Module 3 - Statistics for Kinesiology

Nominal curve

The normal distribution is a probability distribution that is symmetric and bell-shaped

Kurtosis 

  • A statistical measure used to describe the distribution of observed data points relative to a normal distribution, indicating the presence of outliers or the heaviness of the tails.

Bimodal & Multimodal curve 

  • Distribution characteristics that include the presence of multiple peaks, indicating varying subpopulations within the data set.

Skewness

  • Statistical measures that describe the shape and features of data distributions.

Normal distribution and standard deviation

  • the mean or standard deviation between each section under the curve

What is a Z-score

Z-score is a raw score expressed in standard deviation units


  • How many SD an observation is away from a mean

    • If it is positive = above the mean

    • If it is negative = below the mean

Z-score and standardized normal distribution

The Z-score quantifies the number of standard deviations an observation is from the mean, providing a way to compare different data points within the same distribution.

Probability

The likelihood of an event occurring

  • Related to standard scores, percentiles and the characteristics of a normal distribution

  • There cannot be a negative probability

Probability density function and the normal curve

The probability density function is a function that describes the relative likelihood for a random variable to fall within a given range

Tests for normality – Lab

  • Histogram

  • Skewness & kurtosis

  • Kolmogorov-smirnov (K-S)

  • Shapiro-Wilk (S-W)

  • Null hypothesis = Data is normally distributed

  • Alternative hypothesis = data is not normally distributed

  • If calculated result > 0.05 (therefore not significant) we accept the null hypothesis

Outliers

Data point distinctly beyond the range of other data points observed

  • Can be identified

    • Visual inspection

    • Frequency tables

    • Histogram and bar graphs

    • Box-plots

    • Scatterplot matrices

  • It is real or an error?

Box-plots

useful for visualizing the distribution of data across different categories, highlighting medians, quartiles, and potential outliers.

Missing Data

2 options

  • Listwise deletion → drop that whole/subject from the analysis

  • Pairwise deletion → drop the variable from the analysis but use the others

Little’s missing completely at random (MCAR) test

  • Used to determine if missing values are random or no

  • This will dictate how to deal with the situation

Imputation: Replacing missing data

  • Multiple imputation

  • Maximum likelihood