Independent Loops
Independent Loops - Related Videos
01:21
Introduction to Test of Independence
0 Views •
2025
In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test: where: O = observed values E = expected values (which should be at least 5) A test of independence determines whether...
01:16
Hypothesis Test for Test of Independence
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2023
The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are: H0: The two variables (factors)...
05:08
Manipulating an Independent Variable through Embodiment
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2023
Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco—Monmouth University In any experiment, the researcher attempts to manipulate participants in one group to have different thoughts, experiences, or feelings than the other groups in the study. Some manipulations are overt, while others can be quite subtle. Embodiment is a growing research area focused on the theory that subtle physical experiences can unconsciously influence a person’s thoughts. For example if a...
17:15
Catheterization of Intestinal Loops in Ruminants
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Cited by 4 •
2009
We describe a novel surgical method for catheterizing 'intestinal loops' within the ileum of sheep. Once animals have recovered from surgery and have cleared antibiotics and analgesics, multiple treatments can be deposited directly in loops via the catheters.
08:15
Cardiac Pressure-Volume Loop Analysis Using Conductance Catheters in Mice
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Cited by 33 •
2015
Cardiac pressure-volume loop analysis is the most comprehensive way to measure cardiac function in the intact heart. We describe a technique to perform and analyze cardiac pressure volume loops, using conductance catheters.
FAQs
That unique branch ensures each loop contributes information that is not duplicated by the other loop equations. Without this condition, applying Kirchhoff’s Voltage Law could produce redundant equations rather than a useful independent set. Engineers therefore select loops strategically so the resulting simultaneous equations represent the network’s distinct electrical paths.
Engineers first assign a current variable to each selected loop, including a direction for each variable. For every circuit element, its voltage is then written from its resistance and the relevant current. If a branch belongs to more than one loop, the voltage expression must reflect the currents assigned to the connected network paths.
For each loop, engineers follow the chosen path and add every voltage change algebraically, preserving the signs associated with rises and drops. Kirchhoff’s Voltage Law requires that this total equal zero. Repeating the process for all independent loops creates simultaneous equations that describe the network’s electrical relationships.
Resistance determines the element-voltage term through the assigned current, while current direction establishes the sign used in that expression. Source polarity likewise determines whether a source contributes a voltage rise or drop as the loop is traversed. Consistent sign choices are essential because the equations depend on algebraic, not merely numerical, voltage sums.
Begin by selecting the independent loops and assigning a current to each one. Next, write the voltage contribution of every element using its resistance and the applicable current, then set the algebraic sum around each loop to zero. Solving the resulting simultaneous equations yields the circuit quantities supported by the model.
They are useful when an electrical network contains multiple branches and sources and requires a systematic analysis. The loop equations can support calculations of branch or loop current, element voltage, power, and overall circuit response. This approach helps engineers organize a complex network without writing duplicate voltage equations.