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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.

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