Before any meaningful analysis can begin, the raw data often requires significant preparation and cleaning. This crucial step ensures the accuracy and reliability of subsequent analyses.

Data Transcription/Entry

If data was collected manually (e.g., paper questionnaires, observation notes), it needs to be accurately transcribed into a digital format (e.g., spreadsheet, statistical software).

Checking for Errors and Inconsistencies

This involves thoroughly reviewing the data for any obvious mistakes, typos, or illogical entries (e.g., a task completion time of -5 seconds, an age of 200 years). Data validation rules can be applied during entry.

Handling Missing Data

Missing data points are a common occurrence. Strategies for addressing them include:
- Exclusion: Removing cases with missing data (listwise deletion) or removing only the specific variables with missing data (pairwise deletion). This can lead to loss of information and potentially bias if data are not missing completely at random.
- Imputation: Estimating missing values based on other available data (e.g., using the mean, median, mode of the variable, or more sophisticated statistical methods like regression imputation).

Data Transformation

Sometimes data needs to be transformed to meet the assumptions of certain statistical tests or to make it more interpretable. Examples include:
- Normalization: Scaling data to a common range.
- Logarithmic transformations: Used for skewed data, particularly common with response times.
- Recoding variables: Changing categorical values (e.g., converting "Male/Female" to "0/1").

Outlier Detection and Treatment

Outliers are data points that significantly deviate from other observations. They can be legitimate data points or errors. Methods to detect them include visual inspection (box plots, scatter plots) or statistical tests. Deciding whether to remove, transform, or retain outliers depends on their nature and impact.

Descriptive statistics are used to summarize and describe the main characteristics of a dataset. They provide a quick and intuitive understanding of the data's distribution.

Measures of Central Tendency

These statistics describe the "center" or typical value of a dataset.
- Mean (Average): The sum of all values divided by the number of values. It's sensitive to outliers. Appropriate for interval and ratio data.
- Median: The middle value in an ordered dataset. If there's an even number of values, it's the average of the two middle values. Less affected by outliers. Appropriate for ordinal, interval, and ratio data.
- Mode: The most frequently occurring value(s) in a dataset. Can be used for all scales of measurement, including nominal data. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode.

Measures of Variability (Dispersion)

These statistics describe the spread or dispersion of data points around the central tendency.
- Range: The difference between the highest and lowest values in a dataset. Simple to calculate but highly sensitive to outliers.
- Variance (σ2 or s2): The average of the squared differences from the mean. It quantifies how far each data point is from the mean. A larger variance indicates greater spread.
- Standard Deviation (σ or s): The square root of the variance. It's the most commonly used measure of spread because it's in the same units as the original data, making it more interpretable than variance. A small standard deviation indicates data points are clustered closely around the mean, while a large standard deviation indicates widely dispersed data.

Inferential statistics go beyond describing the data; they are used to make inferences, draw conclusions, or make predictions about a larger population based on a sample of data. They help determine if observed patterns or differences are statistically significant or likely due to random chance.

Hypothesis Testing

This is a formal procedure for making decisions about a population based on sample data.
- Null Hypothesis (H0): A statement of no effect, no difference, or no relationship between variables. It's the default assumption that researchers try to disprove. For example, "There is no difference in task completion time between Layout A and Layout B."
- Alternative Hypothesis (H1): A statement that contradicts the null hypothesis, suggesting that there is an effect, a difference, or a relationship. For example, "There is a significant difference in task completion time between Layout A and Layout B."
- Significance Level (α): The predetermined threshold for rejecting the null hypothesis. Commonly set at 0.05 or 0.01.
- P-value: The probability of obtaining observed results if the null hypothesis were true. If the p-value is less than α, the null hypothesis is rejected, suggesting that the observed effect is statistically significant and unlikely due to chance. If the p-value is greater than α, the null hypothesis is not rejected.
- Statistical Significance vs. Practical Significance: A statistically significant result means the observed effect is unlikely due to chance, but it does not necessarily mean that the effect is practically important.

The choice of statistical test depends on the type of data (measurement scale), the number of groups, and the research question.

T-tests

Used to compare the means of two groups.
- Independent Samples T-test: Compares the means of two independent groups.
- Paired Samples T-test (Dependent T-test): Compares the means of two related groups or measurements from the same participants under two conditions.

ANOVA (Analysis of Variance)

Used to compare the means of three or more groups or to analyze the effects of multiple independent variables and their interactions.
- One-Way ANOVA: Compares the means of three or more independent groups for a single independent variable.
- Repeated Measures ANOVA: Compares the means of three or more related groups.
- Two-Way ANOVA (or Factorial ANOVA): Examines the effect of two or more independent variables on a dependent variable and their interaction effects.

Correlation Analysis

Measures the strength and direction of a linear relationship between two continuous variables. A correlation coefficient ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation.

Regression Analysis

Used to model the relationship between a dependent variable and one or more independent variables.
- Simple Linear Regression: One independent variable predicts a continuous dependent variable.
- Multiple Linear Regression: Multiple independent variables predict a continuous dependent variable.

Non-parametric Tests

Used when data do not meet the assumptions of parametric tests.
- Chi-Square Test: Used for categorical data to assess significant associations between two nominal variables.
- Mann-Whitney U Test: Non-parametric equivalent of the independent samples t-test.
- Wilcoxon Signed-Rank Test: Non-parametric equivalent of the paired samples t-test.

Effective data visualization is crucial for understanding the data, identifying patterns, and communicating findings clearly and concisely.

Bar Charts

Ideal for comparing discrete categories or illustrating the means of different groups.

Line Graphs

Best for showing trends over time or relationships between continuous variables.

Scatter Plots

Used to visualize the relationship between two continuous variables, often for correlation analysis, to identify patterns or outliers.

Histograms

Show the distribution of a single continuous variable, revealing its shape, spread, and central tendency.

Box Plots (Box-and-Whisker Plots)

Provide a quick summary of the distribution of a numerical dataset through quartiles, median, and potential outliers.

Pie Charts

Used to show proportions of a whole, though often less effective than bar charts for comparisons.