Descriptive Data Analysis

Descriptive Data Analysis

Descriptive data analysis involves techniques and statistical methods to describe the characteristics and performance of a group.

• Focuses on the overall sample.
• Can be used to compare individual scores to the group.
• Differs from inferential data analysis as it does not draw conclusions or infer training methods.

Types of Descriptive Statistics

• Measures of Frequency: How often a score or test result occurs.
• Measures of Distribution: The spread of the frequency.
• Measures of Central Tendency: Points around which most scores are concentrated (mean, median, mode).
• Measures of Variability: The spread of the data.

Measures of Central Tendency

Indicate the most common test scores or results.

Mode

• Describes the most frequent score in the test.
• Suitable for nominal data (data that cannot be ranked).
• Example: Determining the most frequently achieved score in a 1RM test or analyzing simple knowledge tests.

Median

• Describes the middle score of the data.
• 50% of the data is below this value, and 50% is above.
• Requires ordinal, interval, or ratio data.
• Should not be used with nominal data.

Mean

• Calculated as the sum of the scores divided by the number of scores.
• Provides an average of the group's performance.
• Formula: $Mean = \frac{\sum<em>{i=1}^{n} x</em>i}{n}$, where $x_i$ represents the individual scores and $n$ is the number of scores.
• Accuracy is affected by the distribution of the data; outliers can impact the mean's magnitude.

Data Distribution

Normal Distribution

• Data is clustered around a central point (symmetrical histogram).
• The mean is generally the most appropriate measure of central tendency.

Skewed Distributions

• Negatively Skewed: Distribution is longer to the left.
• Positively Skewed: Distribution has more scores towards the right.
• The median should be used in these cases as it is not affected by the magnitude of scores.

Importance of Distribution

• Most statistical measures (particularly those related to means) rely on normally distributed data.
• Normal distribution is defined where most values fall within two standard deviations of the mean.
• $(\approx 95\% \text{ of data falls within 2 standard deviations})$
• If data is not normally distributed, using the median and appropriate statistical models is recommended.

Measures of Variability

Describe the spread of the data.

Range

• Calculated by finding the minimum and maximum values in the dataset.
• Provides the least amount of information about the spread.

Interquartile Range

• Gives a representative idea of the spread around the median.
• Calculated using the 25th percentile below and above the median.

Standard Deviation

• Describes the amount a score differs from the mean.
• Indicates the accuracy of the mean value estimate.
• Smaller standard deviation: athletes are closer to the mean.
• Wider standard deviation: greater variability in the data.

Describing Individual Level Characteristics

Percentiles

• Rank athletes' scores from worst to best.
• Assign a percentile based on their rank within the data range.
• Example: An athlete at the 60th percentile has 60% of the scores below them.

Standard Scores

• Describe how far an individual's test scores are from the mean of the group.
• Z Score:
  • A common standard score in strength and conditioning.
  • Formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the athlete's test score, $\mu$ is the mean score for the group, and $\sigma$ is the standard deviation for the group.
  • Indicates how many standard deviations an athlete is away from the mean.
• Standard Error of the Mean:
  • Describes the distance the population mean is likely to be away from the sample mean.
• Confidence Intervals:
  • Allow assessment of the accuracy of the sample mean estimate using standard deviation or standard error of the mean.