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50 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Null hypothesis |
A statement you want to test and that states things are the same as each other or that they match a theoretical expectation. |
The average foot size of a male chicken is the same as a female chicken. |
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Alternative hypothesis |
Statement that things are different than each other or from a theoretical expectation. |
The average foot sizes of male and felmale chickens are different. |
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What is the primary goal of a statistical test? |
To determine whether an observed data set is so different than what you expect under the null hypothesis that you should reject the null hypothesis. |
Null hypothesis |
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P-value |
The probability of getting the observed result or a more extreme result if the null hypothesis is true. |
"The p value (or probability) of getting 17 or fewer males out of 48 total chickens if the null hypothesis is true is .030." |
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What are the different types of variables? |
Nominal, measurement, ranked |
Dick size (inches) Female or Male Smallest to largest |
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Measurement Variables |
Things you can measure. |
Length |
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Probability |
The proportion of individuals in a population that have a particular characteristic |
Males vs females 50/50% |
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When do you reject a null hypothesis? |
When the P value is less than .05. |
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Why do we reject null hypotheses when the p value is lower than .05? |
P value is the probability, and we reject that because or has less than a 5% chance of happening. |
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Significance level |
The probability of rejecting a null hypothesis in a statistical test. Most common is 5% or.05, but there can be different values. |
Rejection |
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What is the difference between a one tailed probability and two tailed test? |
The rejection of the null hypothesis only lies in one direction with the one tailed tests (only greater than or less than on the probability curve ). With a two tailed test, the rejection of the null hypothesis can happen if it's greater or less than (on both sides of the probability curve) |
One tail null hypothesis "The proportion of males is 50% or more." Vs Two tail null hypothesis - "The proportion of males is 50%" |
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Confidence interval |
An estimated interval that tells us where the values of data are most likely to be. There are upper and lower boundaries to each confidence interval. |
Confidence |
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When do you use an exact test of goodness of fit? |
You use an exact test of goodness of fit when you have one nominal variable, you want to see whether the number of observations in each category fits a theoretical expectation, and the sample size is small. |
Example: will a cat use his right paw or left paw more? Expectation 1:1 ratio |
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Sign Test |
An application of the exact binomial test when there are two nominal variables and one measurement variable -- one of the nominal variables must have a "before" and "after" variable, or some kind of either/or nominal variable. |
A study wants to determine whether cats attack toys quicker if they have catnip so measurements in seconds are taken both before and after the addition of catnip. |
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If the null hypothesis is that the mean or median difference between two pairs of observations is zero, then what tests could you use instead of the sign test to analyse the data? |
Paired t-test or a wilcoxon-signed ranked test. |
Paired socks and rank |
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What value should n (sample size) be under to use an exact goodness of fit test? |
Less than 1000. |
Small less than Large greater than |
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If you use a g test or chi squared goodness of fit test instead of an exact goodness of fit test, for a small sample size, what should you know about the results? |
The results may be somewhat inaccurate. |
Smaller sample sizes have higher chance of error |
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When should you use a chi squared goodness of fit test? |
You use the chi squared goodness of cit test when you have one nominal variable worth two our more bdays, you want to see if the number of observations in each category fits a theorhetical expectation, and the sample size is large |
Theory Large one Example null hypothesis: the null hypothesis is that a 3:1 ratio of smooth w ings to wrinkled wings exists in offspring of fly crosses. |
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What affects the shape of the chi-squared distribution? |
The degrees of freedom |
Be free - eagle |
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How do you know whether to use the chi squared test of goodness of fit or the chi squared test of independence? |
Two nominal variables instead of one. |
Nominal |
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Can you try using two different tests and choose the one that gives the best results? Why or why not? |
No you should not do that because it is unethical and you should choose the test before you collect the data. |
Cheating |
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G test of goodness of fit |
You use the g test of goodness of fit when you have one nominal variable, you want to see whether the number of observations in each category fits a theorhetical expectation, and the sample size is large |
1:1 sex ratio |
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What test is similar to and can be used in place of the g test? |
Chi squared goodness of fit test |
Flexible |
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Chi squared test of independence |
Use the chi squared test of independence when toy have two nominal variables and you want to see whether the proportions are different for one variable compared to another. |
Example: the null hypothesis is that the proportions of children given the thigh injection who have severe reactions is the same as the proportion of children given the arm injections who have severe reactions |
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How do you find the degrees of freedom for any given statistical test? |
n-1 -- sample size minus one |
How many times can the data be different? |
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What test could you use instead of a chi-squared test of independence if your sample size is smaller than 1000? (N<1000) |
Fishers exact test |
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What is the difference between the chi-squared and g test of independence? |
The chi-squared gives approximately the aame results as the g test -- unlike the chi, the. G values are additive, which means they can be used foe more elaborate designs. |
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G-test of independence |
Use the G test of independence when you have two nominal variables and you want to see whether the proportions of one variable are different for different values of the other variant. |
The null hypothesis is that the proportion of children given thigh injections who have severe reactions to the thigh injection is equal to the proportion of children given arm injections who have severe reactions |
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What test would you use in place of the g test if the sample size was smaller? |
Fishers exact test |
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Fishers exact test of independence |
Use the fishers exact test of independence when you have two nominal variables and yoy want to see whether the proportions of one variable is defective depending on the values of the other |
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What tests could you use in place of the fishers exact test of independence if the sample size is large? |
G test or the chi-squared |
n is greater than 1000 |
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What kind of test should you use if the sample size is less than 1000? |
An exact test (check with teacher) |
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What is the most common statistic of central tendency? |
Arithimetic mean |
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What do statistical tests of measurement variables assume about the probability distribution? |
The tests for measurement variables assume that the probability distribution of the observations fits the normal or bell shaped curve. |
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What is a normal distribution? |
It has a bell curve, is linked to the central limit theorem, observations can become normally distributed when the number of observations is sufficiently large even if the individual observations are not normal. |
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Arithmetic mean |
The sum of the observations divided by the number of observations to find the average. |
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Median |
The single value of y in the middle of a list sorted from highest to lowest. When you have an even number of values for y, the median is the arithmetic mean of the two middle values. |
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Mode |
The most common value in a data set. The most repeated value. |
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Range |
This is the difference between the largest and smallest observations. |
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Sum of Squares |
Adding together all the data that had been squared. It forms the basis of variance and standard deviation. |
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Parametric variance |
If you take the sum of Squares and divide it by the numbee of observations, n, then you arw computing the average squared deviation from the mean. As thr observations get more ans mlre apread out, they get further from the mean, and the average squared deviate increases. This is not very useful for biological tests. |
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Sample variance |
This is the kind of variance we use for biostatistics because it assumes that a sample is a sample that is applicable to all in the population. Ex: a sample of cats is representative of all the cats. |
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Standard deviation |
Square root of the sample variance, and is more understandable than variance because it is not squared. So it returns data back to its original units (cm=cm not cm=cm^2) |
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How does sample size affect the standard error of the mean? |
As you increase your sample size, the standard error of the mean will get smaller. |
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What do confidence levels and standard error of the mean have in common? |
Both express the reliability of an estimate of the mean. |
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Coefficient of variation |
This is the standard deviation divided by the mean. It is used to compare the amount of variation for one variable among groups with doffwrent means or amomg different measurement variables. It summarizes the ampunt of variation as a percentage or proportion. ax+b where a = Coefficient of variation. |
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Based on your statistical test, what value determines whether you accept or reject the null hypothesis? |
The p value - above 5% means accept null hypothesis. Below 5% is reject |
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What does it mean when the p-value of a test is below 5%? |
The null hypothesis is rejected. That means there is a siginficant difference from the observed values and the theorhetical values in the null hypothesis. |
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What does it mean when a p-value is above 5%? |
Accept the null hypothesis. This also means that the onserved data matches the expectations of the null hypothesis. |
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What are all the tests you can use to evaluate data with nominal variables? |
-Exact goodness of fit test -Chi-squared test of goodness of fit -G test of goodness of fit -Chi-squared test of independence -G-test of independence -Fisher's exact test -Cochran-Mantel-Haenszel test |
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