Snehalathak at 07:17, 22 January 2019

2019-01-22T07:17:45Z

Madhurig at 07:37, 14 January 2019

2019-01-14T07:37:42Z

Madhurig at 07:20, 14 January 2019

2019-01-14T07:20:07Z

Vidhya: Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this '''tutorial''' on '''Probability and Distributions in..."

2018-10-31T06:45:49Z

Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this '''tutorial''' on '''Probability and Distributions in..."

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{|border=1
| | '''Visual Cue'''
| | '''Narration'''

|-
| | '''Slide Number 1'''

'''Title Slide'''
| | Welcome to this '''tutorial''' on '''Probability and Distributions in GeoGebra'''.
|-
| | '''Slide Number 2'''

'''Learning Objectives'''
| | In this '''tutorial''', we will:

Learn how to use '''Probability Calculator''' in '''GeoGebra'''

Look at different distributions and parameters.
|-
| | '''Slide Number 3'''

'''System Requirement'''
| | Here I am using:

'''Ubuntu Linux''' OS version 16.04

'''GeoGebra''' 5.0.481.0-d
|-
| | '''Slide Number 4'''

'''Pre-requisites'''
| | To follow this '''tutorial''', you should be familiar with

'''GeoGebra''' interface

Statistics
|-
| | '''Slide Number 5'''

'''Fish Feed'''

A fishery is testing four types of feed formulation on its fish: '''A, B, C '''and''' D'''

Length (mm)
Weight (lbs)
Girth (mm)
| | '''Fish Feed'''

Let us look at an example.

A fishery is testing four types of feed formulation on its fish: '''A, B, C''' and '''D'''.
Data to be collected after feeding the fish for 6 months are:

Length in '''millimeters'''

Weight in '''pounds'''

Girth in '''millimeters'''

Let’s look at some of these data.
|-
| | '''Slide Number 6'''

'''Fish Feed Data'''

[[Image:|top]]
| | '''Fish Feed Data'''

We will use these data for our '''analyses'''.

Please download the '''code file''', '''Fishery-data''', provided along with this '''tutorial'''.
|-
| | '''Slide Number 7'''

'''Probability'''

Probability of an event P(A), from 0 to 1

P(A) is ratio of frequency of event A to number of trials

Sampling distribution (normal, t etc)

Probabilities compare 2 independent sample proportions or means
| |
'''Probability'''

Probability of an event P(A) is the likelihood that event A will occur.
P(A) lies between 0 and 1.

P(A) is the ratio of frequency of event A to the number of trials.

Statistics are calculated for each sample.
The probability distribution of these statistics is called a sampling distribution.
Examples are normal, t etc.

Probabilities compare 2 independent sample proportions or means.
|-
| | '''Slide Number 8'''

'''Hypothesis testing'''

'''Statistical hypothesis'''

'''Hypothesis testing: H0, Ha'''

'''z-, t-, F-tests''' etc
| |

'''Hypothesis testing'''

A '''statistical hypothesis''' is an assumption about a population parameter

'''Hypothesis testing''' asks: should a '''statistical hypothesis''' be accepted or rejected?

'''H zero''', the '''null hypothesis''', says observations arise from pure chance.

'''Ha''', the''' alternative hypothesis''', says observations arise due to non-random causes.

'''z-, t-''' and '''F-'''tests '''test population parameters''' in different situations.
|-
| |
| | Please refer to '''additional material''' provided along with this '''tutorial'''.
|-
| | Show the '''GeoGebra''' window.
| | I have opened the '''GeoGebra''' interface.
|-
| | Click on '''View''' tool and select '''Spreadsheet'''.
| | Click on '''View''' tool and select '''Spreadsheet'''.
|-
| | Click on '''X''' at top right corner of '''Graphics''' and '''Algebra''' views.
| | Click on '''X''' at top right corner of '''Graphics''' and '''Algebra''' views.

This will close these views.
|-
| | In the '''code file''', use the '''mouse''' to highlight length data in column '''B'''.
| | In the '''code file''', use the '''mouse''' to highlight length data in column '''B'''.
|-
| | Hold '''Ctrl''' key down and press '''C''' to copy the data.
| | Hold '''Control''' key down and press '''C''' to copy the data.
|-
| | Click on '''Spreadsheet''' view in '''GeoGebra'''.
| | Click in the top of the '''Spreadsheet''' in '''GeoGebra'''.
|-
| | Hold '''Ctrl''' key down and press '''V'''.
| | Hold '''Control''' key down and press '''V'''.
|-
| | Point to the data pasted into '''GeoGebra'''.
| | This will copy and paste the highlighted data from the '''code file''' into '''GeoGebra'''.
|-
| | Drag and adjust the column width.
| | Drag and adjust the column width.
|-
| | Click on '''Text''' and change name to '''Length (mm)-A'''.

Close the '''dialog box'''.
| | As shown earlier in the series, right-click on the heading.

Change the name to '''Length (mm) hyphen A'''.

Close the '''dialog box'''.
|-
| | Adjust the '''column''' width.
| | Adjust the '''column''' width.
|-
| | Highlight data in '''columns E, H''' and '''K'''.

Copy and paste data from '''code file''' into '''GeoGebra'''.

Change names of data from '''columns E, H''' and '''K''' to:

'''Length (mm)-B'''

'''Length (mm)-C'''

'''Length (mm)-D'''
| | Repeat this with data in '''columns E, H''' and '''K'''.
|-
| | Drag '''mouse''' to highlight all labels and data in the four '''columns'''.
| | Select all data in the four '''columns''' by dragging.
|-
| | Under the '''menubar''', under '''One Variable Analysis''', click on '''Multiple Variable Analysis'''.
| | Under the '''menubar''', under '''One Variable Analysis''', click on '''Multiple Variable Analysis'''.
|-
| | Show '''Data Source''' popup window.

Click on '''Analyze''' button.
| | A'''Data Source''' popup window appears.

Click on '''Analyze''' button.
|-
| | Show the '''Data Analysis''' window.
| | A '''Data Analysis''' window appears.
|-
| | Drag the boundary to see it properly.
| | Drag the boundary to see it properly.
|-
| | Point to '''Stacked box plots''' appearing in all four '''columns'''.
| | '''Stacked box plots''' appear for data for all four '''columns'''.
|-
| | Click anywhere in the '''GeoGebra''' window and then click on '''Show Statistics''' tool.

Point to '''Statistics''' displayed below the '''box plots'''.
| | Click anywhere in the '''GeoGebra''' window and then click on '''Show Statistics''' tool.

'''Statistics''' are displayed below the '''box plots'''.
|-
| | Above the statistics, click on '''menu button''' next to the display.

Select '''ANOVA'''.
| | Above the statistics, click on '''menu button''' next to the word '''Statistics'''.

Select '''ANOVA'''.
|-
| | Drag boundaries to increase size of statistics tables.
| | Drag the boundaries and resize the window to increase size of statistics tables.
|-
| | Place the '''cursor''' on the boundary below the plots.

And drag to increase the size of the tables.
| | Place the '''cursor''' on the boundary below the plots.

And drag to increase the size of the tables.
|-
| | Point to the results.
| | The '''between groups mean square (MS)''' is much greater than '''within groups MS'''.

'''F value''' is the ratio of '''between groups MS''' to '''within groups MS'''. Hence, '''F value''' is quite large (36.5892).

'''P value''' is 0. This means it is probably less than 0.001. The difference in the means of all groups is '''statistically significant'''.

The feed does make a '''statistically significant''' difference to the length of the fish.

Hence, the '''null hypothesis''' can be rejected in this case. The '''null hypothesis''' here is that none of the length means are different. That is, none of the feeds make any difference to the length of the fish.
|-
| | Click on the '''menu button''' next to the '''ANOVA display'''.
| | Next to the '''ANOVA display''', click on the '''menu button'''.
|-
| | Point to two options appearing for '''T Test''' and '''T Estimate'''.
| | Two options appear for '''T Test''': '''Difference of Means''' and '''Paired Differences'''.
|-
| | Point to '''T Test''' in the '''menu'''.
| | The same two options appear for '''T Estimate'''.

'''Difference of Means''' is for '''unpaired T Test'''.

'''Paired Differences''' is for '''paired T Test'''.
|-
| |
| | The '''T Test''' compares two groups at a time.
|-
| | Select '''T Test: Difference of Means'''.
| | Select '''T Test: Difference of Means'''.
|-
| | Point to '''Sample 1''' and '''Sample 2'''.
| | '''Column A''' data are denoted by default as '''Sample 1'''. '''Column B''' data are denoted by default as '''Sample 2'''
|-
| | Click on '''menu buttons''' next to the displays to reverse the order.
| | Click on the '''menu buttons''' next to the displays to reverse the order.

As mean of '''column B''' is greater than mean of '''column A''', '''T values''' and '''limits''' will now be positive.
|-
| | Point to '''t''' and '''P''' values in '''T tests'''.
| | '''T Tests''' give '''t''' and '''P''' values.

Comparing '''A''' and '''B''' gives '''P''' less than 0.001 and '''T value''' greater than 4.

Thus, feeds '''A''' and '''B''' have a significant effect on lengths of fish.
|-
| | Click on the '''menu button''' and choose '''T estimates, Difference of Means'''.
| | Click on the '''menu button''' and choose '''T estimates, Difference of Means'''.
|-
| | Show the statistics tables.

Point to '''Confidence Level''' 0.95.
| | '''T Estimates''' give '''lower''' and '''upper limits''' for the '''mean difference'''.

The '''confidence level''' is 95%.

We can be 95% sure that the '''mean difference''' is between the '''lower''' and '''upper limits'''.

You can change '''column''' pairs for comparison and look at the '''T Test''' results.
|-
| | Close the '''Data Analysis window'''.
| | Close the '''Data Analysis window'''.
|-
| |
| | Now let us look at the '''Probability Calculator'''.
|-
| | Point to '''Spreadsheet''' view.

Use '''mouse''' to drag and highlight length data for '''feed A'''.
| | We are in the '''Spreadsheet''' view.

Use the '''mouse''' to drag and highlight length data for '''feed A'''.
|-
| | Click on '''One Variable Analysis''' tool.
| | Click on '''One Variable Analysis''' tool.

In the '''Data Source''' popup window that appears, click on '''Analyze''' button.
|-
| | At the top of the '''Data Analysis''' window, click on the 2nd '''Show Statistics''' button.

Note down '''mean mu (µ)''' and '''standard deviation sigma (σ)'''. (745.5, 29.0215)
| | At the top of the '''Data Analysis''' window, click on the 2nd '''Show Statistics''' button.

Note down '''mean mu (µ)''' and '''standard deviation sigma (σ)'''.
|-
| | Close the '''Data Analysis''' window and follow the same steps for '''feed B'''. (801.5, 21.2191)
| | Close the '''Data Analysis''' window and follow the same steps for '''feed B'''.
|-
| | Drag and highlight '''feed A''' length data.
| | Again, drag and highlight '''feed A''' length data.
|-
| | Click on '''View''' and then click on '''Probability Calculator'''.
| | Click on '''View''' and then click on '''Probability Calculator'''.
|-
| | Point to the '''Probability Calculator''' window that pops up.
| | The '''Probability Calculator''' window pops up.
|-
| | Drag the boundary to see it properly.
| | Drag the boundary to see it properly.
|-
| | Point to the plot and the '''Distribution tab''' above the plot.

Below the plot, point to the '''Normal display box'''.
| | We are looking at a '''normal distribution''' in the '''Distribution''' window.
|-
| | Place your '''cursor''' on the horizontal boundary below the '''distribution curve'''.

Drag the arrow upwards to see the data entry window below the '''curve''' properly.
| | Place your '''cursor''' on the horizontal boundary below the '''distribution curve'''.

Drag the arrow upwards to see the data entry window below the '''curve''' properly.
|-
| |
| | Let us look at a '''normal distribution''' for fish given feed '''A'''.
|-
| | Type 745.5 in the box next to '''mu''' >> press '''Enter'''.
| | In the box next to '''mu (μ)''', type 745.5 and press '''Enter'''.
|-
| | Type 29.0215 in the box next to '''sigma''' >> press '''Enter'''.
| | In the box next to '''sigma (σ)''', type 29.0215 and press '''Enter'''.
|-
| | Point to '''normal distribution''' plot.
| | A '''normal distribution''' plot appears with mean 745.5 and '''sigma''' 29.0215.
|-
| | Click on the 1st of three buttons below the '''mean''' and '''σ''' boxes.
| | Click on the 1st of three buttons below the '''mean''' and '''σ''' boxes.
|-
| | Point to the right side bracket indicates this is the upper limit.
| | The right side bracket indicates this is the upper limit.
|-
| | Type 770 in the box next to '''P (X ≤''' and press '''Enter'''.
| | In the box next to '''P of X''' less than or equal to, type 770 and press '''Enter'''.
|-
| | Point to the '''probability P''' appearing in the box to the right, 0.8007.
| | Note that the '''probability P''' appears in the box to the right, 0.8007.

Thus, 80.07% fish fed feed '''A''' are 770 mm long or shorter.
|-
| | Type 0.09 in the '''P''' box to the right and press '''Enter'''.
| | Let us do the reverse.

In the '''P''' box to the right of the equal to sign, type 0.09.

Press '''Enter'''.
|-
| |
| | We want to know how long 9% of the fish are, on the lower side of the group.
|-
| | Point to '''X''' 706.5893 appearing in the box.
| | When you press '''Enter''', '''X''' less than or equal to 706.5893 appears in the box.
|-
| | Point to the value.
| | Thus, 9% of the fish are shorter than this length.
|-
| | Click on the '''curve symbol''' next to the '''Normal''' display box.
| | Next to the '''Normal''' display box, click on the '''curve symbol'''.
|-
| | Point to the '''cumulative distribution function curve''' appears.
| | The '''cumulative distribution function curve''' appears.
|-
| | Point to '''Probability''' on '''y-axis''' and length of feed on '''x-axis'''.
| | '''Probability''' is plotted on the '''y-axis''', length of '''feed A''' group is plotted on '''x-axis'''.
|-
| | Click on '''curve symbol''' to return to the '''normal distribution bell curve'''.
| | Click on '''curve symbol''' to return to the '''normal distribution bell curve'''.
|-
| | Click on 2nd of three buttons below '''mu''' and '''sigma''' displays.
| | Below '''mu''' and '''sigma''' displays, click on 2nd of the three buttons.
|-
| | Point to the two brackets indicate that lower and upper limits can be specified.
| | The two brackets indicate that lower and upper limits can be specified.
|-
| | Type 705 in the first box and 758 in the second box and press '''Enter'''.
| | In the first box, type 705 and in the second box, 758, and press '''Enter'''.
|-
| | Point to '''P (705 ≤ X ≤ 758) = 0.5852'''.
| | '''P''' equal to 0.5852 appears.

This means 58.52% of fish fed '''feed A''' are 705 to 758 mm long.
|-
| | Click on the 3rd of the three buttons showing a left bracket.
| | Finally, click on the 3rd button showing a left bracket.
|-
| | Type 760 in the box and press '''Enter'''.
| | In the box, type 760 and press '''Enter'''.
|-
| | Point to 0.3087.
| | 30.87% of fish fed '''feed A''' are longer than 760 mm.
|-
| | Click on '''Statistics''' tab next to '''Distribution''' tab.
| | Next to '''Distribution''' tab, click on '''Statistics''' tab.
|-
| | Close the '''Probability Calculator''' window.
| | Close the '''Probability Calculator''' window.
|-
| | Point to '''Spreadsheet''' view.
| | Let us look at the '''Spreadsheet''' in '''GeoGebra'''.
|-
| | Use '''mouse''' to drag and highlight length data in '''columns A''' and '''B'''.
| | Use '''mouse''' to drag and highlight length data in '''columns A''' and '''B'''.
|-
| | Under '''One Variable Analysis''', select '''Probability Calculator'''.
| | Under '''One Variable Analysis''', select '''Probability Calculator'''.
|-
| | Point to '''Statistics''' window.
| | We are looking, as before, at the '''Statistics''' window.
|-
| | From the dropdown menu at the top, select '''T Test, Difference of Means'''.
| | From the dropdown menu at the top, select '''T Test, Difference of Means'''.
|-
| | Type '''means, standard deviation σ''' and '''N=10''' in respective boxes.

Press '''Enter''' after entering all values.
| | You can type '''mean, standard deviation σ''' and total number of samples '''N''' in the boxes.

We will type 10 for '''N''' as each feed group has 10 fish.

Press '''Enter''' after entering all values.
|-
| |
| | '''Feed A''' mean is lower than '''feed B''' mean.
|-
| | Choose '''feed B''' group as '''Sample 1''' and '''feed A''' as '''Sample 2'''.
| | So we will choose '''feed B''' group as '''Sample 1''' and '''feed A''' as '''Sample 2'''.

This will result in positive values for different statistical parameters.
|-
| |
| | Note '''t''', standard error '''SE''', degrees of freedom '''df''' and '''P''' values.

Compare them to results from '''Multiple Variable Analysis'''.

Select different tests for different pairs of columns in the '''Spreadsheet'''.

Interpret the results and compare with your calculations.
|-
| |
| | Let us summarize.
|-
| | '''Slide Number 9'''

'''Summary'''
| | In this '''tutorial''', we have learnt how to use '''Probability Calculator''' in '''GeoGebra'''.

We looked at different '''distributions''' and '''parameters'''.
|-
| | '''Slide Number 10'''

'''Assignment'''
| | '''Assignment'''

Perform statistical analyses for weight and girth data given in this '''tutorial'''.

Four oils were used to deep fry chips. Six chips were chosen from each batch fried in a given oil. Amount of absorbed fat was measured for these chips. Is any of the oils absorbed more than the others?

[[Image:|top]]
|-
| | '''Slide Number 11'''

'''About Spoken Tutorial project'''
| | The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it.
|-
| | '''Slide Number 12'''

'''Spoken Tutorial workshops'''
| | The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.

For more details, please write to us.
|-
| | '''Slide Number 13'''

'''Forum for specific questions:'''

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them
| | Please post your timed queries on this forum.
|-
| | '''Slide Number 14'''

'''Acknowledgement'''
| | '''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
|-
| |
| | This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.

Thank you for joining.
|-
|}

@@ Line 425: / Line 425: @@
 ||Let us summarize.
 |-
-||'''Slide Number 9'''
+||'''Slide Number 8'''
 '''Summary'''
@@ Line 432: / Line 432: @@
 Looked at different '''distributions''' and '''parameters'''.
 |-
-||'''Slide Number 10'''
+||'''Slide Number 9'''
 '''Assignment'''
@@ Line 446: / Line 446: @@
 |-
-||'''Slide Number 11'''
+||'''Slide Number 10'''
 '''About Spoken Tutorial project'''
@@ Line 453: / Line 453: @@
 Please download and watch it.
 |-
-||'''Slide Number 12'''
+||'''Slide Number 11'''
 '''Spoken Tutorial workshops'''
@@ Line 460: / Line 460: @@
 For more details, please write to us.
 |-
-||'''Slide Number 13'''
+||'''Slide Number 12'''
 '''Forum for specific questions:'''
@@ Line 475: / Line 475: @@
 ||Please post your timed queries on this forum.
 |-
-||'''Slide Number 14'''
+||'''Slide Number 13'''
 '''Acknowledgement'''

@@ Line 79: / Line 79: @@
 P(A) is ratio of frequency of event A to number of trials
-Sampling distribution (normal, t etc)
+Sampling distribution ('''normal, t''' etc)
 Probabilities compare 2 independent sample proportions or means
@@ Line 89: / Line 89: @@
 The probability distribution of these statistics is called a sampling distribution.
-Examples are normal, t etc.
+Examples are '''normal''', '''t''' etc.
 Please refer to  '''Additional material'''  provided along with this tutorial.

Applications-of-GeoGebra/C3/Probability-and-Distributions/English - Revision history

Snehalathak at 07:17, 22 January 2019

Madhurig at 07:37, 14 January 2019

Madhurig at 07:20, 14 January 2019

Vidhya: Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this '''tutorial''' on '''Probability and Distributions in..."