Quantitative Reasoning

Statistics

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Affirmations

• I am building my future
• I will handle whatever happens, like I always do
• I can have a positive impact on another student’s life

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Data Collection Basics

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Learning Goals

1 Understand the difference between a census and a sample, and be able to identify the population being studied

2 Distinguish between a value calculated from a sample and one calculated from a population

3 Categorize a measurement as either numeric or qualitative

Deepen your understanding and form connections within these skills:

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Population

The population of a study is the group the collected data is intended to describe.

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Parameter

A parameter is a number that summarizes a characteristic of the entire population. It can be an average, percentage, or any other value that is calculated using data from the whole population.

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Census

A census is a type of survey where data is collected from every single member of the population. It's like counting or surveying every person or object in a group.

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Sample

A sample is a smaller subset of the entire population, ideally one that is fairly representative of the whole population.

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When we want to study a big group of people but can't survey everyone, we choose a smaller group called a sample.

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Statistic

A statistic is a value (average, percentage, etc.) calculated using the data from a sample.

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Observational Units

Observational units are the group of individuals, animals, or objects that are being studied or surveyed in a research. They are the ones we want to learn about and collect information from.

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Variables

Variables are the different characteristics or qualities of the observational units that we measure or record in a study.

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Qualitative and Quantitative Data

Data can be divided into two types: qualitative and quantitative.

• Qualitative data describes qualities or attributes of a group, like hair color or blood type. It uses words or categories to describe these attributes, such as black hair or blood type AB+.
• Quantitative (or categorical) data involves counting or measuring things. It uses numbers to represent information, like the amount of money you have or the weight of an object. It can be further divided into discrete data (counting whole numbers) or continuous data (numbers including fractions or decimals), such as the number of phone calls you receive in a day or the length of those calls.

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Try It!

1 You are conducting a survey to gather information about people's commuting habits. List at least three examples of qualitative data and three examples of quantitative data that you might collect in this survey.

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2 A researcher is studying the habits of plants in a garden. Identify and categorize the types of data (qualitative or quantitative) that the researcher might collect: color of flowers, height of plants, type of plants, and soil pH level.

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Discussion: Discuss the importance of distinguishing between qualitative and quantitative data in research. How does the type of data collected influence the analysis and interpretation of results in a study?s would be beneficial?

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Sampling and Experimentation

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Learning Goals

Deepen your understanding and form connections within these skills:

• Identify methods for obtaining a random sample of the intended population of a study
• Identify types of sample bias
• Identify the differences between observational studies and experiments, and the treatment in an experiment
• Determine whether an experiment may have been influenced by confounding

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Sampling Bias

When collecting a sample, it's important to choose it in a way that represents the whole group. Sampling bias happens when some members of the population are more likely to be chosen than others, which can lead to wrong conclusions about the entire group.

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Random samples are preferred because they have no bias, but even random samples can vary and may not perfectly represent the population.

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Simple Random Sample

Simple random sampling means that when selecting a sample, every individual or entity in the population has an equal and fair chance of being chosen. It ensures that each member and any group from the population has an equal probability of being selected for the sample.

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Systematic Sampling

In systematic sampling, each person or object in the population is assigned a number. Then, we choose individuals at regular intervals, like every 5th or 10th person, starting from a randomly selected point. This way, we ensure that every "n"th member of the population is included in the sample.

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Systematic Sampling

• Stratified sampling is when a population is split into different groups based on certain criteria, like location or age. Then, a sample is chosen from each group using methods like random selection, but the size of each sample is based on the size of the group in the population. This helps ensure that each subgroup is represented properly in the sample.
• Quota sampling is a modified version of stratified sampling where samples are collected from each subgroup until a specific target or quota is reached.

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Cluster Sampling

Cluster sampling is a method where instead of selecting individual people or objects, the population is divided into smaller groups called clusters. Then, a few of these clusters are randomly chosen to be part of the sample for the study.

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Convenience Sampling and Voluntary Response Sampling

Convenience samples and voluntary response samples are considered among the least reliable sampling methods.

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• Convenience sampling is when samples are chosen based on who is readily available or convenient to include.
• Voluntary response sampling is a method where individuals choose to participate in the sample on their own accord.

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Sources of Bias

• Sampling bias – when the sample is not representative of the population
• Voluntary response bias – the sampling bias that often occurs when the sample is volunteers
• Non-response bias – when people refusing to participate in the study can influence the validity of the outcome
• Response bias – when the responder gives inaccurate responses for any reason
• Self-interest study – bias that can occur when the researchers have an interest in the outcome
• Perceived lack of anonymity – when the responder fears giving an honest answer might negatively affect them
• Loaded questions – when the question wording influences the responses
• Undercoverage occurs when some groups of the population are left out of the sampling process.

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Try It!

1 You are reading a research paper where the participants were all volunteers who are members of a specific online community. Identify the potential source of bias in this study and explain how it might affect the results.

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2 A company conducts a survey on employee satisfaction but excludes remote workers from the sample. Identify the potential source of bias and discuss how it might influence the study's conclusions.

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Discussion: Discuss the implications of different sources of bias on the validity and reliability of research findings. How can researchers mitigate these biases to ensure more accurate and representative results?

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Confounding

Confounding happens when there are two possible factors that could have caused a result, but we can't tell which one is actually responsible.

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Observational Studies and Experiments

An observational study is a study based on observations or measurements.

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An experiment is a study in which the effects of a treatment are measured.

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Try It!

1 A researcher is studying the effects of diet on heart health. They divide participants into two groups: one follows a specific diet plan, while the other continues with their regular diet. The researcher then measures the heart health of participants in both groups after a few months. Identify whether this study is an observational study or an experiment and explain your reasoning.

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2 A sociologist is studying the relationship between educational level and job satisfaction. They collect data from various individuals about their educational qualifications and their level of job satisfaction. Identify whether this study is an observational study or an experiment and explain your reasoning.

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Treatments and Placebos

Treatments are experimental conditions into which the participants are divided, some into the group receiving the treatment of interest and others into a control group that does not receive the treatment (a placebo).

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A placebo is a harmless version of the treatment that does not contain any active ingredients (e.g., a sugar pill).

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Placebo Effect

The placebo effect is when the effectiveness of a treatment is influenced by the patient’s perception of how effective they think the treatment will be, so a result might be seen even if the treatment is ineffectual.

A placebo is a dummy treatment given to control for the placebo effect.

An experiment that gives the control group a placebo is called a placebo controlled experiment.

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Blind Studies

A blind study is one in which the participant does not know whether or not they are receiving the treatment or a placebo.

A double-blind study is one in which those interacting with the participants don’t know who is in the treatment group and who is in the control group.

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Advanced Experimental Design

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Learning Goals

1 Review an experiment and explain if it has been designed well

2 Use randomized block design to create a hypothetical experiment to answer a research question

Deepen your understanding and form connections within these skills:

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Experimental Design

Experimental design consists of two key components:

• the factor of interest, which is the variable we think has an impact
• the response variable, which is the variable we believe is influenced by the factor of interest

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Randomized Block Design

Randomized block design is a method used in experiments where similar subjects are grouped into blocks, each differing in ways that might affect the outcome. Nuisance factors can be controlled by adding them to the experimental design, and blocking refers to grouping similar subjects together and randomly assigning them to different treatments within each group.

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Vocabulary Activity

We have seen a lot of vocabulary terms in this module.

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With your partner, work through the vocabulary sheet to define the term in your own words and visualize the meaning.

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Statistical Analysis in Practice: Exploring Flavanol Research and Experiment Design

Within your group, read the article on the impacts of flavanol consumption on cognitive performance and discuss the questions provided.

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If time permits, within your group, design your own experiment.

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Closing Slide

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Next Steps…..

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Questions…..

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Anything else….

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