Stat-final
Give 7 examples of Nonparametric Statistics
Chi-square test Sign test Wilcoxon signed rank test Fisher Exact test Wilcoxon rank sum test Kruskal-Wallis test Friedman Test
Examples of when to use the sample or population standard deviation
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The standard deviation is used in conjunction with the mean, to summarise continuous data not categorical data. In addition, the standard deviation, like the mean, is normally only appropriate when the continuous data is not significantly skewed or has outliers.
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What type of data should you use when you calculate a standard deviation?
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The dependent variable is ...
... a variable that is dependent on an independent variable(s). For example, in our case the test mark that a student achieves is dependent on revision time and intelligence. Whilst revision time and intelligence (the independent variables) may (or may not) cause a change in the test mark (the dependent variable), the reverse is implausible
what are the 3 components of Anova?
1. Anova is a parametric method 2. evaluates the differences of 3 or more means of a population (K) 3. it has 1 independent discrete variable (gender, race, etc.) and 1 dependent continuous variable (Not a bell shaped curve but we treat the same way)
Unique things about Anova in regards shape and sign 4
1. Anova is always positive, thus is always on the positive side of the graph) 2. it is skewed to the Right 3. the higher the degree of freedom, the more bell-shaped the F distribution becomes 4. Anova is the Ratio of Variability
Determine the 7 Criteria for the Nonparametric Statistics:
1. Dependent variables 2. Independent variables 3. Assumption 4. Check Normality 5. Sample size 6. Summary table 7. Review
deciding on an appropriate statistical test - what are the questions to ask?
1. Do I have groups of data or continuous scores on two variables? If you have groups you need to use a test that looks at groups such as an independent t-test. If you want to compare the scores on two different variables, correlation/ regression is your best bet. 2. Do I have a hypothesis? T tests or ANOVA can be used to test hypotheses when we have a categorical independent variable whereas orrelation/regression is usually not used in this manner (these techniques can be used for categorical data but are more often used on continuous variables). 3. If you have groups, are they independent or paired? Independent groups are unrelated to each other. Paired scores are usually either before-after or matched pairs type designs.
Describe the Hypothesis of Anova Ho and Ha (same as H1)
1. all population means are equal - no variation among groups (Ho = µ1 = µ2 = µ3 and so on. 2. but because Ho = µ1 = µ2, etc, and the Ha the opposite in the t and z test, with Anova, we have that at least 1 population mean is different Ha ≠ some µ -- but not all pop means are different! Also, there is Anova with and without treatment!!!! Before and after treatment type of thing or not!!!!!
what is independent discrete variable and 3 examples
1. independent discrete variable is also called a FACTOR. Examples: race, ethnicity, gender
what is dependent continuous variable - give 3 examples
2. dependent continuous variable and examples:
Anova do we compare mean or variance and what is the purpose of it?
5 employees - layoff - during layoff - see if lo causes stress samples: 3 samples 5 observations for each group we can compare the 3 means or 3 variances. with Anova, we compare the differences between the means and we calculate the variances to see how variances change within samples Sum of Sq within, between and total SS last calculation: group 1 + 2 + 3
Q. One of the questions on a national consensus survey asks for respondent's age. Which standard deviation would be used to describe the variation in all ages received from the consensus? sample or population
A. Population standard deviation. A national consensus is used to find out information about the nation's citizens. By definition, it includes the whole population, therefore, a population standard deviation would be used.
Q. A teacher sets an exam for their pupils. The teacher wants to summarize the results the pupils attained as a mean and standard deviation. Which standard deviation should be used- sample or population?
A. Population standard deviation. Why? Because the teacher is only interested in this class of pupils' scores and nobody else.
Q. A researcher has recruited males aged 45 to 65 years old for an exercise training study to investigate risk markers for heart disease, e.g. cholesterol. Which standard deviation would most likely be used - sample or population?
A. Sample standard deviation. Although not explicitly stated, a researcher investigating health related issues will not be simply concerned with just the participants of their study; they will want to show how their sample results can be generalised to the whole population (in this case, males aged 45 to 65 years old). Hence, the use of the sample standard deviation.
Anova or F test (refer to the F-table) assumptions:
An -O- Va - Analysis of variance we want to test 1 experiment but with 2 or more layers - we treat as a bell curve like z or t, we set a rejection region - accept of reject Null Hypothesis depending on the result of the calculation SSt, SSw and SSb and degree of freedom.
What are the similarities between descriptive and inferential statistics?
Both descriptive and inferential statistics rely on the same set of data. Descriptive statistics rely solely on this set of data whilst inferential statistics also rely on this data in order to make generalisations about a larger population.
Select the Correct Statistical Test A researcher is interested in differing interventions designed to reduce racist graffiti in an inner city area. He recruited nine neighborhoods that have a problem with racist graffiti and asked members to monitor the frequency, location, and content of racist graffiti. After four weeks of baseline recording, a six week sensitivity training workshop was begun. Community members continued to monitor the frequency, location and content of any racist graffiti during this time, yielding data for 10 consecutive weeks, 4 prior to workshops and 6 after workshops began. The researcher now wants to analyze his data comparing the frequency and location of the graffiti before the workshop and after the workshop. What statistical technique would you advise?
Correct! Repeated measures Anova can be used to test hypotheses regarding the equality of groups and changes in a DV over time. In this example, Repeated Measures would assess both differences in communities and changes over time with regard to the amount of graffiti present. Regression Analysis One Way ANOVA Chi-Square Repeated Measures AnovaIncorrect. Chi-square is a non-parametric technique used to assess differences in categorical data (e.g. yes/no responses). Additionally, chi-square is appropriate only for research situations in which the DV is measured once. In this problem, the DV is measured 10 times. Incorrect. One Way Anova can be used to test hypotheses regarding the equality of 3 or more groups. However, One Way ANOVA is appropriate only for research situations in which the DV is measured once. In this problem, the DV is measured 10 times.
Select the Correct Statistical Test: Imagine you are a researcher interested in sex differences in student's attitudes toward homosexuals. Specifically, you want to test the idea that women are more accepting of homosexuals and thus have more positive attitudes toward homosexuals than do men. You collect data from 10 men and 10 women using a scale that measures homophobia. Your data look like this (note: higher scores equal more positive attitudes). MEN: 2,4,6,8,1,2,5,9,10, 2 WOMEN: 5,5,6,8,9,9,4,2,7,6 Which of the following tests would you use to test your hypothesis: a. Pearsons Correlation Coefficient (r) b. Regression Analysis c. t-test for Independent Means d. t-test for Correlated Means (aka Paired t-test)
Correct! The t test for independent means is used to compare means derived from unrelated (uncorrelated) samples. We have 2 independent groups here, women and men. To test a hypothesis regarding the differences between the 2 groups, we can use a t-test for independent means.
A psychologist is interested in the relationship between job satisfaction and stress. Within a large corporation, the psychologist asked a random sample of workers 2 questions. The first question asked how satisfied workers were with their job and had them rate their satisfaction on a scale from 1 to 50. The second question asked how stressful they found their job in a given week. Again the workers rated their stress level on a scale from 1 to 50. What type of statistical test best assesses the relationship between job satisfaction and level of stress? Correlation One Way ANOVA ANCOVA (Analysis of Covariance) Partial Correlation
Correct! a correlation is a useful tool for describing the relationship between two paired variables, in this case job satisfaction and stress. Recall that stating that two variables are correlated does not allow for a researcher to make causal statements about the two variables or to test a specific relationship concerning the two variables. It merely measures the strength or the relationship between the two variables. Incorrect. One Way Anova can be used to test hypotheses regarding the equality of 3 or more groups. One Way ANOVA is appropriate only for research situations in which we have one continuous DV and 3 or more categorical levels of a single independent variable. Incorrect! Partial correlation is a statistical technique that is used to control for the effects of confounding variables. We have no variables that are thought to confound the relationship. Incorrect. Analysis of CoVariance is used to remove/control for the effects of confounding variables when we have independent variables with 3 or more levels. Here we have no IV's of this form no are we interested in removing the effects of certain variables.
Select the Correct Statistical Test A psychologist wants to investigate the relationship between stress and mental health during the first year of college. The researcher developed scales that measure 1) the frequency of stressful events, 2) the perceived importance of these events, 3) the desirability of such events, and 4) the impact of these events of the student. The researcher had 150 first year college students fill out this questionnaire as well as a Symptom Checklist, which is designed to assess the presence or absence of psychological disorders. What statistical procedure would help this researcher discover if psychological disorders can be predicted from the different aspects of stress that have been measured? Multiple Regression One Way ANOVA Chi-Square Correlation
Correct. Regression analysis can be used to derive an equation from which we can predict scores on one variable (e.g. mental health) based on scores on one or more variables (e.g. our 4 mental health scales). Incorrect. One Way Anova can be used to test hypotheses regarding the equality of 3 or more groups. One Way ANOVA is appropriate only for research situations in which we have one continuous DV and 3 or more categorical levels of a single independent variable. Incorrect. Chi-square is a non-parametric technique used to assess differences in categorical data (e.g. yes/no responses). Incorrect. Repeated measures Anova can be used to test hypotheses regarding the equality of groups and changes in a DV over time. Our example measures all DV's one time only. Additionally, for any ANOVA design we need distinct groups of scores. He we have one group (college students) so ANOVA is not appropriate.
what are the Data Characteristics of Nonparametric statistics?
Data Characteristics: Dependent variable of Nonparametric statistics: NOIR Nominal (categorical) Ordinal (ranked) Interval/ratio (when the data is not normally distributed) or (used for the fast look at data before parametric statistics)
What are the components of the Sign Test and definition of each?
Data: the paired data Assumption: Each paired difference is meaningful. Computation: Step 1: Compute the differences of the measurements for each paired data Step 2: Discard all zero differences Step 3: Apply Sign test formula Step 4: Hypothesis testing
a tutor asks 100 students to complete a maths test. The tutor wants to know why some students perform better than others. Whilst the tutor does not know the answer to this, she thinks that it might be because of two reasons: (1) some students spend more time revising for their test; and (2) some students are naturally more intelligent than others. As such, the tutor decides to investigate the effect of revision time and intelligence on the test performance of the 100 students. what are the dependent and independent variables for the study?
Dependent Variable: Test Mark (measured from 0 to 100) Independent Variables: Revision time (measured in hours) Intelligence (measured using IQ score)
_____ statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data.
Descriptive statistics
What are the limitations of descriptive statistics?
Descriptive statistics are limited in so much that they only allow you to make summations about the people or objects that you have actually measured. You cannot use the data you have collected to generalize to other people or objects (i.e. using data from a sample to infer the properties/parameters of a population). For example, if you tested a drug to beat cancer and it worked in your patients, you cannot claim that it would work in other cancer patients only relying on descriptive statistics (but inferential statistics would give you this opportunity).
How can we visualize the data through Descriptive statistics?
Descriptive statistics are very important, as if we simply presented our raw data it would be hard to visualize what the data was showing, especially if there was a lot of it.
True or false: Descriptive statistics allow us to make conclusions beyond the data we have analysed and reach conclusions regarding hypotheses we might have made.
Descriptive statistics do NOT allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data.
What are Factorial Designs?
Designs that employ more than 1 Independent Variable (remember: Factor = independent variable)
What is Nonparametric Statistics also called?
Distribution-free statistics
Based on the results - outside of the rejection zone, there is no difference between the topical antimicrobial for each of the 3 microorganisms studied
Example of Anova hypothesis conclusion
F distribution degrees of freedom - define
F distribution relates to 2 df: 1. Column or Numerator: # population K - 1 2. Row or Denominator: total # observations - # population (K) Example: 3 groups with 5 obs each 1. df numerator = 3-1 = 2 2. de denominator = 15 - 3 = 12 ∴ n, d = F (2,12) → go to the table F and find 3.88 value -- this value is the limit of rejection
what are the other names for Anova?
F-test, univariate Anova, simple Anova one-factor Anova single-classification Anova
What is Factor for Anova?
Factor is the independent variable! Factors are variable by which the groups are formed.
How to find the 2 Degree of freedom for Anova why 2 (numerator and denominator) if we have 3 groups? and what do they mean for the result? Consider Groups 1, 2, 3 and 5 observations within each group (3 times 5 = 15 obs)
Find the degree of freedom for the groups = #samples minus 1 (3-1) and the total df is 15 minus 3 samples = 12 2, 12 find if in the F table: 3.88
How to find F when you have SSw and SSt? Steps:
Formula: SSt = SSb + SSw ∴ we need to find SSb: SSt - SSw = SSb Find the degree of freedom for both SSb and SSw The formula for Anova or F is: SSb/df is Mean square for b and SSw/df is mean square for w: F = (Mean squareb) ÷ (Mean squarew) F = (SSb/ df) ÷ (SSw/ dfw) SSb/ df = SSw/ dfw =
sign test on the web:
Generally, you run down the columns until you hit your degrees of freedom, go along the row until you hit the probability that meets your critical values (typically 5% for one-tail and 2.5 for two). Then you take that figure and compare it to your test statistic. If your test stat is more extreme, then it falls within the critical region and is therefore significant to that level (p > 0.05).
Null hypothesis for the Two Way Anova
Ho for two-way Anova: The population means for the 1st. factor are equal The population means for the 2nd. factor are equal There is NO interaction between the 2 factors!!!!!!!!!!!!!!!
Define Randomized Complete Block Design
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter. An example of a blocking factor might be the sex of a patient; by blocking on sex, this source of variability is controlled for, thus leading to greater accuracy.
How to interpret Anova results:
In the video example, 3.88 is the limit for the area of rejection and 22.58 is the result (way larger than the area of rejection) - we conclude that the amount of layoffs really causes stress in the population studied.
Select the Correct Statistical Test A psychologist investigated the relationship between SAT score and academic success. She determined that students with high SAT score were more likely to experience academic success. She was very excited about her results and shared them with you. You quickly pointed out to her that students who have high IQ's tend to have high SAT scores and also tend to experience academic success. You explain that the relationship between SAT score and academic success might be due to the fact that both academic success and SAT are related to IQ. Since the psychologist has information concerning IQ scores for her sample, she decides to do some additional analyses which control for the effects of IQ, what would you recommend? Correlation One Way ANOVA ANCOVA Partial Correlation
Incorrect. Correlation is used to assess the relationship of 2 variables, as the researcher did when she looked at the relationship between academic success and GPA. When we introduce a third variable, simple correlation is no longer appropriate. Correct! Partial correlation is a statistical technique that is used to control for the effects of confounding variables. For our example, the procedure would statistically equate everyone at the same IQ level and then produce an estimate of the correlation between academic success and SAT score. The effects of IQ are said to be "removed," leaving an estimate of correlation that is not affected by IQ levels. If the correlation remains high, then we could conclude that academic success is related to SAT scores. If the correlation lowers, we would conclude that the correlation between SAT and success was the result of IQ levels. Incorrect. One Way Anova can be used to test hypotheses regarding the equality of 3 or more groups. One Way ANOVA is appropriate only for research situations in which we have one continuous DV and 3 or more categorical levels of a single independent variable. Incorrect. Analysis of CoVariance is used to remove/control for the effects of confounding variables (such as IQ in relation to SAT score) when we have independent variables with 3 or more levels. Here we have no IV's of this form.
Anova starting calculation for the 3 groups - steps
Mean of each group - group 1 first: mean, obs minus the mean, square and sum the bottom (SS) do the same for group 2 and the group 3
Does Nonparametric Statistics involve rigorous assumptions about the distribution of the critical variables?
No! Nonparametric Statistics is the second class of inferential statistics that does NOT involve rigorous assumptions about the distribution of the critical variables.
Is the following parametric or nonparametric statistics: Sign test Chi-square test Friedman Test
Nonparametric
Is the following parametric or nonparametric statistics: Wilcoxon signed rank test, Kruskal-Wallis test, Friedman Test
Nonparametric
Define Nonparametric Statistics:
Nonparametric Statistics is also called: distribution-free statistics; it is the second class of inferential statistics that does not involve rigorous assumptions about the distribution of the critical variables usually use for nominal or ordinal measures (may be used for a fast-look for interval or ratio measures)
Select the Correct Statistical Test A researcher believes that recall of verbal material differs with the level of processing. He divided his subjects into three groups. In the low processing group, participants read each word and were instructed to count the number of letters in the word. In the medium processing group, participants were asked to read each word and think of a word that rhymed. In the high processing group, participants were asked to read each word and try to memorize it for later recall. Each group was allowed to read the list of 30 words three times, then they were asked to recall as many of the words on the list as possible. If the researcher wants to know whether the three groups have different amounts of recall, what type of statistical test should be used? Regression Analysis One Way ANOVA t-test for Independent Means Two Way Anova
One Way ANOVA Correct! One Way Anova can be used to test hypotheses regarding the equality of 3 or more groups. If after testing your data you found significant differences amongst your groups, you could use a post-hoc technique such as Tukey's test to determine which specific groups performed better than others.
What are the strengths of using descriptive statistics to examine a distribution of scores?
Other than the clarity with which descriptive statistics can clarify large volumes of data, there are no uncertainties about the values you get (other than only measurement error, etc.).
Is the following parametric or nonparametric statistics: ANOVA, Independent t test, ANCOVA
Parametric
Is the following parametric or nonparametric statistics: pearson product-moment correlation Independent t test Paired t test
Parametric
Define Parametric Statistics
Parametric Statistics is a class of inferential statistics that involves: 1. assumptions about the distribution of the variables, such as the assumption that the variables are normally distributed in the population 2. the estimation of at least one parameter the use of at least interval measures
Explain between the One factor Anova components: SSt SSb SSw
Partition of Total Variation = SSt SSb is the variation due to 'treatment' SSw = variation due to random sampling SSt = SSb + SSw
Recap - Statistical Testing 4 components:
Recap - Statistical Testing 1. Data 2. Assumption 3. Computation 4. Hypothesis testing null hypothesis alternative hypothesis decision rule for an alpha level
What is Homoskedasticity and Heteroskedasticity?
Respectively equal and different variances.
Anova how to find SSb, SSw and SSt and why do we need these values?
SSt = SSb + SSw SSt - SSw = SSb + SSw - SSw SSt - SSw = SSb Now, the SSb/ df divided by the SSt/ dft is the result to be compared to the Ftable result and see if it's in the rejection area or not.
what are the other names for SSb? 6
Sum of Squares between, among, explained, model, SS treatment and SS variation
what are the other names for SSw? 4
Sum of Squares within, within groups variation, unexplained, error
What are the limitations of inferential statistics?There are two main limitations to the use of inferential statistics.
The first, and most important, limitation, which is present in all inferential statistics, is that you are providing data about a population that you have not fully measured and, therefore, cannot ever be completely sure that the values/statistics you calculate are correct. Remember, inferential statistics are based on the concept of using the values measured in a sample to estimate/infer the values that would be measured in a population; there will always be a degree of uncertainty in doing this. The second limitation is connected with the first limitation. Some, but not all, inferential tests require the user (i.e. you) to make educated guesses (based on theory) to run the inferential tests. Again, there will be some uncertainty in this process, which will have repercussions on the certainty of the results of some inferential statistics.
what are the 4 Anova assumptions?
These are Assumptions to use Anova: 1. sample sizes are equal 2. samples are randomly drawn 3. variances are relatively equal among groups (homogeneity of variances) 4. Dependent variable is continuous and from a normally distributed population
What are Treatments?
Treatment is the same as number of levels of the factor - the number of Groups defined by a given Factor
When do we reject Ho or fail to reject Ho?
We reject Ho if F calculated is ≥ then the value on the table We fail to reject Ho if F calculated is ∠ then the value on the table, thus not in the zone of rejection. Remember, it's always a positive number!
When deciding on an appropriate statistical test,what are the 2 essential components?
When deciding on an appropriate statistical test, it is essential to pay attention to your data and your hypotheses.
we had the results of 100 pieces of students' coursework, we may be interested in the overall performance of those students. We would also be interested in the distribution or spread of the marks. Can we do both through Descriptive statistics?
Yes. we can measure the overall performance of those students and the distribution or spread of the marks. Descriptive statistics allow us to do this.
Sign Test formula:
Z = |number of '+' - number of '-' |- ½ divided by √ number of '+' + number of '-'
What are Categorical variables?
also known as discrete or qualitative variables. Categorical variables can be further categorized as either nominal, ordinal or dichotomous.
What are Continuous variables?
are also known as quantitative variables. Continuous variables can be further categorized as either interval or ratio variables.
since we can make a series of t-tests, why Anova instead of t-test in regards error?
could compare the means of 1 by 1 but each z or t test comes with an error (type I error) - for every statistical test performed, there is a 5% risk of a false positive. If only 1 test is performed, 5% is OK error - acceptable. However, when we do for example 4 individual tests, each carries 5% error, then the chances to hit a false positive is much higher (4 x 5% = 20%) which is a net 15% error (20 minus 5 error).
What are Ratio variables?
interval variables but with the added condition that 0 (zero) of the measurement indicates that there is none of that variable. So, temperature measured in degrees Celsius or Fahrenheit is not a ratio variable because 0C does not mean there is no temperature. However, temperature measured in Kelvin is a ratio variable as 0 Kelvin (often called absolute zero) indicates that there is no temperature whatsoever. Other examples of ratio variables include height, mass, distance and many more. The name "ratio" reflects the fact that you can use the ratio of measurements. So, for example, a distance of ten metres is twice the distance of 5 metres.
Two Way Anova!!!!! 3
it's an extension of the one-way Anova it evaluates 2 factors on the Dependent Variable and the interaction between different levels of these 2 factors For each Factor, there is 2+ levels within it and the df for each factor is 1 minus the number of levels (Remember Factor is the independent variable!)
what are Dichotomous variables?
nominal variables which have only two categories or levels. For example, if we were looking at gender, we would most probably categorize somebody as either "male" or "female". This is an example of a dichotomous variable (and also a nominal variable). Another example might be if we asked a person if they owned a mobile phone. Here, we may categorise mobile phone ownership as either "Yes" or "No". In the real estate agent example, if type of property had been classified as either residential or commercial then "type of property" would be a dichotomous variable.
Give examples of Parametric Statistics
pearson product-moment correlation coefficient ( r ) Independent t test Paired t test = aka Dependent ANOVA ANCOVA
Anova - how do we find the SSt?
put all 3 groups together now, find the mean for this bigger group, find the total SS (SStotal)
Can you use One-way Anova for Randomized Complete Block Design?
randomized block design and should not be analyzed with the one-way ANOVA.
Select the Correct Statistical Test A large university wants to compare the mathematical abilities of its male and female students. A researcher selects 100 men and 100 women at random from each of the four classes, and administers a math test. The men average 500 on the test, with a standard deviation of 120. The women average 450 on the test, with a standard deviation of 110. What test would be appropriate to determine whether the difference between men and women is real or due to chance variation? Pearsons Correlation Coefficient (r) Regression Analysis t-test for Independent Means t-test for Correlated Means (aka Paired t-test)
t Test for Independent Means - Correct! The t- test for independent groups is used when comparing means derived from two different and unrelated groups. We have two independent groups in this example, men and women. To test a hypothesis regarding the differences between the two groups, we can use a t test for independent groups. Pearson's Correlation Coefficient (r) Incorrect. While correlation is a useful tool for describing the relationship between 2 paired variables it does not serve as a test of our hypothesis. Correlation is used to describe to what degree pairs of data are related. For example, correlation could be used to describe the relationship between gender and math abilities, but not to test a specific hypothesis about this relationship. Incorrect. A paired samples t test is appropriate for data which is paired, matched or before/after. In this case we have two groups which we have no reason to believe constitute a pair. Because our groups are not considered a pair, they are termed independent. Incorrect. Regression analysis can be used to derive an equation from which we can predict scores on one variable based on scores on another. Regression is however, inappropriate in this case for a variety of reasons. First, regression analysis is not usually used to test hypotheses about the differences between groups (though advanced uses of regression analysis do allow for this option). Additionally, regression is inappropriate for our data because we have 2 distinct groups rather than paired data.
Sign Test Definition:
tests the equality of the median of two comparative groups the simplest nonparametric test used for a fast look at data before applying a more sensitive parametric test
Define Randomized Complete Block Design
the experimental units are divided into homogeneous groups (or blocks) to which treatments are applied; each treatment is applied to every block and every block receives each treatment.
What is the number of levels of the factor?
the number of Groups defined by a given Factor
Define Complete Randomized Experimental Design
treatments of interest are assigned to the subjects completely at random - next is to determine the effectiveness of the treatment.
Why do we use nonparametrical Statistics?
usually used for nominal or ordinal measures (may be used for a fast-look for interval or ratio measures)
What are Interval variables?
variables for which their central characteristic is that they can be measured along a continuum and they have a numerical value (for example, temperature measured in degrees Celsius or Fahrenheit). So the difference between 20C and 30C is the same as 30C to 40C. However, temperature measured in degrees Celsius or Fahrenheit is NOT a ratio variable.
What are Nominal variables?
variables that have two or more categories but which do not have an intrinsic order. For example, a real estate agent could classify their types of property into distinct categories such as houses, condos, co-ops or bungalows. So "type of property" is a nominal variable with 4 categories called houses, condos, co-ops and bungalows. Of note, the different categories of a nominal variable can also be referred to as groups or levels of the nominal variable. Another example of a nominal variable would be classifying where people live in the USA by state. In this case there will be many more levels of the nominal variable (50 in fact).
What are Ordinal variables?
variables that have two or more categories just like nominal variables only the categories can also be ordered or ranked. So if you asked someone if they liked the policies of the Democratic Party and they could answer either "Not very much", "They are OK" or "Yes, a lot" then you have an ordinal variable. Why? Because you have 3 categories, namely "Not very much", "They are OK" and "Yes, a lot" and you can rank them from the most positive (Yes, a lot), to the middle response (They are OK), to the least positive (Not very much). However, whilst we can rank the levels, we cannot place a "value" to them; we cannot say that "They are OK" is twice as positive as "Not very much" for example.
what is Multiple testing error?
when results from many treatments are to be compared , multiple t-tests should not be used - this leads to increased risk of false positives. Multiple testing is the general term for such repeated analysis with their attendant risk of false positives.
difference between Anova and t-test
with t-test we compare 2 sets of data. with Anova or AoV: we compare sets of 3 or more sets of data. Anova is like a minor expansion of the two-sample t-test