Inverse Variation: Definition, Equation & Examples. Direct Variation: . An example of this is relationship between age and height. As the age in. Most commonly, standardisation is used to control for age. There are two methods of standardisation, direct and indirect, and both are explained here. Read the. Direct variation describes a simple relationship between two variables. We say y varies directly with x (or as x, in some textbooks) if.
Here the rate is divided back by to give the basic rate; e. The reason for the difference between the crude mortality rates between country A and country B is that these two populations have markedly different age-structures.
Country A has a much older population than country B.
Standard population In the direct method of standardisation, 'age adjusted rates' are derived by applying the category specific mortality rates of each population to a single standard population table 3. This produces age standardized mortality rates that these countries would have if they had the same age distribution as the standard population.Direct and Inverse Relationships
Note that the 'standard population' used may be the distribution of one of the populations being compared or may be an outside standard population such as the 'European' or 'World' standard population. The weighted average of the category-specific rates with the weights taken from the standard population provides for each population a single summary rate that reflects the numbers of events that would have been expected if the populations being compared had the same age distribution 1.
The ratio of the directly standardized rates can then be calculated to provide a single summary measure of the difference in mortality between the two populations. The ratio of the standardized rates is called the Comparative Mortality Ratio CMR and is calculated by dividing the overall age adjusted rate in country B by the rate in country A. Note that while the crude rates presented in table 1 represent the actual mortality experience of countries A and B, it is not possible to use these crude rates to make a valid comparison between the two countries because they have very different age distributions.
However, by using the direct method of standardisation while the values of the adjusted rate do not reflect the 'true' mortality experience of countries A and Bit enables us to calculate 'hypothetical' age adjusted rates that can be used to make a valid comparison of overall mortality between the two countries. Indirect method of standardisation The indirect method of standardisation is commonly used when age-specific rates are unavailable.
For example if we did not know the age specific mortality rates for country B. Indirect method of standardisation: Number of expected deaths if the population had the same age-specific mortality rates as Country A. In table 4, the indirect method of standardisation is used to calculate how many deaths would be expected in Country B if it had the same age-specific mortality rates as Country A. The expected deaths in Country B are calculated by multiplying the age specific rate for Country A by the population of Country B in the corresponding age group.
The sum of the age categories gives the total number of deaths that would be experienced in country B if it had the same mortality experience as country A. An overall summary measure can then be calculated, that is, the standardized mortality ratio SMRwhich is the ratio of the observed number of deaths to the expected number of deaths. Issues in the use of standardisation Standardised rates are used for the comparison of two or more populations; they represent a weighted average of the age specific rates taken from a 'standard population' and are not actual rates.
The direct method of standardisation requires that the age-specific rates for all populations being studied are available and that a standard population is defined. The indirect method of standardisation requires the total number of cases The ratio of two directly standardised rates is called the Comparative Incidence Ratio or Comparative Mortality Ratio. The ratio of two indirectly standardised rates is called the Standardized Incidence Ratio or the Standardized Mortality Ratio.
Indirect standardisation is more appropriate for use in studies with small numbers or when the rates are unstable. As the choice of a standard population will affect the comparison between populations, it should always be stated clearly which standard population has been applied.
Standardisation may be used to adjust for the effects of a variety of confounding factors including age, sex, race or socio-economic status.
Standardisation of rates can be difficult to understand and is explained in several different ways depending on the literature source. For example, in social research, you may want to establish a relationship between height and weight. You could show that the weight of an individual is the dependent variable, dependent on the height of an individual, and height is an independent variable.
More height is going to mean, ceteris paribus other things being equalgreater weight. Less height is likely going to mean a lower weight.
A dependent variable changes in relation to an independent variable, while an independent variable changes, for purposes of analysis, freely in value.
A relationship could be thought of as a connection; you connect two variables to establish an association.
How is inverse variation used in everyday life?
There are two relationships you need to know about in economics. A positive or direct relationship is one in which the two variables we will generally call them x and y move together, that is, they either increase or decrease together. An excellent example is the price of steel, and the response of steel suppliers to bring steel to the market; as the price increases, so does the willingness of producers to bring more of the good to the market. The example we gave of the relationship between height and weight is a direct or positive relationship.
In a negative or indirect relationship, the two variables move in opposite directions, that is, as one increases, the other decreases. Consider the price of coffee and the demand for the good. As the price of coffee, for example, goes to higher and higher levels, we can predict that people will substitute tea or hot chocolate for it, and buy less. As the price of coffee declines, people will buy more and more of it, and quite possibly buy more than they would regularly buy, and store or accumulate it for future consumption, or to sell it to others.
This relationship is negative or indirect, that is, as the price variable typically, in economics, the y variable increases, the quantity variable typically, the x variable decreases; and, as the price variable decreases, the quantity demanded increases.
These relationships between positivly- and negatively-related variables are demonstrated in the graphs Figure 1 which follow, positive first and negative second: What is the value of graphs in the study of economics? Graphs are a very powerful visual representation of the relationship between or among variables. They assist learners in grasping fairly quickly key economic relationships.
Years of statistical analysis have gone into the small graph you can examine to learn about key forces and trends in the economy. Further, they help your instructor to present data in a way which is small-scale or economical, and establish a relationship, frequently historical, between variables in a certain kind of relationship. They permit learners and instructors to establish quickly the peaks and valleys in data, to establish a trend line, and to discuss the impact of historical events such as policies on the data that we wish to analyze.
Types of Graphs in Economics There are various kinds of graphs used in business and economics that illustrate data.
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These include pie charts segments are displayed as portions, usually percentages, of a circlescatter diagrams points are connected to establish a trendbar graphs results for each year can be displayed as an upward or downward barand cross section graphs segments of data can be displayed horizontally. You will deal with some of these in economics, but you will be dealing principally with graphs of the following variety.
Certain graphs display data on one variable over a certain period of time.
For example, we may want to know how the inflation rate has varied in the Canadian economy from We would choose an appropriate scale for the rate of inflation on the y vertical axis; and on the x horizontal axis show the ten years from to with on the left, and on the right. We would notice right away a trend. The trend in the inflation rate data is a decline, actually from a high of 5. We would see that there has been some increase in the inflation rate since its absolute low inbut not anything like the high.
And, if we did such graphs for each of the decades in Canada sincewe would see that the s were a unique decade in terms of inflation. No decade, except the s, shows any resemblance to the s. We can then discuss the trends meaningfully, since we have ideas about the data over a major period of time. We can link the data with historical events such as government anti-inflation policies, and try to establish some connections.
Other graphs are used to present a relationship between two variables, or in some instances, among more than two variables. Consider the relationship between price of a good or service and quantity demanded.
The two variables move in opposite directions, and therefore demonstrate a negative or indirect relationship. Aggregate demand, the relationship between the total quantity of goods and services demanded in the entire economy, and the price level, also exhibits this inverse or negative relationship.
If the price level based on the prices of a given base year rises, real GDP shrinks; while if the price level falls, real GDP increases. Further, the supply curve for many goods and services exhibits a positive or direct relationship. The supply curve shows that when prices are high, producers or service providers are prepared to provide more goods or services to the market; and when prices are low, service providers and producers are interested in providing fewer goods or services to the market.
The aggregate expenditure, or supply, curve for the entire Canadian economy the sum of consumption, investment, government expenditure and the calculation of exports minus imports also shows this positive or direct relationship. Construction of a Graph You will at times be asked to construct a graph, most likely on tests and exams.
You should always give close attention to creating an origin, the point 0, at which the axes start. Label the axes or number lines properly, so that the reader knows what you are trying to measure. Most of the graphs used in economics have, a horizontal number line or x-axis, with negative numbers on the left of the point of origin or 0, and positive numbers on the right of the origin. Figure 2 presents a typical horizontal number line or x-axis.
In economics graphs, you will also find a vertical number line or y-axis. Here numbers above the point of origin 0 will have a positive value; while numbers below 0 will have a negative value.
Figure 3 demonstrates a typical vertical number line or y-axis. When constructing a graph, be careful in developing your scale, the difference between the numbers on the axes, and the relative numbers on each axis.
The scale needs to be graduated or drawn properly on both axes, meaning that the distance between units has to be identical on both, though the numbers represented on the lines may vary. You may want to use single digits, for example, on the y-axis, while using hundreds of billions on the x-axis.
Using a misleading scale by squeezing or stretching the scale unfairly, rather than creating identical distances for spaces along the axes, and using a successive series of numbers will create an erroneous impression of relationship for your reader.
Direct and inverse relationships - Math Central
If you are asked to construct graphs, and to show a knowledge of graphing by choosing variables yourself, choose carefully what you decide to study. Here is a good example of a difficulty to avoid. Could you, for example, show a graphical relationship between good looks and high intelligence?
I don't think so. First of all, you would have a tough time quantifying good looks though some social science researchers have tried! Intelligence is even harder to quantify, especially given the possible cultural bias to most of our exams and tests.
Finally, I doubt if you could ever find a connection between the two variables; there may not be any.