Standard Deviation and Student T Test

• Standard Deviation


  A measure of the spread of data points from the mean
• Large Standard Deviation


  Indicates a greater variation
• Small Standard Deviation


  Indicates a lesser variation
• Spread of the Data


  Refers to the range of values around the mean
• Measure of Repeatability

  Standard deviation indicates how much repeated measurements differ
• Comparing Standard Deviations

  Allows for comparison of variability in different datasets
• Displaying Data

  Histograms can be used to compare values visually
• Calculating Standard Deviation

  Involves summing the squared differences from the mean and taking the square root
• Worked Example


  Demonstrates the process of adding or subtracting the standard deviation to or from the mean
• Error Bars


  Represent the range of values around a data point, indicating uncertainty
• Adding Error Bars


  Involves adding or subtracting one standard deviation from the value to show the range of uncertainty
• Interpreting Error Bars


  Indicates the overlap and significance of different test outcomes
• Overlap of Standard Deviations


  Indicates the similarity between repeated measurements
• Student's T Test


  A statistical test used to compare the means of two sets of data
• Null Hypothesis


  States that there is no significant difference between the means of two datasets
• Unpaired Data


  Data from two different groups being compared
• Normally Distributed Data

  Data that follows a bell-shaped curve around the mean
• Comparing Distributions


  Histograms are used to determine the normal distribution of datasets
• Student's T Formula


  Calculates the t-value to compare means and standard deviations
• Degrees of Freedom


  The number of independent values used in the calculation of the t-value
• Critical Value


  A threshold value used to determine the significance in a t-test