Descriptive Statistics and Introduction to SPSS: Study Notes for Health Sciences

Applied Statistics for the Health Sciences

Course 1: Descriptive Statistics & Introduction to SPSS

This section introduces foundational concepts in statistics, focusing on descriptive statistics and practical data analysis using SPSS, tailored for health sciences students.

The 3 Research Components

Overview of Research Structure

• Variable Interaction: Understanding how different variables relate and interact within a study.

• Research Sample: The group of subjects or data points selected for analysis.

• Statistical Approach: The methods and techniques used to analyze and interpret data.

Example: In a study examining the effect of exercise on blood pressure, the variables might be exercise frequency and blood pressure readings, the sample could be adults aged 18-65, and the statistical approach might involve comparing means.

Statistical Analyses

Types of Statistical Analyses

• Descriptive Statistics: Summarize and describe the main features of a dataset.

• Inferential Statistics: Make predictions or inferences about a population based on sample data.

Example: Descriptive statistics might include calculating the average age in a sample, while inferential statistics could involve testing whether a new drug is effective compared to a placebo.

Overview of Descriptive Statistics

Main Topics Covered

• Descriptive statistics

• Measures of central tendency

• Measures of variability

• Introduction to SPSS

Descriptive Statistics

Definition and Purpose

• Descriptive statistics are used to summarize and describe the main features of a dataset.

• They help to make sense of data by providing simple summaries about the sample and measures.

Types of Descriptive Statistics:

• Measures of central tendency

• Measures of variability

Measures of Central Tendency

Definition and Types

Measures of central tendency represent an indicator of the typical score in a dataset. The three main measures are:

• Mean

• Median

• Mode

Mean

• The most frequently used measure of central tendency.

• Calculated by adding all scores and dividing by the number of scores.

Formula:

$\text{Mean} = \frac{\sum x}{N}$

Example: For scores 3, 5, 7, 8, 4: $\text{Mean} = \frac{3+5+7+8+4}{5} = \frac{27}{5} = 5.4$

Problems with the Mean

• Influenced by extreme scores (outliers).

• May not represent the typical value if the data is skewed.

Median

• The middle score after all scores have been ranked in ascending order.

• Not influenced by extreme scores.

Example: For scores 3, 5, 7, 8, 4 (ordered: 3, 4, 5, 7, 8), the median is 5.

Formula:

$\text{Median} = \text{Middle value of ordered data}$

Mode

• The most frequently occurring score in a dataset.

• Useful for categorical data.

Example: For scores 3, 5, 7, 7, 8, the mode is 7.

Graphical Representation

• Bar Chart: Heights of bars represent mean scores for groups.

• Line Graph: Means represented as end points of lines.

Measures of Variability

Definition and Importance

Measures of variability indicate the spread or dispersion of scores in a dataset. They help to understand how much scores differ from the typical value.

• Range

• Interquartile Range

• Standard Deviation

Range

• The difference between the highest and lowest scores in a sample.

Formula:

$\text{Range} = \text{Maximum score} - \text{Minimum score}$

Example: For scores 3, 5, 7, 8, 4: $\text{Range} = 8 - 3 = 5$

Interquartile Range (IQR)

• Measures the spread of the middle 50% of scores.

• Calculated by finding the difference between the 75th percentile (Q3) and the 25th percentile (Q1).

Formula:

$\text{IQR} = Q_3 - Q_1$

Example: For ordered scores 3, 4, 5, 7, 8, Q1 = 4, Q3 = 7, so $\text{IQR} = 7 - 4 = 3$

Standard Deviation

• Indicates how much the scores in a dataset typically vary from the mean.

• Calculated as the square root of the variance.

Formula:

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N}}$

Where $x_i$ is each score, $\bar{x}$ is the mean, and $N$ is the number of scores.

Example: For scores 3, 5, 7, 8, 4:

• Mean = 5.4

• Deviations: -2.4, -0.4, 1.6, 2.6, -1.4

• Squared deviations: 5.76, 0.16, 2.56, 6.76, 1.96

• Sum = 17.2

• Variance = $\frac{17.2}{5} = 3.44$

• Standard deviation = $\sqrt{3.44} \approx 1.86$

Introduction to SPSS

Why Learn SPSS?

• SPSS (Statistical Package for the Social Sciences) is a widely used software for statistical analysis in health sciences.

• It simplifies data management, analysis, and graphical representation.

Steps for Downloading SPSS:

• Download SPSS to your computer.

• Open the provided SPSS database file.

• Double-click the file to open in SPSS.

Calculating Descriptive Statistics in SPSS

• Open the SPSS database.

• Go to Analyze > Descriptive Statistics > Descriptives.

• Select the variable of interest (e.g., Coping variable).

• Click the blue arrow to move the variable to the analysis box.

• Click Options and select desired statistics (mean, standard deviation, etc.).

• Click Continue and OK to view results.

Example Output: SPSS will display a table with mean, standard deviation, minimum, and maximum values for the selected variable.

Graphing in SPSS

• To graph mean scores for groups, go to Graphs > Chart Builder.

• Select Bar or Line chart.

• Drag the variable to the appropriate axis.

• Click OK to generate the graph.

Data Cleaning in SPSS

• Check for data entry errors.

• Review missing data and outliers.

• Ensure the number of missing data is not excessive (e.g., less than 2.5% of total cases).

Example: If a variable has many missing values, results may be affected or not significant.

Summary Table: Measures of Central Tendency and Variability

Measure	Definition	Formula	Strengths	Limitations
Mean	Arithmetic average of scores	$\frac{\sum x}{N}$	Uses all data points	Affected by outliers
Median	Middle value in ordered data	Middle value	Not affected by outliers	Ignores magnitude of values
Mode	Most frequent score	Most common value	Useful for categorical data	May not be unique
Range	Difference between highest and lowest scores	$\text{Max} - \text{Min}$	Simple to calculate	Ignores distribution of scores
Interquartile Range	Spread of middle 50% of scores	$Q_3 - Q_1$	Not affected by outliers	Ignores extreme values
Standard Deviation	Average deviation from the mean	$\sqrt{\frac{\sum (x_i - \bar{x})^2}{N}}$	Uses all data points	Complex to calculate

Additional info: These notes expand on the original slides by providing full definitions, formulas, and examples for each concept, as well as a summary table for comparison.