View source for Applications-of-GeoGebra/C3/Probability-and-Distributions/English-timed

{|border=1
||'''Time'''
||'''Narration'''

|-
||00:01
||Welcome to this '''tutorial''' on '''Probability and Distributions in GeoGebra'''.
|-
||00:08
||In this '''tutorial''', we will: 

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

|-
||00:16
||Look at different distributions and parameters.
|-
||00:20
||Here I am using:

'''Ubuntu Linux''' Operating System version 16.04

'''GeoGebra''' 5.0.481.0 hyphen d
|-
||00:34
||To follow this '''tutorial''', you should be familiar with

'''GeoGebra''' interface, Statistics
|-
||00:42
||'''Fish Feed'''

|-
||00:44
||Let us look at an example.

|-
||00:47
||A fishery is testing four types of feed formulation on its fish: '''A''', '''B''', '''C''' and '''D'''. 

|-
||00:56
||Data to be collected after feeding the fish for 6 months are:

|-
||01:01
||Length in '''millimeters'''

|-
||01:04
||Weight in '''pounds'''

|-
||01:07
||Girth in '''millimeters'''

|-
||01:10
||Let’s look at some of these data. 
|-
||01:13
||'''Fish Feed Data'''

|-
||01:15
||We will use these data for our analysis. 

|-
||01:20
||Please download the '''code file''', '''Fishery-data''', provided along with this '''tutorial'''. 
|-
||01:29
||'''Probability'''

|-
||01:31
||Probability of an event P(A),  lies between 0 and 1.

|-
||01:38
||Statistics are calculated for each sample. 

|-
||01:42
||The probability distribution of these statistics is called a sampling distribution. 

|-
||01:48
||Examples are '''normal''', '''t''' etc.

|-
||01:53
||Please refer to  '''Additional material'''  provided along with this tutorial.
|-
||01:59
||I have opened the '''GeoGebra''' interface.
|-
||02:03
||Click on '''View''' tool and select '''Spreadsheet'''. 
|-
||02:09
||Click on '''X''' at top right corner of '''Graphics''' and '''Algebra''' views.

|-
||02:16
||In the '''code file''', use the '''mouse''' to highlight length data in column '''B'''.
|-
||02:24
||Hold '''Control''' key down and press '''C''' to copy the data. 
|-
||02:30
||Click in the top of the '''Spreadsheet''' in '''GeoGebra'''. 
|-
||02:35
||Hold '''Control''' key down and press '''V'''. 
|-
||02:39
||Drag and adjust the column width.
|-
||02:42
||As shown earlier in the series, change the name to '''Length milimeter hyphen A'''. 

|-
||02:55
||Adjust the '''column''' width. 
|-
||02:58
||Repeat this with data in '''columns E''', '''H''' and '''K'''. 
|-
|| 03:05
||Select all data in the four '''columns''' by dragging.
|-
||03:10
||Under the '''menubar''', under '''One Variable Analysis''', click on '''Multiple Variable Analysis'''.
|-
|| 03:18
||A'''Data Source''' popup window appears. 

|-
||03:22
||Click on '''Analyze''' button. 
|-
||03:25
||A '''Data Analysis''' window appears. 
|-
||03:29
||Drag the boundary to see it properly. 
|-
||03:33
||'''Box plots''' appear for data for all four '''columns'''. 
|-
|| 03:39
||Click anywhere in the '''GeoGebra''' window and then click on '''Show Statistics''' tool. 

|-
||03:48
||'''Statistics''' are displayed below the '''box plots'''. 
|-
||03:53
||Above the statistics, click on '''menu button''' next to the word '''Statistics'''. 

Select '''ANOVA'''. 
|-
||04:03
||Drag the boundaries and resize the window to increase size of statistics tables. 
|-
||04:11
||Place the cursor on the boundary below the plots. 

And drag to increase the size of the tables. 
|-
|| 04:20
||'''F value''' is the ratio of '''between groups MS''' to '''within groups MS'''. 

|-
||04:28
||Hence, '''F value''' is quite large (36.5892). 

|-
||04:34
||'''P value''' is 0. 

|-
||04:37
||This means it is probably less than 0.001. 

|-
||04:43
||The feed does make a '''statistically significant''' difference to the length of the fish. 

|-
||04:50
||Hence, the '''null hypothesis''' can be rejected in this case. 

|-
||04:56
||The '''null hypothesis''' here is that none of the feeds make any difference to the length of the fish.
|-
||05:05
||Next to the '''ANOVA display''', click on the '''menu button'''. 
|-
||05:11
||Two options appear for '''T Test''': '''Difference of Means''' and '''Paired Differences'''. 
|-
||05:19
||The same two options appear for '''T Estimate'''. 

|-
||05:24
||'''Difference of Means''' is for '''unpaired T Test'''. 

|-
||05:29
||'''Paired Differences''' is for '''paired T Test'''. 
|-
||05:34
||The '''T Test''' compares two groups at a time. 
|-
||05:38
||Select '''T Test: Difference of Means'''. 
|-
|| 05:42
||'''Column A''' data are denoted by default as '''Sample 1'''.

|-
||05:48
||'''Column B''' data are denoted by default as '''Sample 2'''
|-
||05:54
||Click on the '''menu buttons''' next to the displays to reverse the order. 

|-
||06:02
||As Mean of '''column B''' is greater than Mean of '''column A''', '''T values''' and '''limits''' will now be positive. 
|-
||06:14
||'''T Tests''' give '''t''' and '''P''' values. 

|-
||06:19
||Comparing '''A''' and '''B''' gives '''P''' less than 0.001 and '''T value''' greater than 4. 

|-
||06:29
||Thus, feeds '''A''' and '''B''' have a significant effect on lengths of fish. 
|-
||06:37
||Click on the '''menu button''' and choose '''T estimates, Difference of Means'''. 
|-
||06:45
||'''T Estimates''' give '''lower''' and '''upper limits''' for the '''Mean Difference'''. 

|-
||06:51
||The '''confidence level''' is 95%. 

|-
||06:55
||We can be 95% sure that the '''Mean difference''' is between the '''lower''' and '''upper limits'''. 

|-
||07:04
||Close the '''Data Analysis window'''. 
|-
||07:07
||Now let us look at the '''Probability Calculator'''. 
|-
||07:12
||We are in the '''Spreadsheet''' view. 

|-
||07:15
||Use the '''mouse''' to drag and highlight length data for '''feed A'''. 
|-
||07:22
||Click on '''One Variable Analysis''' tool. 

|-
||07:27
||In the '''Data Source''' popup window that appears, click on '''Analyze''' button. 
|-
||07:33
||At the top of the '''Data Analysis''' window, click on the second( 2nd) '''Show Statistics''' button. 

|-
||07:41
||Note down '''Mean mu (µ)''' and '''Standard deviation sigma (σ)'''. 
|-
||07:49
||Close the '''Data Analysis''' window and follow the same steps for '''feed B'''. 
|-
||07:57
||Again, drag and highlight '''feed A''' length data. 
|-
||08:02
||Click on '''View''' and then click on '''Probability Calculator'''. 
|-
|| 08:08
||The '''Probability Calculator''' window pops up.
|-
||08:12
||Drag the boundary to see it properly. 
|-
||08:16
||We are looking at a '''normal distribution''' in the '''Distribution''' window. 
|-
|| 08:22
||Place your '''cursor''' on the horizontal boundary below the '''distribution curve'''. 

|-
||08:28
||Drag the arrow upwards to see the data entry window below the '''curve''' properly. 
|-
||08:36
||Let us look at a '''normal distribution''' for fish given feed '''A'''. 
|-
|| 08:42
||In the box next to '''mu (μ)''', type 745.5 and press '''Enter'''.
|-
||08:51
||In the box next to '''sigma (σ)''', type 29.0215 and press '''Enter'''. 
|-
||09:01
||A '''normal distribution''' plot appears with mean 745.5 and '''sigma''' 29.0215. 
|-
||09:13
||Click on the 1<sup>st</sup> of three buttons below the '''Mean''' and '''σ''' boxes. 
|-
||09:20
||The right side bracket indicates, this is the upper limit.
|-
||09:25
||In the box next to '''P of X''' less than or equal to, type 770 and press '''Enter'''. 
|-
||09:35
||Note that the '''probability P''' appears in the box to the right, 0.8007. 

|-
||09:44
||Thus, 80.07% fish fed feed '''A''' are 770 milimeters long or shorter. 
|-
||09:55
||Let us do the reverse. 

|-
||09:58
||In the '''P''' box to the right of the equal to sign, type 0.09. 

Press '''Enter'''. 
|-
||10:08
||When you press '''Enter''', '''X''' less than or equal to 706.5893 appears in the box. 
|-
||10:17
||Thus, 9% of the fish are shorter than this length. 
|-
||10:23
||Next to the '''Normal''' display box, click on the '''curve symbol'''. 
|-
||10:28
||The '''cumulative distribution function curve''' appears.
|-
||10:33
||'''Probability''' is plotted on the '''y axis''', length of '''feed A''' group is plotted on '''x axis'''.
|-
||10:43
||Click on '''curve symbol''' to return to the '''normal distribution bell curve'''. 
|-
||10:50
||Below '''mu''' and '''sigma''' displays, click on 2nd of the three buttons.
|-
||10:57
||The two brackets indicate that lower and upper limits can be specified.
|-
||11:04
||In the first box, type 705 and in the second box, 758, press '''Enter'''. 
|-
||11:14
||'''P''' equal to 0.5852 appears. 

|-
||11:20
||This means 58.52% of fish fed '''feed A''' are 705 to 758 milimeter long. 
|-
||11:32
||Finally, click on the 3<sup>rd</sup> button showing a left bracket. 
|-
||11:38
||In the box, type 760 and press '''Enter'''.
|-
||11:45
||30.87% of fish fed '''feed A''' are longer than 760 mm.
|-
||11:54
||Next to '''Distribution''' tab, click on '''Statistics''' tab. 
|-
||11:59
||Close the '''Probability Calculator''' window. 
|-
|| 12:03
||Let us look at the '''Spreadsheet''' in '''GeoGebra'''.
|-
||12:08
||Use '''mouse''' to drag and highlight length data in '''columns A''' and '''B'''.
|-
||12:16
||Under '''One Variable Analysis''', select '''Probability Calculator'''. 
|-
||12:22
||We are looking, as before, at the '''Statistics''' window. 
|-
||12:27
||From the dropdown menu at the top, select '''T Test, Difference of Means'''. 
|-
||12:34
||You can type '''mean, standard deviation σ''' and total number of samples '''N''' in the boxes. 

|-
||12:43
||We will type 10 for '''N''' as each feed group has 10 fish. 

|-
||12:50
||Press '''Enter''' after entering all values. 
|-
||12:54
||'''Feed A''' Mean is lower than '''feed B''' Mean. 
|-
||13:00
||So we will choose '''feed B''' group as '''Sample 1''' and '''feed A''' as '''Sample 2'''. 

|-
||13:08
||Note '''t''', standard error, degrees of freedom and '''P''' values.

|-
||13:15
||Compare them to results from '''Multiple Variable Analysis'''. 

|-
||13:21
||Select different tests for different pairs of columns in the '''Spreadsheet'''. 

|-
||13:27
||Interpret the results and compare with your calculations. 
|-
||13:33
||Let us summarize. 
|-
||13:35
||In this '''tutorial''', we have learnt how to use '''Probability Calculator''' in '''GeoGebra'''.

|-
||13:43
||Looked at different '''distributions''' and '''parameters'''.
|-
||13:48
||Assignment

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

|-
||13:57
||Four oils were used to deep fry chips. 

|-
||14:02
||Amount of absorbed fat was measured for six chips fried in the four oils.

|-
||14:10
||Is any of the oils absorbed more than the others? 

|-
||14:16
||The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it.
|-
||14:25
||The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.

For more details, please write to us.
|-
||14:35
||Please post your timed queries on this forum.
|-
||14:39
||'''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
|-
||14:52
||This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.

Thank you for joining.
|-
|}