Statistics

# Statistics - Basic Statistics for Emg Lab   ...

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Unformatted text preview: Basic Statistics for Emg Lab    Introduction   Statistics is a mathematical science pertaining to the collection, analysis,  interpretation or explanation, and presentation of data.   There are two types of  statistical methods we will be using in the emg lab: descriptive statistics and  inferential statistics.      Descriptive statistics such as the mean, standard deviation and standard error can  be used to summarize or describe a collection of data. In addition, patterns in the  data may be modeled in a way that accounts for randomness and uncertainty in the  observations, and then used to draw inferences about the process or population  being studied; this is called inferential statistics.  A t‐test and an Analysis of Variance  (ANOVA) are both types of inferential statistics.    Mean  Definition – the mean is the arithmetic average of a set of values or a statistical  distribution.  For a data set, the mean is the sum of the observations divided by the  number of observations.  Ex:  Suppose you are a swimmer training for the Olympic Games in 2012 and you  want to know what the mean time was for the men in the 100 meter butterfly.  The  times in the finals are listed below.  Swimmer Name  Michael Phelps  Milorad Cavic  Andrew Lauterstein  Ian Crocker  Jason Dunford  Takuro Fujii  Andrii Serdinov  Ryan Pini    Time (seconds)  50.58  50.59  51.12  51.13  51.47  51.50  51.59  51.86  To calculate the mean you would sum the times and divide the sum by the number  of swimmers (below).  sec  Standard Deviation (σ )  Definition – a measure of the variability of a collection of values.  Calculating SD  1) 2) 3) 4) 5) Find the mean of the values in your data set: xm = (x1+ x2+...+ xn) ÷n.  For each value (xi) calculate its deviation from the mean (xi‐xm).  Calculate the squares of these deviations (xi‐xm)2.  Find the mean of the squared deviations.  This quantity is the variance.  Take the square root of the variance.  This quantity is the standard deviation.  Ex:  Find the standard deviation for the men’s 100meter butterfly times.  1) Mean =51.23  2) Deviation from the mean  a. Michael Phelps = (50.58‐51.23) = ‐0.65  b. Milorad Cavic = (50.59‐51.23) = ‐0.64  c. Andrew Lauterstein = (51.12‐51.23) = ‐0.11  d. Ian Crocker = (51.13‐51.23) = ‐0.1  e. Jason Dunford = (51.47‐51.23) = 0.24  f. Takuro Fujii = (51.50‐51.23) = 0.27  g. Andrii Serdinov = (51.59‐51.23) = 0.36  h. Ryan Pini = (51.86‐51.23) = 0.63  3) Calculate the square of the deviations  a. Michael Phelps =  ‐0.652 = 0.4225  b. Milorad Cavic = ‐0.642 = 0.4096  c. Andrew Lauterstein = ‐0.112 = 0.0121  d. Ian Crocker = ‐0.12 = 0.01  e. Jason Dunford = 0.242 = 0.0576  f. Takuro Fujii = 0.272 = 0.0729  g. Andrii Serdinov = 0.362 = 0.1296  h. Ryan Pini = 0.632 = 0.3969  4) Find the mean of the squared deviations (the variance σ2).    5) Take the square root of the variance which is the standard deviation (σ).  sec    Standard Error of the Mean (SEM)  Purpose – The mean of a sample of data is an estimate: it estimates the “true” mean  of the whole population, or the “true” mean of the statistical distribution.  For  example, the mean height of students in this lab is an estimate of the mean height of  the whole population of Harvard students.  We want to quantify the likely error  between the sample mean and the “true” mean.  Definition – SEM is an unbiased estimate of expected error in the sample estimate  of the population mean.  SEM is calculated by dividing the standard deviation of a  sample by the square root of the sample size.    Ex:  Suppose you want to know the amount of standard error for the average time  for the men’s 100 meter butterfly.   sec  The average and standard error for this data set would be presented as  51.23±0.15sec.    T­test  Purpose:  If you want to compare two data sets to determine whether there is a  significant difference between the means of the two data sets, you would use a t‐test  to determine a P‐value.  Types of t­tests  Unpaired t­tests:  This type of t‐test is used when you have independent samples –  in other words, samples that are not directly related to each other.  For example:  Test scores between males and females.  Paired t­tests:  This type of t‐test is used when you have dependent samples, for  example when you collect data both before and after some manipulation of your  subjects.  Ex:  Stress hormone levels before and after an exam.     Analysis of Variance (ANOVA)  Purpose: If you want to compare three or more data sets to each other to determine  if there is a significant difference between the means of the data sets you would use  an ANOVA to determine a P‐value.    Interpreting Your Results  Both t‐tests and ANOVA tests, when run on either Excel or SPSS, will generate a  number called a p‐value.  A p‐value is the smallest significance level at which a null  hypothesis may be rejected: the smaller the p‐value, the stronger the evidence  against the null hypothesis.  A p‐value of 0.05 or smaller is usually considered  statistically significant in the biological sciences.  Therefore if you run your tests and  the resultant p‐value is less than or equal to 0.05, you have a statistically significant  difference in the mean values you measured.    ...
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## This note was uploaded on 03/29/2012 for the course LS 2 taught by Professor Andrewa.biewener,petert.ellison,anddaniele.lieberman during the Fall '10 term at Harvard.

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