statistics in exercise science

mean

• average value

• calculated by adding all values and dividing by the number of values

median

• middle value when data are ordered from lowest to highest

mode

• value that occurs most frequently in a data set

standard deviation

• measure of how dispersed values are around the mean

minimum

the lowest value in a dataset

maximum

highest value in a dataset

rank

position of a blue in an ordered list of data

percentile

the ranked position of a value expressed as a percentage relative to all the values in a dataset

relationships

• methods for correlation which can provide different interpretations of the same data

  • assess association or agreement

• establishes the relationship between two variables

  • the main result is the correlation coefficient

    • this is known as the “r value”

r value

• describes the strength and direction of the relationship

• strength is expressed by the number

  • 1 is strong/perfect

  • 0 is no relationship

    • the closer the r-value is to 1 there is a strong trend between the two values

• direction is described by the sign

  • -ve indicates that as one variable increases the other decreases

  • +ve indicates that as one variable increases the other also increases

    • must match both directionally and by amount

pearson correlation

• assesses association

• can only be used with 2 raters/measuremnts

• can use excel

  • for a simple comparison =CORREL(array1,array2)

  • for a matrix use “data” then “data analysis” → “correlation”

intraclass correlation

• asses agreement

• can be used with 2+ raters/measurmetns

• can partially use excel but does ot provide CI so must use SPSS, R, python etc.

r-value strength

• .7-1 → very strong

• .5-.7 → strong

• .3-.5 → moderate

• 0-.3 → weak

• 0 → none

  • can be both positive or negative

  • in exercise science we like to be 0.7 or above to make correlations whereas other sciences ushc as physics require higher values of 0.97 or above

correlation ≠ causation

• relationships do not describe the exact relationship or forms

  • a linear regression is needed to determine this

• does not describe non-linear (plynomial) relationships

  • in this case advanced methods are needed

bias

• Bland-Altman plots used to anaulse the agreement between two measures

  • plots difference between two measures against the mean of both measures

  • limits of agreement are set at 1.96 SD

  • looking ot see if there is systematic bias

    • relationship between mean and difference

      • ie. increasing mean = increased difference?

agreement of Bias

1. at least 95% of measures should fall within LOA

2. bias should close to mean

   • ie. zero or close to it

3. LOA should be small relative to mean

bias analysis in excel

• Calculate average of the two variables

• Calculate the difference between the variables (=Var2-Var1)

• Calculate SD (STD.S) of the difference

• Calculate the bias (the average difference)

• Calculate upper limit of agreement (LOA) =bias+1.96*SD

• Calculate lower limit of agreement (LOA) =bias-1.96*SD

• Calculate minimum and maximum of average of the two variables

• Highlight the data in the two columns containing the average and the difference

  • On the “Insert” tab, in the “Charts” menu, select “Scatter Plot”

  • Add axis titles (x=Mean, y=Difference)

  • Select data, Add a Series;

    • Name=Upper LOA, x=MinMean MaxMean, y=Upper LOA, Upper LOA

    • Name=Lower LOA, x=MinMean MaxMean, y=Lower LOA, Lower LOA

    • Name=Bias, x=MinMean MaxMean, y=Bias, Bias

One at a time, click each pairs of dots, go to fill, solid line (LOA can be dotted w/ bias solid or all solid or all dotted)