Statistics

Data types: Catagorical vs Numerical Data

In the world of research, data comes in two main flavors: 

1. Numerical 

2. Categorical

Numerical data

As the name suggests, deals with numbers. This could be anything from exam scores and reaction times to income levels and website visits. You can perform math operations on numerical data, like calculating averages or finding correlations. There are 2 main types:

• Discrete: Numbers of patients, visits to a hospital

Imagine a bucket full of marbles. Each marble is a separate entity, and you can only have whole numbers of them. This type of data, called discrete data, represents distinct values and often comes from counting things. It can be finite (like the number of apples in a basket) or infinite (like the number of stars in the sky). Here are some common examples of discrete data:

Counts: The number of people attending an event, the number of cars on a highway, the number of correct answers on a multiple-choice test.

Ranks: Positions in a race, shirt sizes (S, M, L, XL), letter grades on a report card.

• Continuous: Height, weight, age

Now, imagine pouring water into a measuring cup. The amount of water can take on any value on a continuous scale, from a single drop to overflowing. This type of data, called continuous data, represents values that can fall anywhere along a spectrum. It often comes from measurements and can be expressed in fractions or decimals. Examples of continuous data include:

• Measurements: Height, weight, temperature, distance traveled, time elapsed.

• Ratios: Speed (distance divided by time), proportions of ingredients in a recipe, unemployment rate (percentage of people without jobs).

Categorical data

On the other hand, is all about classification. It tells you what category something belongs to, like hair color (blonde, brunette, etc.) or preferred brand of shoes (Nike, Adidas, etc.). Categorical data doesn't involve numbers themselves, but rather labels or groups. Understanding these differences is crucial for researchers to choose the right tools to analyse their data and draw meaningful conclusions. There are 2 main types:

• Nominal: Eye or hair colour, Male or female (no particular order), Yes / No

• Ordinal: Mild-moderate-severe, Pass-merit-distinction.

Paired vs Unpaired data

In simple terms if your statistical test in comparing the mean bewteen groups this is unpaired, if you are comparing the mean in the same group (before & after) this is unpaired.  For a further explaination see below.

Paired AKA Related Data (Paired t-test):

• Data comes from the same group or subjects measured under two different scenarios. Think of it as comparing the same individuals before and after something (treatment, intervention, etc.). Because it's the same group, any underlying characteristics of the subjects (age, genetics, etc.) are assumed to be relatively consistent between the two scenarios. This allows the paired t-test to focus solely on the differences caused by the change in scenario, making it less reliant on the assumption of equal variance between groups.

• Methods paired tests are used for:

  1. Pre test post test method: e.g Measure stress levels (e.g., using a validated scale) before and after a 6-week mindfulness program for the same group of students. 

  2. Matched-Pair design: e.g Match participants in the app group with those in the standard care group based on similar age, gender, and baseline HbA1c levels. Measure HbA1c after 12 weeks.

  3. Repeated Measures on the Same Subject : Measure fatigue levels at the start, midpoint, and end of the shift for each nurse. 

  4. Crossover Trials: In a crossover design, participants receive caffeine in one session and a placebo in another (order randomized). Measure reaction times after each condition. 

Unpaired AKA Unrelated Data (Unpaired t-test):

• Data comes from two completely independent or unrelated groups. Imagine comparing the average height of students from two different schools with no connection between them. Since the data originates from separate groups, there's no guarantee that underlying characteristics are similar between the groups. Therefore, the unpaired t-test assumes the variances of the two independent groups are equal to ensure a fair comparison of means.

• Methods unpaired tests are used for:

  1. Comparing Two Independent Groups: Collect exam scores from a sample of male and female students. 

  2. Control vs. Intervention Groups: Randomly assign participants to a drug group or a placebo group and measure their blood pressure after 12 weeks.  

  3. Cross-Sectional Studies:  Collect physical activity data (e.g., step counts) from a random sample of urban and rural residents. 

  4. Different Cohorts or Time Periods: Compare admission rates from two independent samples, one before and one after the policy implementation. 

  5. Unmatched Case-Control Studies: Collect smoking rates for cases (lung cancer patients) and controls (non-cancer patients). 

  6. Two Independent Treatments: Randomly assign patients to two groups (e.g., Program A or Program B) and measure knee function scores after the intervention. 

  7. Group Differences in Surveys: Administer a satisfaction survey to two independent groups of patients, one from private hospitals and one from public hospitals.