scopes and Methods

Population

The entire group of people, place, events or other cases that you want to study

Parameter

A size fixed that described something about a population. This is often the average, median or standard deviation of a variable. Examples include average age, proportion of non-voters, etc.

Sample

A selected set unit from a population collected with the ogal of understanding more about the population

Statistic

A numerical value calculated from a sample used to estimate an unknown parameter

Variable

A characteristic that can take different values

Independent variable

The variable used to explain or predict a difference

Dependent variable

the outcome you want to explain

What makes a good sample?

It should reflect the population you want to study, be reliable and measure what it is intended to measure without systemic bias

Law of Large Numbers

As the number of sampled cases increases, the sample average tends to get closer to the true population average. It does not automatically eliminate bias - a very large, unrepresentative sample can still provide misleading results.

Coverage bias

Some members of the population are excluded by the methods used to select participants. An example of this is using a telephone directory that excludes those without listed landlines.

Non-response bias

Certain types of people are less likely to respond to a survey. An example os this is that younger respondents are less likely to complete a curevey, so their opinions are underrepresented.

Convenience sampling

A sampling method that selects people who are easy to reach. This is quick, but often bias.

Quota sampling

A sampling method that selects convenient participants to full target categories. Matching categories does not guarantee representativeness.

Snowball sampling

A sampling method that uses existing participants to recruit more participants. Useful for finding people through social networks.

Simple random sampling

A sampling method that selects cases randomly from the population. Each eligible case has an equal chance of selection.

Stratified sampling

Divides the population into important subgroups, then randomly samples within each. Helps ensure subgroups are represented

Cluster sampling

Divides the population into clusters and randomly selects clusters. Useful when sampling individuals across a large population is difficult.

Question wording (respondent error)

Different wording chances how respondents interpret a question

Question order (respondent error)

Earlier questions influence later answers

Social desirability bias (respondent error)

People give answers they think are socially acceptable rather than answers reflecting their actual behaviour or beliefs

Uncertainty (respondent error)

A respondent genuinely does not know the answer

Ambivalence (respondent error)

A respondent has mixed feelings or does not clearly agree or diagree

Priming (respondent error)

A question or cue makes certain ideas more prominent when a person responds

Acquiescence bias (respondent error)

People tend to agree with statements, particularly when response options are limited. When someone chooses “yes” or true” options regardless of their true feeling or content.

Leading question (respondent error)

Wording encourages respondents towards a particular answer

Double-barreled questions (respondent error)

One question answers about two things at once, making it hard to answer correctly

Classical theory (survey response theory)

People have relatively stable preferences, and surveys measure those preferences

Converse (survey response theory)

People can hold conflicting opinions, so their answers may not reflect a consistent underlying belief

Zaller (survey response theory)

Survey answers reflect both existing preferences and the content in which the question is asked

RAS Model

Receive information or cues

Accept or reject the information based partly on existing beliefs

Sample a consideration that helps form the answer in the current context

Mean

The average: add all values and divide by the number of values

Median

The middle value when values are arranged in order

Mode

The most frequently occurring value

Range

Highest value minus value - sensitive to outliers

Interquartile range

Spread of the middle 50% of observations — less affected by extreme values

Deviation

The distance between an individual value and the mean

Variance

The average of squared deviations from the mean

Standard deviation

The square root of variance — measures spread in the original units

Standard error

Measures uncertainty in a sample estimate, such as a sample mean

The different between standard deviation and standard error

Standard deviation asks, “how spread out are the individual observations"?

Standard error asks, “how precisely have we estimated the population mean?”

Symmetrical distribution

Mean = median

Values are distributed evenly around the center

Left-skewed distribution

Tail extends toward lower values

Mean is generally less than the median

Right-skewed distribution

Tail extends toward higher values

Main is generally greater than the median

Unimodal

One peak

Bimodal

Two peaks

Multimodal

More than two peaks

Uniform

Values are distributed aprox. evenly across the range

Continuous or interval graph

Histogram

Ordinal

Bar lot

Nominal

Bar plot or pie chart

Yes/no variable

Display the percentage in each category

Categories measured over time

A line chart can show changes over time

Transforming data

Change the scale of a variable. Ex. taking the logarithm of a strongly right-skewed variable such as income

Aggregate data

Combine values into meaningful groups. Ex. converting exact ages into age categories

Within 1 SD

About 68% of observations

Within 2 SD

About 95% of observations

Within 3 SD

About 99.7 of observations

Central limit theorem

States that, under appropriate conditions, the distribution of sample means becomes approx. normal as somaple size increases, even if the original population distribution is not normal

Alternative hypothesis

Ha or H1 — The claim you are interested in testing. It predicts an effect, relationship or difference.

Null hypothesis

H0 — The opposing claim, usually that there is no effect or difference

What makes a good hypothesis?

Specifies the population, independent variable, dependent variable and expect direction of the effect

What does a t-test do?

Evaluates how compatible your observed sample result is with the null hypothesis

One sample t-test

Compares a sample mean with a specified value

Two sample t-test

Compares the means of two groups. The null hypothesis usually states that the difference between the population means is zero.

What happens to the t-statistic: the greater distance between the observed result and the null value

Increases t

What happens to the t-statistic": greater sample standard deviation

Decreases t

What happens to the t-statistic: larger sample size

Increases t

P-value

the probability of observing a result at least as extreme as the one obtained, assuming the null hypothesis is true and using the specified test. threshold is alpha = 0.05

If the p-value is below 0.05…

we REJECT the null hypothesis

If the p-value is above 0.05…

we FAIL TO REJECT the null hypothesis

Never say the following

“We accept the null hypothesis.”

“We have proven the alternative hypothesis.”

“There is less than a 5% probability that the null hypothesis is true.”

One-sided test

Tests a directional prediction, such as whether one group’s mean is higher than another’s

Two-sided test

Test whether a value different in either direction, higher or lower

Point estimate

A single number used to estimate a population parameter

Confidence interval

Gives a range of plausible values for the population parameter based on sample data

Bivariate analysis

Examines the relationship between two variables