Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
PARAMETRIC TESTS
STATISTICAL TEST
• Statistical tests are intended
to decide whether a
hypothesis about distribution
of one or more populat...
PARAMETRIC TESTS
Parametric test is a statistical test that makes assumptions
about the parameters of the population distr...
APPLICATIONS
• Used for Quantitative data.
• Used for continuous variables.
• Used when data are measured on approximate i...
PARAMETRIC TESTS
1. t-test
t-test
t-test for one
sample
t-test for two
samples
Unpaired two
sample t-test
Paired two
sampl...
Contd..
2. ANOVA
3. Pearson’s r correlation
4. Z test
ANOVA
One way ANOVA
Two way ANOVA
STUDENT’S T-TEST
• Developed by Prof.W.S.Gossett
• A t-test compares the difference between two means of
different groups ...
One Sample t-test
Assumptions:
• Population is normally distributed
• Sample is drawn from the population and it should be...
Contd..
• In one sample t-test , we know the population mean.
• We draw a random sample from the population and then
compa...
Let x1, x2, …….,xn be a random sample of size “n” has drawn from a
normal population with mean (µ) and variance 𝜎2.
Null h...
Two sample t-test
• Used when the two independent random samples come from the
normal populations having unknown or same v...
Contd…
Assumptions:
1. Populations are distributed normally
2. Samples are drawn independently and at random
Conditions:
1...
If two independent samples xi ( i = 1,2,….,n1) and yj ( j = 1,2, …..,n2) of
sizes n1and n2 have been drawn from two normal...
Paired t-test
Used when measurements are taken from the same subject
before and after some manipulation or treatment.
Ex: ...
Assumptions:
1. Populations are distributed normally
2. Samples are drawn independently and at random
Conditions:
1. Sampl...
Null Hypothesis:
H0: µd = 0
Under H0, the test statistic
𝒕 =
ǀ𝒅̅ǀ
𝒔
𝒏
Where, d = difference between x1 and x2
d̅ = Average...
Z-Test
• Z-test is a statistical test where normal distribution is applied
and is basically used for dealing with problems...
Contd…
Assumptions:
• Population is normally distributed
• The sample is drawn at random
Conditions:
• Population standard...
Let x1, x2, ………x,n be a random sample size of n from a normal
population with mean µ and variance σ2 .
Let x̅ be the sampl...
Under Hο, the test statistic is
𝒁 =
ǀ 𝒙 − µ 𝝄ǀ
𝒔
𝒏
If the calculated value of Z < table value of Z at 5% level of
signific...
Pearson’s ‘r’ Correlation
• Correlation is a technique for investigating the relationship
between two quantitative, contin...
Types of correlation
Type of correlation Correlation coefficient
Perfect positive correlation r = +1
Partial positive corr...
ANOVA (Analysis of Variance)
• Analysis of Variance (ANOVA) is a collection of statistical
models used to analyse the diff...
ANOVA
One way ANOVA
Two way ANOVA
One way ANOVA
Compares two or more unmatched groups when data are categorized in
one factor
Ex:
1. Comparing a control gro...
Two way ANOVA
• Used to determine the effect of two nominal predictor variables on a
continuous outcome variable.
• It ana...
Assumptions of ANOVA:
• The samples are independent and selected randomly.
• Parent population from which samples are take...
• ANOVA compares variance by means of F-ratio
F =
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠
• It again depends on e...
ANOVA Table
Sources of
Variation
Sum of squares
(SS)
Degrees of
freedom (d.f)
Mean squares
(MS)
𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒔
𝒅̅𝒆𝒈𝒓𝒆𝒆𝒔 𝒐𝒇...
S.No Type of group Parametric test
1. Comparison of two paired groups Paired t-test
2. Comparison of two unpaired groups U...
Parametric tests
Upcoming SlideShare
Loading in …5
×

of

Parametric tests Slide 1 Parametric tests Slide 2 Parametric tests Slide 3 Parametric tests Slide 4 Parametric tests Slide 5 Parametric tests Slide 6 Parametric tests Slide 7 Parametric tests Slide 8 Parametric tests Slide 9 Parametric tests Slide 10 Parametric tests Slide 11 Parametric tests Slide 12 Parametric tests Slide 13 Parametric tests Slide 14 Parametric tests Slide 15 Parametric tests Slide 16 Parametric tests Slide 17 Parametric tests Slide 18 Parametric tests Slide 19 Parametric tests Slide 20 Parametric tests Slide 21 Parametric tests Slide 22 Parametric tests Slide 23 Parametric tests Slide 24 Parametric tests Slide 25 Parametric tests Slide 26 Parametric tests Slide 27 Parametric tests Slide 28 Parametric tests Slide 29 Parametric tests Slide 30 Parametric tests Slide 31
Upcoming SlideShare
Z-Test with Examples
Next
Download to read offline and view in fullscreen.

134 Likes

Share

Download to read offline

Parametric tests

Download to read offline

parametric tests

Related Books

Free with a 30 day trial from Scribd

See all

Related Audiobooks

Free with a 30 day trial from Scribd

See all

Parametric tests

  1. 1. PARAMETRIC TESTS
  2. 2. STATISTICAL TEST • Statistical tests are intended to decide whether a hypothesis about distribution of one or more populations or samples should be rejected or accepted. Statistical Tests Parametric tests Non – Parametric tests
  3. 3. PARAMETRIC TESTS Parametric test is a statistical test that makes assumptions about the parameters of the population distribution(s) from which one’s data is drawn.
  4. 4. APPLICATIONS • Used for Quantitative data. • Used for continuous variables. • Used when data are measured on approximate interval or ratio scales of measurement. • Data should follow normal distribution.
  5. 5. PARAMETRIC TESTS 1. t-test t-test t-test for one sample t-test for two samples Unpaired two sample t-test Paired two sample t-test
  6. 6. Contd.. 2. ANOVA 3. Pearson’s r correlation 4. Z test ANOVA One way ANOVA Two way ANOVA
  7. 7. STUDENT’S T-TEST • Developed by Prof.W.S.Gossett • A t-test compares the difference between two means of different groups to determine whether the difference is statistically significant.
  8. 8. One Sample t-test Assumptions: • Population is normally distributed • Sample is drawn from the population and it should be random • We should know the population mean Conditions: • Population standard deviation is not known • Size of the sample is small (<30)
  9. 9. Contd.. • In one sample t-test , we know the population mean. • We draw a random sample from the population and then compare the sample mean with the population mean and make a statistical decision as to whether or not the sample mean is different from the population.
  10. 10. Let x1, x2, …….,xn be a random sample of size “n” has drawn from a normal population with mean (µ) and variance 𝜎2. Null hypothesis (H0): Population mean (μ) is equal to a specified value µ0. Under H0, the test statistic is 𝒕 = 𝒙−µ 𝒔 𝒏
  11. 11. Two sample t-test • Used when the two independent random samples come from the normal populations having unknown or same variance. • We test the null hypothesis that the two population means are same i.e., µ1 = µ2
  12. 12. Contd… Assumptions: 1. Populations are distributed normally 2. Samples are drawn independently and at random Conditions: 1. Standard deviations in the populations are same and not known 2. Size of the sample is small
  13. 13. If two independent samples xi ( i = 1,2,….,n1) and yj ( j = 1,2, …..,n2) of sizes n1and n2 have been drawn from two normal populations with means µ1 and µ2 respectively. Null hypothesis H0 : µ1 = µ2 Under H0, the test statistic is 𝒕 = ǀ 𝒙 − 𝒚ǀ 𝑺 𝟏 𝒏 𝟏 + 𝟏 𝒏 𝟐
  14. 14. Paired t-test Used when measurements are taken from the same subject before and after some manipulation or treatment. Ex: To determine the significance of a difference in blood pressure before and after administration of an experimental pressure substance.
  15. 15. Assumptions: 1. Populations are distributed normally 2. Samples are drawn independently and at random Conditions: 1. Samples are related with each other 2. Sizes of the samples are small and equal 3. Standard deviations in the populations are equal and not known
  16. 16. Null Hypothesis: H0: µd = 0 Under H0, the test statistic 𝒕 = ǀ𝒅̅ǀ 𝒔 𝒏 Where, d = difference between x1 and x2 d̅ = Average of d s = Standard deviation n = Sample size
  17. 17. Z-Test • Z-test is a statistical test where normal distribution is applied and is basically used for dealing with problems relating to large samples when the frequency is greater than or equal to 30. • It is used when population standard deviation is known.
  18. 18. Contd… Assumptions: • Population is normally distributed • The sample is drawn at random Conditions: • Population standard deviation σ is known • Size of the sample is large (say n > 30)
  19. 19. Let x1, x2, ………x,n be a random sample size of n from a normal population with mean µ and variance σ2 . Let x̅ be the sample mean of sample of size “n” Null Hypothesis: Population mean (µ) is equal to a specified value µο H0: µ = µο
  20. 20. Under Hο, the test statistic is 𝒁 = ǀ 𝒙 − µ 𝝄ǀ 𝒔 𝒏 If the calculated value of Z < table value of Z at 5% level of significance, H0 is accepted and hence we conclude that there is no significant difference between the population mean and the one specified in H0 as µο.
  21. 21. Pearson’s ‘r’ Correlation • Correlation is a technique for investigating the relationship between two quantitative, continuous variables. • Pearson’s Correlation Coefficient (r) is a measure of the strength of the association between the two variables
  22. 22. Types of correlation Type of correlation Correlation coefficient Perfect positive correlation r = +1 Partial positive correlation 0 < r < +1 No correlation r = 0 Partial negative correlation 0 > r > -1 Perfect negative correlation r = -1
  23. 23. ANOVA (Analysis of Variance) • Analysis of Variance (ANOVA) is a collection of statistical models used to analyse the differences between group means or variances. • Compares multiple groups at one time • Developed by R.A.Fischer
  24. 24. ANOVA One way ANOVA Two way ANOVA
  25. 25. One way ANOVA Compares two or more unmatched groups when data are categorized in one factor Ex: 1. Comparing a control group with three different doses of aspirin 2. Comparing the productivity of three or more employees based on working hours in a company
  26. 26. Two way ANOVA • Used to determine the effect of two nominal predictor variables on a continuous outcome variable. • It analyses the effect of the independent variables on the expected outcome along with their relationship to the outcome itself. Ex: Comparing the employee productivity based on the working hours and working conditions.
  27. 27. Assumptions of ANOVA: • The samples are independent and selected randomly. • Parent population from which samples are taken is of normal distribution. • Various treatment and environmental effects are additive in nature. • The experimental errors are distributed normally with mean zero and variance σ2.
  28. 28. • ANOVA compares variance by means of F-ratio F = 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒𝑠 • It again depends on experimental designs Null hypothesis: Hο = All population means are same • If the computed Fc is greater than F critical value, we are likely to reject the null hypothesis. • If the computed Fc is lesser than the F critical value , then the null hypothesis is accepted.
  29. 29. ANOVA Table Sources of Variation Sum of squares (SS) Degrees of freedom (d.f) Mean squares (MS) 𝒔𝒖𝒎 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆𝒔 𝒅̅𝒆𝒈𝒓𝒆𝒆𝒔 𝒐𝒇 𝒇𝒓𝒆𝒆𝒅̅𝒐𝒎 F - Ratio Between samples or groups (Treatments) Treatment sum of squares ( TrSS) (k-1) 𝑇𝑟𝑆𝑆 (𝑘 − 1) 𝑇𝑟𝑀𝑆 𝐸𝑀𝑆 Within samples or groups ( Errors ) Error sum of squares (ESS) (n-k) 𝐸𝑆𝑆 (𝑛 − 𝑘) Total Total sum of squares (TSS) (n-1)
  30. 30. S.No Type of group Parametric test 1. Comparison of two paired groups Paired t-test 2. Comparison of two unpaired groups Unpaired two sample t-test 3. Comparison of population and sample drawn from the same population One sample t-test 4. Comparison of three or more matched groups but varied in two factors Two way ANOVA 5. Comparison of three or more matched groups but varied in one factor One way ANOVA 6. Correlation between two variables Pearson Correlation
  • SoundaryaSerenaJ

    Nov. 23, 2021
  • SufiyanAhmedShaikh3

    Nov. 22, 2021
  • KushaniDesai

    Nov. 20, 2021
  • ManuYr1

    Nov. 7, 2021
  • ElizabethMathew43

    Oct. 30, 2021
  • GupthaSuma

    Oct. 24, 2021
  • IndraniInguva

    Sep. 15, 2021
  • ShwetaPote2

    Aug. 23, 2021
  • DrKshamaShah

    Aug. 23, 2021
  • PramiPaul

    Aug. 10, 2021
  • SandhyaSandhya35

    Aug. 6, 2021
  • YaminiKishore2

    Jul. 31, 2021
  • RathieshShankar

    Jul. 22, 2021
  • NandhanapriyaPS

    Jul. 16, 2021
  • SagarTKulkarni

    Jul. 15, 2021
  • MedikondaGowthami

    Jul. 1, 2021
  • DRxAbulKalam

    Jun. 3, 2021
  • UviVerma

    Jun. 2, 2021
  • JeyOweikeye

    May. 20, 2021
  • BolleddulaRaji

    May. 16, 2021

parametric tests

Views

Total views

38,899

On Slideshare

0

From embeds

0

Number of embeds

127

Actions

Downloads

1,232

Shares

0

Comments

0

Likes

134

×