Applications-of-GeoGebra/C3/Probability-and-Distributions/English-timed

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	AData 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 1st 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 3rd 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?
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14:52	This is Vidhya Iyer from IIT Bombay, signing off. Thank you for joining.

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