Year 13 Stats EXTERNAL

EXTERNAL

Bias

Something that causes favouritism

Census

A study that attempts to measure every unit in a population

Continuous Data

Data that can take any value in an (appropriately sized) interval of numbers

Control variable

A variable that is controlled in an experiment to help ensure the results are valid.

Discrete Data

Data that can only take on distinct values, often whole numbers

Explanatory variable

The variable in which may provide information about the other variable, (the response variable).

Mean

Calculated by adding the values and then dividing this total by the number of values.

Median

The central or middle value of an ordered dataset

Mode

A value in a distribution of a numerical variable that occurs more frequently than other values.

Point Estimate

A statistic calculated from a sample that is used as an approximate value for a population parameter.

Population

A collection of all objects or individuals of interest that have properties that someone wishes to record.

Qualitative Data

Data in which the values can be organised into distinct groups

Quantitative Data

Data in which the values result from counting or measuring. Measurement data are quantitative, as are whole-number data

Response Variable

The variable which may be affected by the other variable, (the

explanatory variable)

Sample

A group of objects, individuals, or values selected from a population. The intention is for this sample to provide estimates of population parameters.

Sample Size

The number of objects, individuals, or values in a sample.

Variable

A measurement, or characteristic (e.g weight or gender)

Causal Claim

A claim that the treatment causes the effect. Only valid if the study was an experiment.

Control group

The group who does not receive the treatment.

Experiment

A study in which a researcher attempts to understand the effect that a variable (an explanatory variable) may have on some phenomenon (the response) by controlling the conditions of the study.

Observational Study

A study in which a researcher attempts to understand the effect that a variable (an explanatory variable) may have on some phenomenon (the response) without having any control over the variables.

Opinion Distribution

The proportion of the target population that has each opinion.

Poll

A systematic collection of data about opinions on issues taken by questioning a sample of people taken from a population in order to determine the opinion distribution of the population.

Population Parameter

A number representing a property of a population, for example the mean, median, a proportion etc.

Random Allocation

Process of randomly assigning experimental units to groups using, for example a deck of cards or flipping a coin.

Survey

A systematic collection of data taken by questioning a sample of people taken from a population in order to estimate a population parameter.

Treatment

An applied change or influence that should result in a change in the response variable.

A study by researchers at Harvard School of Public Health, investigated the relationship between low childhood IQ and adult mental health disorders. The study participants were a group of children born in 1972 and 1973 in Dunedin. Their IQs were assessed at ages 7, 9 and 11 and mental health disorders were assessed at ages 18 through to 32 in interviews by health professionals who had no knowledge of the individuals’ IQ or mental health history.

This is an observational study because the researchers had no control over the explanatory variable, childhood IQ. The researchers could only record the assessed childhood IQ. The response was whether or not the individual had suffered from a mental disorder during adulthood.

In the 1980s the Physicians’ Health Study investigated whether a low dose of aspirin had an effect on the risk of a first heart attack for males. The study participants, about 22,000 healthy male physicians from the United States, were randomly allocated to receive aspirin or a placebo. About 11,000 were allocated to each group.

This is an experiment because the researchers allocated individuals to two groups and decided that one group would receive a low dose of aspirin and the other group would receive a placebo. The treatments are aspirin and placebo. The response was whether or not the individual had a heart attack during the study period of about five years.

In 2017 the AA asked its members how many of them would be willing to support the speed limit lowering from 100km/h on open roads to 90 km/h.

This is a poll as the final result would give a percentage of people in each group.

The Ministry of Business, Innovation and Employment conducts a study of international visitors to New Zealand where they are asked how much money they have spent while visiting New Zealand.

This is a survey as the final result would allow population parameters such as means, medians or quartiles to be estimated.

Global market research group Ipsos asked 501 New Zealanders in July 2018 if they, or someone they knew, had been affected by cyber bullying.

Poll

Stockholm School of Economics studied the behaviours and life satisfaction of people who had won and not won the Swedish lottery.

Observational Study

The New Zealand Herald asked people what their salary using an online popup.

Survey

16 males and 16 females who attended the Bing Nursery School of Stanford University were randomly allocated into two groups, half of the children were given two marshmallows and told they could eat one now or have two in 10 minutes time; the other half were only given one marshmallow and told they could have it now, or be given two in 10 minutes time. If they chose to eat the one marshmallow, or wait to eat two was recorded.

Experiment

Simple Random Sampling (Method, Advantages, Disadvantages)

Method - Allocate a number to every unit in the sampling frame. Generate random numbers. Match the random numbers generated to the units. Record the points of interest about the units. E.g. drawing names out of a hat or using a generator would be used to select participants randomly.

Advantage - An ideal method; each member of the population has an equal chance of being selected.

Disadvantage - Requires a sampling frame to identify every individual in the target population. It is time-consuming or impossible to carry out with large populations.

Systematic random sampling (Method, Advantages, Disadvantages)

Method - Using a random number to find a starting point on the sampling frame. Divide the total by the sample size (and round) to find how many units to count to select the next unit. E.g., the sample is made up of every Kth member on the list.

Advantage - It spreads the sample evenly over the whole population. It is simpler than simple random sampling ordered.

Disadvantage - If the target population has recurring patterns in it, the sample may not be representative.

Stratified Random Sampling (Method, Advantages, Disadvantages)

Method - Split the population into layers or strata by category, e.g. male or female. Allocate each unit in the population to a layer according to its category. Calculate the number to be selected from each layer in the same proportion as the number in each layer in the same proportion as the number in each layer in the population. Using this number, take a simple random sample or systematic random sample from each layer. E.g., you divide the population into meaningful groups (strata) — like grades, genders, or income levels — and then randomly select people within each group so the final sample reflects the population’s proportions.

Advantage - This method generates better coverage of the whole population

Disadvantage - The usefulness of the method depends on whether the strata (non-overlapping groups) have different underlying average values for the parameter being estimated. Need to know the proportion of the population in each layer. Complex to organise.

Cluster Radom Sampling (Method, Advantages, Disadvantages)

Method - Define a cluster. Randomly sample from the cluster. E.g., A city has 10 schools, each with about 300 students. You want to survey 600 students about their study habits. The clusters are the schools. You randomly choose 2 schools out of the 10.

Advantage - It is easier and cheaper than sampling from the whole population

Disadvantage - The success of the method depends on the choice of cluster.

Nonprobability Sampling (Method, Advantages, Disadvantages)

Method - Choose the most convenient place; e.g., the people who are most easily accessible are sampled (people on the streets)

Advantage - Very time- and cost-efficient

Disadvantage - The sample may not be representative of the population

Nonprobability sampling - Quota sampling (Method, Advantages, Disadvantages)

Method - Target numbers are set for groups the represents the groups in a population. Random or non-random samples of that number are taken within the group. The researcher pre‑decides the number of people needed from each group. E,g.,

• Participants are chosen non‑randomly (convenience-based).

• The final sample matches the desired proportions, not the actual population proportions.

Advantage - Feels like a representative method. Quick and cheap to organise.

Disadvantage - The people in the sample may not be representative of the population.

Nonprobability sampling - Snowball (Method, Advantages, Disadvantages)

Method - A person is selected who meets the required criteria, and they select the next person and so on; e.g., you start with a few people, and they help you find more people like them.

Advantage - It can locate hard-to-find data or people.

Disadvantage - May not be a representive of a population

Non-probability Sampling - Self-selected (Method, Advantages, Disadvantages)

Method - The sample is collected by people volunteering to contribute information, e.g. text in votes, responding to a magazine or newspaper or Facebook or Twitter question/survey

Advantage - Easy to set up and adiminster

Disadvantage - Responses are often extreme. High chance that the sample obtained will not be representative of the target population. It is highly likely that the inferences made would not be valid.

Selection Bais (Description + example)

Description - The sampling process is such that a specific group is excluded or under-represented in the sample, deliberately or inadvertently. If the excluded or under-represented group is different, with respect to survey issues, then bias will occur.

Example - If the target population is adults in New Zealand, and the survey is done by phoning people, there are going to be people missed as not all adults in New Zealand have a phone.

Self-Selection Bias (Description + example)

Description - The sampling process allows individuals to select themselves. Individuals with strong opinions about the survey issues or those with substantial knowledge will tend to be over-represented, creating bias.

Example - With polls on the internet normally only people who are interested in a particular topic will respond. This usually results in only people with strong opinions one way or another responding, and not giving a representative sample.

Behavioural Considerations (Description + example)

Description - Answers given by respondents do not always reflect their true beliefs because they may feel under social pressure not to give an unpopular or socially undesirable answer.

Example - For example in a survey about using cell phones when driving, people are less likely to be honest, as they know it is illegal to use a cell phone when driving.

Interviewer Effects (Description + example)

Description - Answers given by respondents may be influenced by the desire to impress an interviewer. The sx, race, religion and manner of the interviewer can all influence how people respond to a particular question.

Example - If the interviewer was a Catholic priest or a leader of a mosque, the way people may respond might be quite different if the interviewer didn't have any obvious religious affiliation.

Transfer of findings (Description + example)

Description - Taking the data from one population and transferring the results to another can lead to incorrect conclusions being made.

Example - A survey done in Wellington may not be able to be applied to people all around New Zealand.

Non-Response Bias (Description + example)

Description - If people who refuse to answer are different, with respect to survey issues, from those who respond then bias will occur. This can also happen with people who are never contacted and people who have yet to make up their mind.
Also, if the response rate (the proportion of the sample that takes part in a survey) is low, bias can occur because respondents may tend consistently to have views that are more extreme than those of the population in general.

Example - In an survey about working hours, those that do not respond are likely to be those who work long hours as they don't have time to respond.

Question Effects (Description + example)

Description - The wording of questions can influence survey results. Even small changes can make big differences in results.

Example - On 18 August 1980 New York Times/CBS News ran a Poll and asked two questions as part of a longer survey:
• "Do you think there should be an amendment to the constitution prohibiting abortions?"
Yes 29% No 62%
• "Do you think there should be an amendment to the constitution protecting the life of the unborn
child?"
Yes 50% No 39%
We can see while the questions are asking opinions on the same topic, the results are very different.

Survey Format (Description + example)

Description - The order in which questions are asked, how the survey is conducted (in person, online, via the phone), and the number and type of options offered can influence survey results.

Example - If this question was asked: "To what extent do you think teenagers are affected by peer pressure when drinking alcohol?"
Followed by:
"Name the top 5 peer pressures you think teenagers face today."
It is likely to result in skewed answers to the second question.
Long surveys are also likely to get people rushing through and not thinking carefully about their answers.