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3.10 Inference HOME | Achievement Objectives | Overview | Statistical Cycle | Introduction & Research Question | Discussing Samples | Sample Variability | Sampling Methods | Informal Confidence Interval | Bootstrapping Confidence Interval | Comparing two populations | Using iNZight | Writing a report | Assessment Practice

Discussing Sample Distribution and Statistics

2


Discussion of a sample - review of Dot / Box plots

Review of Sample Statistics & making Box plots.

Notes on Discuss the box plot, the dot plots and the sample statistics, review of 2.9 Inference

Better box plots; How to identify outliers and extreme values

Sheet on discussing Sample Distributing Student worksheet

Sampling Distributions: Introduction to the Concept (Excellent)

 

Starter 3

Class notes,Class notes
Class site

Activity: Box plot discussing Quiz on
centrality | Spread | Symmetry | Tail length
| Histograms & Box plots (considering outliers) (links to Murdoch University)

Box plots: discussing and identifying outliers (link to Murdoch University)

 

3

Discussion of a sample

Initial Visual Interpretation (State the obvious)
Centre    (Media and mean)
Shape     (Symmetry, Skew, Tail, dot plot)
Spread    (Middle 50%, standard deviation, dotplot)
Overlap   (middle 50%)
Unusual Features (gaps, outliers)

*** In CONTEXT  ***

*** With Numerical values ***

And for merit: ‘I notice... I expected ... I was surprised that...’

Also consider possible reasons or causes of these features (in the context) or relate to research
(Merit & Excellence)

AIS Exemple, Elite Athletes, Sample Discussion Student worksheetd Class notes

 

Starter 4

Class notes,Class notes

Student example - dolphin write up describing Sample

Stats Learning Workbook Ex C pg 89 - 91 (with notes on pg 87)

IAS 3.10 pg 7,8

 

 

Car Crash Injury Practice:
Data set, csv Variable Info
Google Doc & Example Report

4

Practice Introduction & Discussion

Summary of common errors/issues:
Not discussing in context. You are discussing the SAMPLE DISTRIBUTION
Not including numerical values.
Not including units.
Not discussing specifically enough.

A suggested approach:
1) State some information for group 'A' (with evidence)
2) State some information for group 'B' (with evidence)
3) Make a comparison between the two groups. (between the two statements above)
4) Was this what you expected? Why?

"The median LBM of the sampled male athletes (74.5kg) is greater than the median female athlete LBM (54.9kg) in the sample. This is a difference of almost 20kg, which reinforces what I suspected the male athletes to be heavier, although I did not expect the difference to be that great"

Starter 5

Car Crash Practice: Student worksheet Class notes1 and Class notes2

 

 

Using iNZight

 

Run iNZight normally, import data

Decide on your variable, and what your two groups are (see iNZight tips page for ordering, removing, grouping, re-categorising, & exporting data, and creating variables)

Add variables to create box plots and show summary statistics. (Adding another variable can also provide more information (iNZight tips page)

 

 

The examples below refer to the Practice write up doc

What is NOT good... in fact rubbish

What it SHOULD be...
(assuming that you have specified what LBM means)

"The male data is more spread out"

"The males have far larger variation of LBM measurements"

"The spread of the males athletes is more than the females"

"The results for the males are a lot more varied"

"male 50% is more spread out than female 50%"

Data? What data?

"In the sample the distribution of male athlete LBM tends to be more spread out than the female athletes LBM. This is confirmed by the difference in the standard deviations, with the male athlete Std.dev of 9.9kg compared with the female athlete Std.dev of 6.9kg. This shows that the male athlete LBM has greater variation than the female athletes LBM. This isn't what I expected because..."

"The middle 50% of male athletes in the sample have a LBM of between 68kg and 80kg which is an IQR of 12kg. This compares with the middle 50% of the female athletes which have a LBM of between 52kg and 59kg with an IQR of only 7kg. This also shows that the male athlete LBM has greater variation than the females athlete LBM..."

"The male range is more than the females range"

"The spread of the male LBM is from roughly 50kg to 110kg"

Do not make a comparison of Range - it is meaningless.
(range is Max value - Min value)

If you want to discuss 'spread' use the IQR or Std.dev

"male 50% is above female 50%"

"The male box is more than the female box"

"The females are further down the table"

"The middle 50% of male athletes in the sample have a LBM of between 68kg and 80kg. This compares with the middle 50% of the female athletes which have a LBM of between 52kg and 59kg. There is no overlap in these groups, rather a 9kg gap. This allows me to be confident in making a call that the male athletes LBM is greater than the females LBM"

"The male centres are higher"

"The male averages are higher"

"The median LBM of the sampled male athletes (74.5kg) is greater than the median female athlete LBM (54.9kg) in the sample. This is a difference of almost 20kg, which reinforces what I suspected the male athletes to be heavier, although I did not expect the difference to be that great"

"There are some outliers in the male data"

"The males have a bigger range than the females"

"There are two outliers in the sample of male athletes, with LBM of 102kg and 106kg (as these values are greater than 1.5 box widths above the upper quartile) These could be weightlifters"

 

 

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