Thursday, October 20, 2011

IB Chemistry Biology t test, mean, uncertainty error, standard deviation, statistical analysis

Central value of a normal distribution curve for a set of data can be recorded as 
  • Mean
  • Mode
  • Median
Consider the following set of data collected 
  • 5, 6, 6, 6, 6, 7, 9
Average can be in the form of Mean, Mode or Median
  • Mean = ( 5 + 6 + 6 + 6 + 6 + 7 + 9 ) /7 = 6.42
  • Median = 6 ( middle number )
  • Mode = 6 ( most common )
  • Conclusion = Can use mean, median or mode if data cluster together (normal distribution)
Consider the following set of data collected
  • 1, 7, 8, 8, 8, 9, 9
Average can be in the form of Mean, Mode or Median
  • Mean = ( 1 + 7+ 8 + 8 +8 +9 +9 )/7 = 7.14
  • Median = 8
  • Mode = 8
  • Conclusion = 1 is an outlier, mean is not appropriate (not normal distribution)
Uncertainty or standard deviation measures the spread/variability of values from the mean
Uncertainty can the the form of
  • standard deviation (SD)
  • standard error (SE)
  • confidence interval (CI)
  • uncertainty ± error

    • High SD - High spread of data - High Uncertainty
    • Low SD - Small spead of data - High Certainty
    • Uncertainty can be expressed in SD, SE and CI if the data is normally distributed
    • Rate can be expressed = (Rate ±SD), (Rate ±SE), (Rate ±CI)





    .........................................................................................................................................................
    IA by two students on effect of Conc on Rate of reaction.
    How concentration of hydrochloric acid affect the rate of reaction?
    Data collected by student 1
    Uncertainty in Rate expressed as SD, SE and CI is small.
    Rate ±SD against Conc was plotted below
    • Error bar/ SD do not overlap
    • High certainty a line passes through error bar
    • Small SD - More precise and highly certain a linear relationship bet Rate and Conc
    • Conc increase - Rate increase
    • Significant different between rates at different concentration




    Data collected by student 2
    Uncertainty in Rate is High
    Rate ±SD against Conc was plotted below

    • Error bar as SD overlap
    • High Uncertainty how the line pass through error bar
    • High SD - Less certain on the relationship between Conc and Rate
    • As Conc increase rate may be constant
    • No significant diff bet rate at higher conc
    • Significant diff bet rate at lower conc

    Data from both student shown below
    Uncertainty/Error bar/SD will determine
    • Small SD - High Certainty - Error bar don't overlap - Significant diff bet rates at diff Conc
    • Small SD - Highly Certain about relationship bet Rate and Conc (Conc up - Rate up)
    • High SD - High Uncertainty - Error bar overlap - No significant diff bet rates at diff Conc
    • High SD - High Uncertainty about relationship bet Rate and Conc (Conc up - Rate constant)
    ...........................................................................................................................................................
    Notes on using statistical t test - Testing of significant difference between two means

    IB Biology statistical analysis, t test, significant difference, hypothesis testing and standard deviation
    .............................................................................................................................
    Good video using Excel for graphing/ error bar plotting



    All notes for the above post is summarised in powerpoint below.

    Thanks to all picture and video contributors use for the above post

    1 comment:

    1. The book was written for people who have little to no experience with R, statistical software, and programming. fengshui

      ReplyDelete

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