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Biostatstics Flashcards

(120 cards)

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1
Q

What is statistical estimation?

A

Statistical estimation is a method of making inferences about a population parameter when the exact value is unknown.

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2
Q

What are the two main types of statistical estimation?

A

Point estimation and interval estimation.

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3
Q

What is point estimation?

A

Point estimation is a procedure that provides a single value as an estimate for a population parameter.

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4
Q

What is interval estimation?

A

Interval estimation provides a range of values within which the true population parameter is likely to fall.

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5
Q

What is an estimator?

A

An estimator is a rule or random variable that helps approximate a population parameter.

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6
Q

What is an estimate?

A

An estimate is a specific value derived from an estimator for a given dataset.

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7
Q

What are the three key properties of a good estimator?

A

Unbiasedness, consistency, and efficiency.

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8
Q

What is an unbiased estimator?

A

An unbiased estimator is one whose expected value equals the population parameter being estimated.

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9
Q

What is a consistent estimator?

A

A consistent estimator gets closer to the true population parameter as the sample size increases.

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10
Q

What is a relatively efficient estimator?

A

An estimator that has the smallest variance among all unbiased estimators of the parameter.

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11
Q

What is the point estimator for the population mean?

A

The sample mean (x̄) is the point estimator of the population mean (μ).

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12
Q

Why do we use confidence intervals?

A

Confidence intervals provide a range of values that likely contain the true population parameter, accounting for sampling variability.

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13
Q

What does the confidence level represent?

A

The confidence level represents the probability that the confidence interval contains the true population parameter.

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14
Q

What are common confidence levels used in estimation?

A

90%, 95%, and 99% confidence levels.

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15
Q

What is the formula for a confidence interval when the population variance is known?

A

CI = x̄ ± z(σ/√n), where x̄ is the sample mean, z is the critical value, σ is the population standard deviation, and n is the sample size.

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16
Q

What is the formula for a confidence interval when the population variance is unknown?

A

CI = x̄ ± t(s/√n), where t is the t-distribution value and s is the sample standard deviation.

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17
Q

What is the effect of increasing the sample size on confidence intervals?

A

Increasing the sample size reduces the width of the confidence interval, making the estimate more precise.

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18
Q

What is the relationship between confidence level and interval width?

A

Higher confidence levels result in wider intervals, while lower confidence levels produce narrower intervals.

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19
Q

What is standard error?

A

Standard error is the standard deviation of a sampling distribution and measures the accuracy of a sample mean as an estimate of the population mean.

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20
Q

What does a larger standard deviation indicate about an estimate?

A

A larger standard deviation indicates more variability in the estimate, leading to a wider confidence interval.

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21
Q

What is Hypothesis Testing?

A

Making inference about a population parameter based on sample data.

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22
Q

What is a Statistical Hypothesis?

A

Assertion about a population evaluated using sample data.

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23
Q

What is a Test Statistic?

A

A random variable determining to accept or reject the hypothesis.

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24
Q

What is a Statistic Test?

A

Procedure to evaluate a statistical hypothesis.

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25
What is the Null Hypothesis?
The hypothesis to be tested, usually denotes no difference.
26
What is the Alternative Hypothesis?
Hypothesis to be considered when the null is rejected.
27
What is a Type I Error?
Rejecting the null hypothesis when it is true.
28
What is a Type II Error?
Failing to reject the null hypothesis when it is false.
29
What is the Power of a Test?
Probability of rejecting the null hypothesis when it is false.
30
What is the Significance Level?
A value set for Type I error.
31
What is the Critical Region?
Area in a distribution where the null hypothesis is rejected.
32
What is a Two-sided Hypothesis?
Ho: u = p Vs Hi: u ≠ p.
33
What is a One-sided Hypothesis (1)?
Ho: u = p Vs Hi: u > p.
34
What is a One-sided Hypothesis (2)?
Ho: u = p Vs Hi: u < p.
35
What is a Z-test?
Used when sampling from a normal distribution with known variance.
36
What is a T-test?
Used when sampling from a normal distribution with unknown variance.
37
What is a Large Sample Test?
Z-test when sampling from a non-normal distribution or unknown functional form.
38
What is a Test of Association?
Determines the independence of two attributes using chi-square.
39
What is the Expected Frequency?
R * C / n.
40
What are Degrees of Freedom?
(r-1)(c-1) for chi-square test.
41
When do we Reject the Null Hypothesis?
When the test statistic exceeds critical value.
42
When do we Accept the Null Hypothesis?
When the test statistic does not exceed critical value.
43
What are the Hypothesis Test Steps?
Specify Ho and Hi, select significance level, identify sampling distribution, calculate statistic, identify critical region, summarize result.
44
What is a Chi-Square Test?
Tests the association between categorical variables.
45
What is the Conclusion in Hypothesis Testing?
Based on whether the calculated statistic falls in the critical region.
46
What is Probability Theory?
The foundation upon which the logic of inference is built.
47
What is an Outcome?
The result of a single trial of a random experiment.
48
What is Sample Space?
A set of all possible outcomes of a probability experiment.
49
What is an Event?
A subset of the sample space; a statement about one or more outcomes of a random experiment.
50
What are Equally Likely Events?
Events which have the same chance of occurring.
51
What is the Complement of an Event?
Non-occurrence of an event A.
52
What is an Elementary Event?
An event having only a single element or sample point.
53
What are Mutually Exclusive Events?
Two events which cannot happen at the same time.
54
What are Independent Events?
Two events where the occurrence of one does not affect the probability of the other occurring.
55
What are Dependent Events?
Two events where the occurrence of one affects the probability of the other occurring.
56
What is a Sample Space Example (Die)?
S = {1, 2, 3, 4, 5, 6}.
57
What are Counting Rules?
Used to calculate probabilities by knowing the number of elements in an event and sample space.
58
What is the Addition Rule?
A method to determine the number of outcomes for events.
59
What is the Multiplication Rule?
A method to determine the number of outcomes for sequential events.
60
What is a Permutation?
An arrangement of objects in a specific order.
61
What is a Combination?
A selection of objects without regard to order.
62
What is the Classical Approach to Probability?
Used when all outcomes are equally likely and total number of outcomes is finite.
63
What is the Frequency Approach to Probability?
Based on the relative frequencies of outcomes belonging to an event.
64
What is the Axiomatic Approach to Probability?
Based on a set of axioms or postulates.
65
What is Conditional Probability?
Probability of an event given that another event has occurred.
66
What is a Random Variable?
A numerical description of the outcomes of an experiment.
67
What is a Discrete Random Variable?
A variable that can assume only specific values.
68
What is a Continuous Random Variable?
A variable that can assume all values within a given range.
69
What is a Probability Distribution?
A value a random variable can assume and the corresponding probabilities of the values.
70
What is Expected Value?
The mean of a random variable.
71
What is Variance?
Measure of the dispersion of a set of values.
72
What is Binomial Distribution?
Probability distribution of the number of successes in a sequence of independent experiments.
73
What is Normal Distribution?
A continuous probability distribution that is symmetric about the mean.
74
What is Standard Normal Distribution?
A normal distribution with mean 0 and variance 1.
75
What is the Permutation Rule?
n!/(n-r)! for r objects chosen from n objects.
76
What is the Combination Rule?
nCr = n! / [(n-r)! r!].
77
What is the Expected Value of a Discrete Random Variable?
Sum of all possible values of the random variable, each multiplied by its probability.
78
What is the Expected Value of a Continuous Random Variable?
Integral of x times the probability density function over the range of X.
79
What is an Example of Tossing a Coin?
Probability distribution of heads in three tosses.
80
What are the Properties of Probability Distribution?
Non-negative probabilities summing to 1.
81
What is an Example of Drawing Balls with Replacement?
Probability of drawing a red ball twice.
82
What is an Example of Drawing Balls without Replacement?
Conditional probability of drawing a red ball.
83
What is a Binomial Experiment?
An experiment with fixed number of trials, each with two possible outcomes.
84
What is the Definition of Probability?
The likelihood or chance of an event occurring.
85
What is an Example of Mutually Exclusive Events?
Rolling a die, getting either a 3 or a 4, not both.
86
What is an Example of Complementary Events?
Event A happening and event A not happening.
87
What is an Example of Independent Events?
Flipping a coin and rolling a die.
88
What is an Example of Dependent Events?
Drawing two cards from a deck without replacement.
89
What is the Variance Formula?
E(X^2) - [E(X)]^2.
90
What is an Example of the Sum of Two Dice?
Probability distribution of the sum of numbers on two dice.
91
What is an Example of Permutation?
Number of ways to arrange the letters in 'PERMUTE'.
92
What is an Example of Combination?
Number of ways to choose 3 books out of 5.
93
What is the Standard Normal Distribution Table?
Used to find areas under the curve.
94
What is the Expected Value of a Game?
The average outcome of the game in the long run.
95
What is an Example of Conditional Probability?
Probability of a project being well executed given it is well planned.
96
What is Statistics in the plural sense?
Statistics are the raw data themselves like statistics of births, deaths, students, etc.
97
What is Statistics in the singular sense?
It is the subject that deals with the collection, organization, presentation, analysis, and interpretation of numerical data.
98
What is a (Statistical) population?
It is the complete set of possible measurements for which inferences are to be made.
99
What is Census?
A complete enumeration of the population.
100
What is a Sample?
A set of measurements collected from the population using predefined sampling techniques.
101
What is a Parameter?
A characteristic or measure obtained from a population.
102
What is a Statistic?
A characteristic or measure obtained from a sample.
103
What is Sampling?
The process or method of sample selection from the population.
104
What is a Sampling unit?
The ultimate unit or element of the population to be sampled.
105
What is a Sampling frame?
A list of elements in a population.
106
What is a Sampling error?
The discrepancy between the population value and sample value.
107
What is a Non-sampling error?
Errors due to procedure bias such as incorrect responses, measurement errors, or errors at different stages in data processing.
108
Why is Sampling conducted instead of Census?
Because it is cost-effective, faster, more accurate, and suitable for infinite populations, among other reasons.
109
What are the types of Sampling techniques?
Random Sampling (Probability Sampling) and Non-Random Sampling (Non-probability Sampling).
110
What is Simple Random Sampling?
A method where every possible sample of a specific size has an equal chance of being selected.
111
What is Stratified Random Sampling?
The population is divided into non-overlapping groups (strata), and simple random samples are chosen from each stratum.
112
What is Cluster Sampling?
The population is divided into non-overlapping clusters, and all elements in selected clusters are surveyed.
113
What is Systematic Sampling?
A method where the kth item is selected from the sampling frame.
114
What is Judgment Sampling?
The sampler has control over which items are selected for the sample based on judgment.
115
What is Convenience Sampling?
The sampler selects a sample from the population in a manner that is relatively easy and convenient.
116
What is Quota Sampling?
The sample contains a certain number of items with specific characteristics.
117
What is the Central Limit Theorem?
The sampling distribution of the sample mean will be approximately normal with mean and variance , when the sample size is large.
118
What is the importance of the Sampling Distribution of the Sample Mean?
It shows the functional relationship between the possible values of a given sample mean and the probability associated with each value.
119
What are the properties of a given Sampling Distribution?
Mean, variance, and functional form.
120
What is an unbiased estimator?
A statistic whose expected value is equal to the parameter it estimates.

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