Stat 1000: Seminar 29

1
Reflex Patterns in Postganglionic Neurons
Supplying Skin and Skeletal Muscle of the Rat
Hindlimb

• Stat 1000 Seminar 29
• Mitchell Thompson III

2
Overview

• Goal To determine if the MVC (muscle)and CVC
  (skin)neurons can be distinguished functionally
  based on their reflex patterns?
• Reflex analysis of postganglionic Vasoconstrictor
  neurons to Muscle (MVC) and skin (CVC) elicited
  through multiple stimuli.
• Terms MVC and CVC classified as postganglionic
  neurons that innervate blood vessels and are
  vasoconstrictor in function
• Muscle
• Cutaneous

3
Neuroanatomy
4
Methods

• Subjects 65 female Wistar rats
• Selection bias?
• The investigator aims to prove that the central
  organization of the sympathetic nervous system in
  rats possess a differentiation with respect to
  function
• Anesthetics 3 types used pentorbitone
  (pentorbital sodium), urethane, and a-chloralose.
• Does this support or damage results?
• Results are supported because the effects of
  anesthesia (confounding variable) can be
  eliminated

5
Subjects

• 65 female Wistar rats
• 59 preparations of spontaneously active MVC
  (skeletal) neurons
• 138 preperations of spontaneously active CVC
  (skin) neurons
• What is/are sample size(s)?
• n1 59 n2 138

6
Spontaneous Activity
7
U and Pooling

• A non-parametric test for assessing whether two
  samples of observations come from the same
  distribution
• The U test (Wilcoxon rank-sum test) is useful in
  the same situations as the independent samples
  Students t-test
• For distributions sufficiently far from normal
• Because the spontaneous activity of neurons under
  the different anesthetics had a similar
  distribution (Pgt0.05) all samples were pooled.

8
Students Distribution

• A test of the null hypothesis that the means of
  two normally distributed populations are equal.
• Given two data sets, each characterized by its
  mean, standard deviation and number of data
  points, we can use two sample t test to determine
  whether the means are distinct, provided that the
  underlying distributions can be assumed to be
  normal.
• All such tests are usually called Student's t
  tests, though strictly speaking that name should
  only be used if the variances of the two
  populations are also assumed to be equal

9
Reflexes elicited by stimulation of the arterial
baroreceptors

• Arterial baroreceptors Stimulation of arterial
  baroreceptors leads to inhibition of activity in
  vasoconstrictor neurons innervating resistance
  vessels.
• Quantification of Neural responses A 20 change
  of neural activity during the first 30s after
  stimulation compared with control activity during
  the 50s preceding stimulation was considered as a
  response.
• Paired vs. Two-sample
• Paired (comparison within sample nx)

10
Arterial Baroreceptor Stimulation
11
Two Sample T-Test

• Equivalent to students distribution?
• Because variances are assumed to be equal
• s.d.1 s.d.2
• Categorical/ Quantitative Variable
• Neuron Type (Categorical)
• MVC (n1 59) vs. CVC (n2 138)
• Cardiac Rhythmicity (Quantitative)
• Requirements
• Unknown population s
• Difference between means not mean of differences
• Sample means normally distributed
• Independent samples
• N 10n

12
Hypothesis

• Null Hypothesis Ho
• (a) µ1 µ2 0
• (b) µ1 µ2
• (c) µ1 -µ2
• Alternative Hypothesis Ha
• (a) µ1 µ2 ? 0
• (b) µ1 µ2
• (c) µ1 gt µ2

13
T-Test

• MVC CR
• x bar1 75 s1 17 n1 59
• CVC CR
• x bar2 44 s2 20 n2 138

14
T-Statistic

• Factors that affect t-statistic
• Difference between x bar1 and x bar2
• Large difference ? Increases t
• Smaller p-value ? Easier to reject Ho
• Sample Sizes n1 and n2
• Small sizes n1 and n2 ? Decreases t
• Larger p-value ? Harder to reject Ho
• S.D. s1 and s2
• Small s.d. s1 and s2 ? Increases t
• Smaller p-value ? Easier to reject Ho

15
Conclusion

• T-statistic large?
• 11.1. Big yes!
• P-value small?
• Plt 0.001 ..Another Big Yes!
• Reject Ho µ1 µ2 0?
• I think you get the picture
• Cardiac Rythmicity is greater in MVC Neurons than
  CVC neurons Although CR is less prominent in CVC
  it is still inhibited by an increase in blood
  pressure (arterial baroreceptor stimulation)

16
Reflections

• Study Design
• Test male rats and compare to females to
  determine if a significant difference of results
  exists
• Paired vs. two-sample t-test
• Two-sample
• Subjects
• No attempt was made to study neurons w/o
  spontaneous activityrecruitment of silent
  neurons within multiunit preparations can not be
  ruled out
• Type I vs. Type II Error?
• Sample size would appear larger than its actual
  value
• Statistic would appear larger (p-value smaller)
  Type I