Research Notes week 6 & 7

Imagine you're a social worker who wants to find out whether a new counselling program helps reduce anxiety. what questins do you need to ask?

Step 1: What are you studying?

Does the counselling program reduce anxiety?

Step 2: How will you collect data?

Use an anxiety questionnaire before and after the program.

Step 3: How will you describe the results?

Calculate average anxiety scores and examine how much scores vary.

Step 4: How will you interpret the results?

Use an appropriate statistical test to assess whether the observed difference is statistically significant.

What is data collection vs. data analysis?

• Data collection is how you obtain information from participants.

• Data analysis is how you organize, summarize, and examine that information to answer your research question.

What is an instrument in research?

A tool used to measure quantitative reasearch

A questionnaire measuring anxiety.

• A scale measuring depression.

• A blood pressure monitor measuring blood pressure.

• A test measuring memory retention.

What is a survey?

Surveys can be used for descriptive, explanatory, and exploratory research. They can be completed at one point in time or at multiple points over time.

Type

Meaning

Cross-sectional

Collect data at one point in time.

Longitudinal

Collect data at multiple points over time.

Desscriptive research

Descriptive research describes a situation, group, or phenomenon. It helps researchers understand what something looks like, how common it is, or what characteristics people have.

Example: A researcher surveys 500 university students to find out how many experience anxiety.

Research question: How many university students experience anxiety?

Remember: It describes what is happening, but it does not necessarily explain why.

Explanitory research

Explanatory research investigates why something happens or how different variables are related. It looks for possible explanations for a situation or phenomenon.

Example: A researcher studies whether financial stress, social isolation, and academic pressure are associated with anxiety among university students.

Research question: Why do some university students experience higher levels of anxiety than others?

Remember: It tries to explain why or how, although finding an association does not automatically prove causation.

Exploritory research

Exploratory research investigates a topic that is not yet well understood. It helps researchers learn more about an issue, identify themes, and develop questions for future research.

Example: A researcher interviews students to explore how they experience anxiety and what challenges they believe contribute to it.

Research question: How do university students experience and understand anxiety?

Remember: It explores an unfamiliar or poorly understood topic to gain insight and guide further research.

What are the 4 types of variables in statistics?

Nominal
Ordinal
Interval
Ratio

The type of data you collect helps determine which statistical test you can use.

Nominal

Think of nominal as putting people into different groups or giving them labels. There is no order.

Examples: employment status, marital status, program completion (yes/no).

You can count how many people belong to each category, but the categories don't have a meaningful numerical order.

Ordinal

Ordinal is similar to nominal because you are still dealing with categories. The difference is that the categories can be ranked from lower to higher.

Examples: low, medium, high stress; strongly disagree through strongly agree.

You know which category is higher or lower, but the distance between categories isn't necessarily equal.

Interval

Now we move from categories to numerical measurements.

Numbers with equal intervals, but no true zero

With interval data, the difference between numbers has a consistent meaning.

Example: 15, 20, 30, 45 ETC.

There is a clear indentified difference between each number.

To clear up confusion:

It means the distance between consecutive units on the measurement scale is consistent. for examle, you’re measuring temperature, the measurment is 1C. So, since the measurment is 1, and the measurment between each variable is the same, this would be interval.

Examples: Standardized test scores, Calander year, IQ scores etc.

Ratio

Is the same as Interval BUT you have a true zero on the scale.

For example: A cale of 0-10

Another example: Hours of sleep 0-10

Interval would have no true zero, for example: Measuring temperature. 0C isn’t actually zero.

Can types of variable be changes?

Yes.

For example, imagine you're studying people's ages.

Ratio variable: You collect participants' exact ages (18, 25, 32, 45).

Ordinal variable: You group their ages into categories (18–24, 25–34, 35–44, 45+).

What is Data preparation and descriptive statistics?

Once you collect the data, you cannot immediately jump into statistical testing.

Your professor describes data preparation as including coding, cleaning, checking for missing data, and organizing the information into a usable database.

For example, you might notice that one participant entered their age as 250, or that some survey responses are missing. These issues need to be examined before analysis.

What are Descriptive statistics

Descriptive statistics summarize the data you collected.

A. Central tendency: What is typical?

• Mean: The average.

• Median: The middle value when the numbers are ordered.

• Mode: The most frequently occurring value.

B. Dispersion: How spread out is the data?

• Range: Highest value minus lowest value.

• Variance: A measure of how spread out the values are around the mean.

C. Distribution: How are the values arranged?

• Normal distribution: a roughly symmetrical, bell-shaped pattern.

• Skewed distribution: values are pulled toward one side.

• Histograms help display the distribution of numerical data.

What is Central Tendancy

Part of descriptive statistics

Central tendency helps you describe what a typical or representative value looks like in a group of people.

• Mean: The average.

• Median: The middle value when the numbers are ordered.

• Mode: The most frequently occurring value.

When to use Mean

When you want to know the average of a group you’re studying.

Add up all the number and divide by the number of numbers.

Median

Median (middle value)

Put the values in order and find the middle one.

Example: 4, 5, 6, 7, 8 → median = 6 hours

When to use it: When your data contains extreme values or is skewed, so the mean might not represent a typical person very well.

Social work example: Finding the typical annual income of clients. If one client earns $200,000 while most earn $20,000–$35,000, the median usually gives a more representative picture.

When to use Mode

The most frequent value.

Mode (most frequent value)

Identify the value that appears most often.

Example: 4, 5, 5, 5, 8 → mode = 5 hours

When to use it: When you want to know which response, category, or value occurs most frequently. It's especially useful for categorical data, where calculating an average doesn't make sense.

Social work example: Identifying the most common presenting concern at an agency, such as housing insecurity, substance use, or anxiety.

Dispersion

If central tendancy tells you what is typical. Dispertion tells you how much people differ from one another or how spread out the data is.

Made up of:

Range: Highest value minus lowest value.

Variance: A measure of how spread out the values are around the mean.

What is Range and when to use it

Part of Dispersion

The highest value minus the lowest value.

• Group A: 6 − 4 = 2

• Group B: 9 − 1 = 8

When to use it: When you want a quick, simple understanding of the overall spread between the smallest and largest values.

Social work example: Looking at the range of wait times for clients accessing counselling, from the shortest wait to the longest.

Limitation: The range only considers the two extreme values. It doesn't tell you how the other values are distributed.

What is Variance and when to use it

Variance measures how much the values differ from the mean, taking into account all the observations.

When to use it: When you want a more detailed statistical measure of variability, especially when comparing groups or conducting further statistical analyses.

Social work example: Comparing how much clients' depression scores vary within two different treatment programs. One group might have very similar scores, while the other has a much wider spread.

Important: Variance is expressed in squared units, which can make it less intuitive to interpret directly.

Subtract the mean from each individual number.

Distribution

Distribution looks at the overall pattern of your data. It helps you understand whether values cluster around the middle, whether there are extreme values, and whether the data is balanced or uneven.

Distribution = How the data is spread out across different values.

Dispersion = How much the data varies or differs from the average.

1. Normal Distribution
2. Skewed Distribution
3. Histograms

Normal Distribution

A normal distribution is approximately symmetrical and bell-shaped. Most values are near the middle, and fewer values appear toward either end.

In a perfectly normal distribution, the mean, median, and mode are equal or coincide at the centre.

Skewed distribution

A skewed distribution is asymmetrical. The data has a longer tail on one side.

For example:

• Right-skewed: Most clients have relatively low monthly incomes, but a few have very high incomes.

• Left-skewed: Most clients report high satisfaction scores, but a few report very low satisfaction.

Skewed distributions can look different depending on how the data is spread out.

Histogram

Is a way of grouping data into “bins” and then plotting them on a graph.

A bin could be a single number, or a range.

For example: You survey 100 people about their stress levels 1-10. You’d put the answers into a “bin” and then create a bar graph with x axis being the stess score (1-10) and the y axis being the number of people in each bin.

How do you decide which method to use to understand data?

How do you decide which one to use in a research study?

This is probably the most important part for your exam. Think about what the researcher is trying to find out.

Research question	Concept to consider	Why?
What is the average age of clients?	Mean	Finds the arithmetic average.
What is the typical income when a few clients earn much more than others?	Median	Less affected by extreme values.
What is the most common reason people seek help?	Mode	Identifies the most frequent category.
How different are the shortest and longest wait times?	Range	Measures the total spread.
How much do clients' scores vary around the average?	Variance or standard deviation	Measures variability across all observations.
Are most clients clustered around the middle, or are scores unevenly distributed?	Distribution	Describes the overall pattern.
How can I visually examine the frequency of numerical scores?	Histogram	Displays the shape and frequency of the data.

Inferential statistics

Purpose: To use data from a sample to draw conclusions or make estimates about a larger population.

Examples include:

• Hypothesis testing

• P-values

• Confidence intervals

• Correlation and regression (when used for inference)

• Inferential statistics = use your data to draw conclusions about a population.

Descriptive statistics

Purpose: To organize, summarize, and describe the data you have collected.

Examples include:

• Mean (average)

• Median and mode

• Range and variance

• Standard deviation

• Frequency tables, histograms, and graphs
  
  

• Descriptive statistics = describe your data.

Do researchers use both descriptive statistics and Inferential statistics?

Yes.

Step 1: Descriptive statistics

The researcher summarizes the data collected from the 200 students.

• 65% of participants are female.

• The average anxiety score is 18.

• Students who work part-time have an average anxiety score of 21, compared with 16 for those who don't.

Purpose: Describe what the sample looks like and what the data show.

Step 2: Inferential statistics

The researcher tests whether the difference between the two groups is statistically significant.

For example, they might use a statistical test and calculate a p-value.

• If the result is statistically significant, there is evidence of a difference in anxiety scores between the groups in the population.

• If it isn't statistically significant, the researcher doesn't have sufficient evidence to conclude that a difference exists.

P-Value

A p-value helps researchers determine whether the difference they observe between two groups is statistically significant.

The p-value scale ranges from 0 to 1 (or 0% to 100%).

The closer the p-value is to 0, the stronger the evidence against the null hypothesis. The closer it is to 1, the less evidence there is against the null hypothesis.

Example: 0.03 on the P scale would mean that there's a 97%