Applications-of-GeoGebra/C3/Probability-and-Distributions/English-timed
From Script | Spoken-Tutorial
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 1^{st} 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^{rd} 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. |