Descriptive Statistics - 2 Flashcards
Ratios
A ratio is just a comparison between two different things. For instance, someone can look at a group of people, and refer to the ‘ratio of men to women’ in the group. Suppose there are 35 people, 15 of whom are men. Then the ration of men to women is ‘15 to 20’.
Notice that the order is important, and must be respected: whichever word came first, its number must come first. If the expression had been ‘the ratio of women to men’, then the numbers would have been ‘20 to 15’.
Expressing the ratio of men to women as ‘15 to 20’ is expressing the ratio in words. There are 2 other notations for this ‘15 to 20’ ratio:
1) odds notation: 15:20
2) fractional notation: 15/20
Let’s return to the 15 men and 20 women in our original group. I had expressed the ratio as a fraction, namely 15/20. This fraction reduces to 3/4. This means that you can also express the ratio of men to women as 3/4, 3:4, or ‘3 to 4’.
This points out something important about ratios: the numbers used in the ratio might not be the absolute measured values.
The simplified or reduced ratio ‘3 to 4’ tells you only that, for every 3 men, there are 4 women.
The simplified ratio also tells you that, in any representative set of 7 people (3+4=7) from this group, 3 will be men. In other words, the men comprise 3/7 of the people in the group. Thus 4 will be women, the women comprise 4/7 of the people in the group.
Estimating results = Exact vs Estimate
In mathematics, it is often stressed getting an exact answer. But in everyday life, estimation is more likely.
In mathematics, approximation describes the process of finding estimates in the form of upper or lower bounds for a quantity that cannot readily be evaluated precisely. For example, you may be expected to estimate the mean or range from a large set of data.
We can round off all the numbers in a maths problem to 1 significant figure to make ‘easier’ numbers. It is often possible to do this in your head.
Appropriate Number of Significant Figures
- All nonzero digits are significant.
- All zeroes between significant digits are significant.
- All zeroes which are both to the right of the decimal point and to the right of all non-zero significant digits are themselves significant.
If a number is too long, for the sake of clarity, we might round it off to the nearest thousand or million. Similarly, if many decimal figures have been obtained by for example using the calculator, round off to 2 or 3 significant figures.
Probability
Many events cannot be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.
In psychology, probability becomes relevant when applying statistical analysis to data. In this context, probability refers to the extent to which we tolerate a (probability) for the findings to have occurred by chance alone before we accept them to be accurate.
Significance level of 0.05 (p=0.05) means that the probability of the findings to have occurred by chance alone is 5%. Consequently, the probability of the results having occurred due to change in IV is 95%.
The general rule for accepting the results to be accurate in psychology is (p is less than or equal to 0.05). This means the probability of the results to have occurred by chance alone is equal or less than 5%.
